id	sid	tid	token	lemma	pos
ejpam-4530	1	1	european	european	PROPN
ejpam-4530	1	2	journal	journal	PROPN
ejpam-4530	1	3	of	of	ADP
ejpam-4530	1	4	pure	pure	ADJ
ejpam-4530	1	5	and	and	CCONJ
ejpam-4530	1	6	applied	apply	VERB
ejpam-4530	1	7	mathematics	mathematic	NOUN
ejpam-4530	1	8	vol	vol	NOUN
ejpam-4530	1	9	.	.	PROPN
ejpam-4530	2	1	15	15	NUM
ejpam-4530	2	2	,	,	PUNCT
ejpam-4530	2	3	no	no	INTJ
ejpam-4530	2	4	.	.	NOUN
ejpam-4530	2	5	4	4	NUM
ejpam-4530	2	6	,	,	PUNCT
ejpam-4530	2	7	2022	2022	NUM
ejpam-4530	2	8	,	,	PUNCT
ejpam-4530	2	9	1637	1637	NUM
ejpam-4530	2	10	-	-	SYM
ejpam-4530	2	11	1648	1648	NUM
ejpam-4530	2	12	issn	issn	PROPN
ejpam-4530	2	13	1307	1307	NUM
ejpam-4530	2	14	-	-	SYM
ejpam-4530	2	15	5543	5543	NUM
ejpam-4530	2	16	–	–	PUNCT
ejpam-4530	2	17	ejpam.com	ejpam.com	X
ejpam-4530	2	18	published	publish	VERB
ejpam-4530	2	19	by	by	ADP
ejpam-4530	2	20	new	new	PROPN
ejpam-4530	2	21	york	york	PROPN
ejpam-4530	2	22	business	business	PROPN
ejpam-4530	2	23	global	global	PROPN
ejpam-4530	2	24	involution	involution	PROPN
ejpam-4530	2	25	t	t	PROPN
ejpam-4530	2	26	–	–	PUNCT
ejpam-4530	2	27	clean	clean	ADJ
ejpam-4530	2	28	rings	ring	NOUN
ejpam-4530	2	29	with	with	ADP
ejpam-4530	2	30	applications	application	NOUN
ejpam-4530	2	31	shaimaa	shaimaa	PROPN
ejpam-4530	2	32	h.	h.	PROPN
ejpam-4530	2	33	ahmad1	ahmad1	PROPN
ejpam-4530	2	34	,	,	PUNCT
ejpam-4530	2	35	mohammed	mohammed	PROPN
ejpam-4530	2	36	al	al	PROPN
ejpam-4530	2	37	-	-	PUNCT
ejpam-4530	2	38	neima2,∗	neima2,∗	PROPN
ejpam-4530	2	39	,	,	PUNCT
ejpam-4530	2	40	ahmed	ahmed	PROPN
ejpam-4530	2	41	ali1	ali1	PROPN
ejpam-4530	2	42	,	,	PUNCT
ejpam-4530	2	43	raida	raida	PROPN
ejpam-4530	2	44	d.	d.	PROPN
ejpam-4530	2	45	mahmood1	mahmood1	PROPN
ejpam-4530	2	46	1	1	NUM
ejpam-4530	2	47	department	department	NOUN
ejpam-4530	2	48	of	of	ADP
ejpam-4530	2	49	mathematics	mathematic	NOUN
ejpam-4530	2	50	,	,	PUNCT
ejpam-4530	2	51	college	college	NOUN
ejpam-4530	2	52	of	of	ADP
ejpam-4530	2	53	computer	computer	NOUN
ejpam-4530	2	54	science	science	NOUN
ejpam-4530	2	55	and	and	CCONJ
ejpam-4530	2	56	mathematics	mathematic	NOUN
ejpam-4530	2	57	,	,	PUNCT
ejpam-4530	2	58	university	university	NOUN
ejpam-4530	2	59	of	of	ADP
ejpam-4530	2	60	mosul	mosul	PROPN
ejpam-4530	2	61	,	,	PUNCT
ejpam-4530	2	62	mosul	mosul	PROPN
ejpam-4530	2	63	,	,	PUNCT
ejpam-4530	2	64	iraq	iraq	PROPN
ejpam-4530	2	65	2	2	NUM
ejpam-4530	2	66	department	department	NOUN
ejpam-4530	2	67	of	of	ADP
ejpam-4530	2	68	civil	civil	ADJ
ejpam-4530	2	69	engineering	engineering	NOUN
ejpam-4530	2	70	,	,	PUNCT
ejpam-4530	2	71	college	college	NOUN
ejpam-4530	2	72	of	of	ADP
ejpam-4530	2	73	engineering	engineering	NOUN
ejpam-4530	2	74	,	,	PUNCT
ejpam-4530	2	75	university	university	PROPN
ejpam-4530	2	76	of	of	ADP
ejpam-4530	2	77	mosul	mosul	PROPN
ejpam-4530	2	78	,	,	PUNCT
ejpam-4530	2	79	mosul	mosul	PROPN
ejpam-4530	2	80	,	,	PUNCT
ejpam-4530	2	81	iraq	iraq	PROPN
ejpam-4530	2	82	abstract	abstract	NOUN
ejpam-4530	2	83	.	.	PUNCT
ejpam-4530	3	1	a	a	DET
ejpam-4530	3	2	new	new	ADJ
ejpam-4530	3	3	class	class	NOUN
ejpam-4530	3	4	of	of	ADP
ejpam-4530	3	5	rings	ring	NOUN
ejpam-4530	3	6	was	be	AUX
ejpam-4530	3	7	introduced	introduce	VERB
ejpam-4530	3	8	,	,	PUNCT
ejpam-4530	3	9	in	in	ADP
ejpam-4530	3	10	which	which	PRON
ejpam-4530	3	11	every	every	DET
ejpam-4530	3	12	element	element	NOUN
ejpam-4530	3	13	in	in	ADP
ejpam-4530	3	14	the	the	DET
ejpam-4530	3	15	ring	ring	NOUN
ejpam-4530	3	16	is	be	AUX
ejpam-4530	3	17	a	a	DET
ejpam-4530	3	18	sum	sum	NOUN
ejpam-4530	3	19	of	of	ADP
ejpam-4530	3	20	involution	involution	NOUN
ejpam-4530	3	21	and	and	CCONJ
ejpam-4530	3	22	tripotent	tripotent	ADJ
ejpam-4530	3	23	elements	element	NOUN
ejpam-4530	3	24	.	.	PUNCT
ejpam-4530	4	1	this	this	DET
ejpam-4530	4	2	class	class	NOUN
ejpam-4530	4	3	called	call	VERB
ejpam-4530	4	4	involution	involution	PROPN
ejpam-4530	4	5	t	t	PROPN
ejpam-4530	4	6	-	-	PUNCT
ejpam-4530	4	7	clean	clean	ADJ
ejpam-4530	4	8	rings	ring	NOUN
ejpam-4530	4	9	,	,	PUNCT
ejpam-4530	4	10	which	which	PRON
ejpam-4530	4	11	is	be	AUX
ejpam-4530	4	12	a	a	DET
ejpam-4530	4	13	generalization	generalization	NOUN
ejpam-4530	4	14	of	of	ADP
ejpam-4530	4	15	invo	invo	ADJ
ejpam-4530	4	16	-	-	ADJ
ejpam-4530	4	17	clean	clean	ADJ
ejpam-4530	4	18	rings	ring	NOUN
ejpam-4530	4	19	and	and	CCONJ
ejpam-4530	4	20	subclass	subclass	NOUN
ejpam-4530	4	21	of	of	ADP
ejpam-4530	4	22	clean	clean	ADJ
ejpam-4530	4	23	rings	ring	NOUN
ejpam-4530	4	24	.	.	PUNCT
ejpam-4530	5	1	some	some	DET
ejpam-4530	5	2	properties	property	NOUN
ejpam-4530	5	3	of	of	ADP
ejpam-4530	5	4	this	this	DET
ejpam-4530	5	5	class	class	NOUN
ejpam-4530	5	6	are	be	AUX
ejpam-4530	5	7	investigated	investigate	VERB
ejpam-4530	5	8	.	.	PUNCT
ejpam-4530	6	1	for	for	ADP
ejpam-4530	6	2	an	an	DET
ejpam-4530	6	3	application	application	NOUN
ejpam-4530	6	4	in	in	ADP
ejpam-4530	6	5	graph	graph	NOUN
ejpam-4530	6	6	theory	theory	NOUN
ejpam-4530	6	7	,	,	PUNCT
ejpam-4530	6	8	a	a	DET
ejpam-4530	6	9	new	new	ADJ
ejpam-4530	6	10	graph	graph	NOUN
ejpam-4530	6	11	is	be	AUX
ejpam-4530	6	12	defined	define	VERB
ejpam-4530	6	13	as	as	ADP
ejpam-4530	6	14	t	t	NOUN
ejpam-4530	6	15	-	-	PUNCT
ejpam-4530	6	16	clean	clean	ADJ
ejpam-4530	6	17	graph	graph	NOUN
ejpam-4530	6	18	of	of	ADP
ejpam-4530	6	19	involution	involution	NOUN
ejpam-4530	6	20	t	t	PROPN
ejpam-4530	6	21	-	-	PUNCT
ejpam-4530	6	22	clean	clean	ADJ
ejpam-4530	6	23	ring	ring	NOUN
ejpam-4530	6	24	.	.	PUNCT
ejpam-4530	7	1	the	the	DET
ejpam-4530	7	2	set	set	NOUN
ejpam-4530	7	3	of	of	ADP
ejpam-4530	7	4	vertices	vertex	NOUN
ejpam-4530	7	5	is	be	AUX
ejpam-4530	7	6	ordered	order	VERB
ejpam-4530	7	7	pairs	pair	NOUN
ejpam-4530	7	8	of	of	ADP
ejpam-4530	7	9	involution	involution	NOUN
ejpam-4530	7	10	and	and	CCONJ
ejpam-4530	7	11	tripotent	tripotent	ADJ
ejpam-4530	7	12	element	element	NOUN
ejpam-4530	7	13	,	,	PUNCT
ejpam-4530	7	14	which	which	PRON
ejpam-4530	7	15	is	be	AUX
ejpam-4530	7	16	the	the	DET
ejpam-4530	7	17	sum	sum	NOUN
ejpam-4530	7	18	of	of	ADP
ejpam-4530	7	19	them	they	PRON
ejpam-4530	7	20	is	be	AUX
ejpam-4530	7	21	involution	involution	ADJ
ejpam-4530	7	22	t	t	PROPN
ejpam-4530	7	23	-	-	PUNCT
ejpam-4530	7	24	clean	clean	ADJ
ejpam-4530	7	25	element	element	NOUN
ejpam-4530	7	26	.	.	PUNCT
ejpam-4530	8	1	the	the	DET
ejpam-4530	8	2	two	two	NUM
ejpam-4530	8	3	vertices	vertex	NOUN
ejpam-4530	8	4	are	be	AUX
ejpam-4530	8	5	adjacent	adjacent	ADJ
ejpam-4530	8	6	if	if	SCONJ
ejpam-4530	8	7	and	and	CCONJ
ejpam-4530	8	8	only	only	ADV
ejpam-4530	8	9	if	if	SCONJ
ejpam-4530	8	10	the	the	DET
ejpam-4530	8	11	sum	sum	NOUN
ejpam-4530	8	12	of	of	ADP
ejpam-4530	8	13	involution	involution	NOUN
ejpam-4530	8	14	elements	element	NOUN
ejpam-4530	8	15	is	be	AUX
ejpam-4530	8	16	zero	zero	NUM
ejpam-4530	8	17	or	or	CCONJ
ejpam-4530	8	18	the	the	DET
ejpam-4530	8	19	product	product	NOUN
ejpam-4530	8	20	of	of	ADP
ejpam-4530	8	21	the	the	DET
ejpam-4530	8	22	tripotent	tripotent	ADJ
ejpam-4530	8	23	elements	element	NOUN
ejpam-4530	8	24	is	be	AUX
ejpam-4530	8	25	zero	zero	NUM
ejpam-4530	8	26	.	.	PUNCT
ejpam-4530	9	1	the	the	DET
ejpam-4530	9	2	graphs	graph	NOUN
ejpam-4530	9	3	are	be	AUX
ejpam-4530	9	4	connecting	connect	VERB
ejpam-4530	9	5	,	,	PUNCT
ejpam-4530	9	6	has	have	VERB
ejpam-4530	9	7	diameter	diameter	NOUN
ejpam-4530	9	8	one	one	NUM
ejpam-4530	9	9	and	and	CCONJ
ejpam-4530	9	10	girth	girth	ADV
ejpam-4530	9	11	three	three	NUM
ejpam-4530	9	12	.	.	PUNCT
ejpam-4530	10	1	2020	2020	NUM
ejpam-4530	10	2	mathematics	mathematic	NOUN
ejpam-4530	10	3	subject	subject	NOUN
ejpam-4530	10	4	classifications	classification	NOUN
ejpam-4530	10	5	:	:	PUNCT
ejpam-4530	10	6	16e50	16e50	NUM
ejpam-4530	10	7	,	,	PUNCT
ejpam-4530	10	8	16u99	16u99	NUM
ejpam-4530	10	9	,	,	PUNCT
ejpam-4530	10	10	05c25	05c25	X
ejpam-4530	10	11	key	key	ADJ
ejpam-4530	10	12	words	word	NOUN
ejpam-4530	10	13	and	and	CCONJ
ejpam-4530	10	14	phrases	phrase	NOUN
ejpam-4530	10	15	:	:	PUNCT
ejpam-4530	10	16	clean	clean	ADJ
ejpam-4530	10	17	ring	ring	NOUN
ejpam-4530	10	18	,	,	PUNCT
ejpam-4530	10	19	invo	invo	ADJ
ejpam-4530	10	20	-	-	ADJ
ejpam-4530	10	21	clean	clean	ADJ
ejpam-4530	10	22	ring	ring	NOUN
ejpam-4530	10	23	,	,	PUNCT
ejpam-4530	10	24	tripotent	tripotent	NOUN
ejpam-4530	10	25	element	element	NOUN
ejpam-4530	10	26	,	,	PUNCT
ejpam-4530	10	27	hosoya	hosoya	NOUN
ejpam-4530	10	28	polynomial	polynomial	ADJ
ejpam-4530	10	29	,	,	PUNCT
ejpam-4530	10	30	wiener	wiener	NOUN
ejpam-4530	10	31	index	index	NOUN
ejpam-4530	10	32	1	1	NUM
ejpam-4530	10	33	.	.	PUNCT
ejpam-4530	10	34	introduction	introduction	NOUN
ejpam-4530	10	35	throughout	throughout	ADP
ejpam-4530	10	36	this	this	DET
ejpam-4530	10	37	paper	paper	NOUN
ejpam-4530	10	38	,	,	PUNCT
ejpam-4530	10	39	the	the	DET
ejpam-4530	10	40	ring	ring	NOUN
ejpam-4530	10	41	r	r	NOUN
ejpam-4530	10	42	is	be	AUX
ejpam-4530	10	43	associative	associative	ADJ
ejpam-4530	10	44	with	with	ADP
ejpam-4530	10	45	identity	identity	NOUN
ejpam-4530	10	46	.	.	PUNCT
ejpam-4530	11	1	the	the	DET
ejpam-4530	11	2	symbols	symbol	NOUN
ejpam-4530	11	3	u(r	u(r	PROPN
ejpam-4530	11	4	)	)	PUNCT
ejpam-4530	11	5	is	be	AUX
ejpam-4530	11	6	the	the	DET
ejpam-4530	11	7	set	set	NOUN
ejpam-4530	11	8	of	of	ADP
ejpam-4530	11	9	unit	unit	NOUN
ejpam-4530	11	10	elements	element	NOUN
ejpam-4530	11	11	in	in	ADP
ejpam-4530	11	12	r	r	NOUN
ejpam-4530	11	13	,	,	PUNCT
ejpam-4530	11	14	idm(r	idm(r	PROPN
ejpam-4530	11	15	)	)	PUNCT
ejpam-4530	11	16	is	be	AUX
ejpam-4530	11	17	the	the	DET
ejpam-4530	11	18	set	set	NOUN
ejpam-4530	11	19	of	of	ADP
ejpam-4530	11	20	idempotent	idempotent	ADJ
ejpam-4530	11	21	elements	element	NOUN
ejpam-4530	11	22	in	in	ADP
ejpam-4530	11	23	r	r	NOUN
ejpam-4530	11	24	,	,	PUNCT
ejpam-4530	11	25	invo(r	invo(r	NOUN
ejpam-4530	11	26	)	)	PUNCT
ejpam-4530	11	27	the	the	DET
ejpam-4530	11	28	subset	subset	NOUN
ejpam-4530	11	29	of	of	ADP
ejpam-4530	11	30	u(r	u(r	NOUN
ejpam-4530	11	31	)	)	PUNCT
ejpam-4530	12	1	consisting	consist	VERB
ejpam-4530	12	2	of	of	ADP
ejpam-4530	12	3	all	all	DET
ejpam-4530	12	4	involution	involution	NOUN
ejpam-4530	12	5	elements	element	NOUN
ejpam-4530	12	6	of	of	ADP
ejpam-4530	12	7	r	r	NOUN
ejpam-4530	12	8	,	,	PUNCT
ejpam-4530	12	9	tri(r	tri(r	PROPN
ejpam-4530	12	10	)	)	PUNCT
ejpam-4530	12	11	=	=	PUNCT
ejpam-4530	12	12	{	{	PUNCT
ejpam-4530	12	13	t	t	NOUN
ejpam-4530	12	14	∈	∈	PROPN
ejpam-4530	12	15	r	r	NOUN
ejpam-4530	12	16	:	:	PUNCT
ejpam-4530	12	17	t3	t3	PROPN
ejpam-4530	12	18	=	=	SYM
ejpam-4530	12	19	t	t	PROPN
ejpam-4530	12	20	}	}	PUNCT
ejpam-4530	12	21	,	,	PUNCT
ejpam-4530	12	22	n2(r	n2(r	PROPN
ejpam-4530	12	23	)	)	PUNCT
ejpam-4530	12	24	=	=	PRON
ejpam-4530	12	25	{	{	PUNCT
ejpam-4530	12	26	x	x	PUNCT
ejpam-4530	12	27	∈	∈	PROPN
ejpam-4530	12	28	r	r	NOUN
ejpam-4530	12	29	:	:	PUNCT
ejpam-4530	12	30	x2	x2	NOUN
ejpam-4530	12	31	=	=	PUNCT
ejpam-4530	12	32	0	0	NUM
ejpam-4530	12	33	}	}	PUNCT
ejpam-4530	12	34	.	.	PUNCT
ejpam-4530	13	1	the	the	DET
ejpam-4530	13	2	aim	aim	NOUN
ejpam-4530	13	3	of	of	ADP
ejpam-4530	13	4	this	this	DET
ejpam-4530	13	5	paper	paper	NOUN
ejpam-4530	13	6	is	be	AUX
ejpam-4530	13	7	to	to	PART
ejpam-4530	13	8	generalize	generalize	VERB
ejpam-4530	13	9	the	the	DET
ejpam-4530	13	10	concept	concept	NOUN
ejpam-4530	13	11	of	of	ADP
ejpam-4530	13	12	invo	invo	ADJ
ejpam-4530	13	13	-	-	ADJ
ejpam-4530	13	14	clean	clean	ADJ
ejpam-4530	13	15	ring	ring	NOUN
ejpam-4530	13	16	,	,	PUNCT
ejpam-4530	13	17	the	the	DET
ejpam-4530	13	18	purpose	purpose	NOUN
ejpam-4530	13	19	to	to	PART
ejpam-4530	13	20	obtain	obtain	VERB
ejpam-4530	13	21	more	more	ADJ
ejpam-4530	13	22	general	general	ADJ
ejpam-4530	13	23	results	result	NOUN
ejpam-4530	13	24	by	by	ADP
ejpam-4530	13	25	generalizing	generalize	VERB
ejpam-4530	13	26	some	some	DET
ejpam-4530	13	27	results	result	NOUN
ejpam-4530	13	28	of	of	ADP
ejpam-4530	13	29	invo	invo	ADJ
ejpam-4530	13	30	-	-	ADJ
ejpam-4530	13	31	clean	clean	ADJ
ejpam-4530	13	32	ring	ring	NOUN
ejpam-4530	13	33	.	.	PUNCT
ejpam-4530	14	1	this	this	DET
ejpam-4530	14	2	prompts	prompt	VERB
ejpam-4530	14	3	researchers	researcher	NOUN
ejpam-4530	14	4	to	to	PART
ejpam-4530	14	5	study	study	VERB
ejpam-4530	14	6	many	many	ADJ
ejpam-4530	14	7	of	of	ADP
ejpam-4530	14	8	the	the	DET
ejpam-4530	14	9	properties	property	NOUN
ejpam-4530	14	10	of	of	ADP
ejpam-4530	14	11	this	this	DET
ejpam-4530	14	12	generalization	generalization	NOUN
ejpam-4530	14	13	.	.	PUNCT
ejpam-4530	15	1	the	the	DET
ejpam-4530	15	2	concept	concept	NOUN
ejpam-4530	15	3	of	of	ADP
ejpam-4530	15	4	clean	clean	ADJ
ejpam-4530	15	5	ring	ring	NOUN
ejpam-4530	15	6	,	,	PUNCT
ejpam-4530	15	7	first	first	ADV
ejpam-4530	15	8	defined	define	VERB
ejpam-4530	15	9	by	by	ADP
ejpam-4530	15	10	nicholson	nicholson	PROPN
ejpam-4530	15	11	in	in	ADP
ejpam-4530	15	12	1977	1977	NUM
ejpam-4530	15	13	[	[	X
ejpam-4530	15	14	9	9	NUM
ejpam-4530	15	15	]	]	PUNCT
ejpam-4530	15	16	,	,	PUNCT
ejpam-4530	15	17	a	a	DET
ejpam-4530	15	18	ring	ring	NOUN
ejpam-4530	15	19	r	r	NOUN
ejpam-4530	15	20	is	be	AUX
ejpam-4530	15	21	called	call	VERB
ejpam-4530	15	22	clean	clean	ADJ
ejpam-4530	15	23	,	,	PUNCT
ejpam-4530	15	24	if	if	SCONJ
ejpam-4530	15	25	for	for	ADP
ejpam-4530	15	26	all	all	DET
ejpam-4530	15	27	x	x	SYM
ejpam-4530	15	28	∈	∈	NOUN
ejpam-4530	15	29	r	r	NOUN
ejpam-4530	15	30	and	and	CCONJ
ejpam-4530	15	31	written	write	VERB
ejpam-4530	15	32	as	as	ADP
ejpam-4530	15	33	x	x	X
ejpam-4530	15	34	=	=	PUNCT
ejpam-4530	15	35	u	u	NOUN
ejpam-4530	15	36	+	+	CCONJ
ejpam-4530	15	37	e	e	NOUN
ejpam-4530	15	38	,	,	PUNCT
ejpam-4530	15	39	where	where	SCONJ
ejpam-4530	15	40	u	u	PROPN
ejpam-4530	15	41	∈	∈	PROPN
ejpam-4530	15	42	u(r	u(r	PROPN
ejpam-4530	15	43	)	)	PUNCT
ejpam-4530	15	44	and	and	CCONJ
ejpam-4530	15	45	e	e	X
ejpam-4530	15	46	∈	∈	PROPN
ejpam-4530	15	47	idm(r	idm(r	PROPN
ejpam-4530	15	48	)	)	PUNCT
ejpam-4530	15	49	.	.	PUNCT
ejpam-4530	16	1	if	if	SCONJ
ejpam-4530	16	2	ue	ue	PROPN
ejpam-4530	16	3	=	=	SYM
ejpam-4530	16	4	eu	eu	PROPN
ejpam-4530	16	5	,	,	PUNCT
ejpam-4530	16	6	get	get	VERB
ejpam-4530	16	7	that	that	SCONJ
ejpam-4530	16	8	r	r	NOUN
ejpam-4530	16	9	is	be	AUX
ejpam-4530	16	10	called	call	VERB
ejpam-4530	16	11	strongly	strongly	ADV
ejpam-4530	16	12	clean	clean	ADJ
ejpam-4530	16	13	.	.	PUNCT
ejpam-4530	17	1	recall	recall	VERB
ejpam-4530	17	2	that	that	SCONJ
ejpam-4530	17	3	a	a	DET
ejpam-4530	17	4	ring	ring	NOUN
ejpam-4530	17	5	r	r	NOUN
ejpam-4530	17	6	is	be	AUX
ejpam-4530	17	7	called	call	VERB
ejpam-4530	17	8	invo	invo	ADJ
ejpam-4530	17	9	-	-	ADJ
ejpam-4530	17	10	clean	clean	ADJ
ejpam-4530	17	11	,	,	PUNCT
ejpam-4530	17	12	if	if	SCONJ
ejpam-4530	17	13	every	every	DET
ejpam-4530	17	14	x	x	SYM
ejpam-4530	17	15	∈	∈	NOUN
ejpam-4530	17	16	r	r	NOUN
ejpam-4530	17	17	can	can	AUX
ejpam-4530	17	18	be	be	AUX
ejpam-4530	17	19	written	write	VERB
ejpam-4530	17	20	as	as	ADP
ejpam-4530	17	21	x	x	X
ejpam-4530	17	22	=	=	X
ejpam-4530	17	23	u+	u+	ADJ
ejpam-4530	17	24	e	e	NOUN
ejpam-4530	17	25	,	,	PUNCT
ejpam-4530	17	26	where	where	SCONJ
ejpam-4530	17	27	u	u	PROPN
ejpam-4530	17	28	∈	∈	PROPN
ejpam-4530	17	29	invo(r	invo(r	NOUN
ejpam-4530	17	30	)	)	PUNCT
ejpam-4530	17	31	and	and	CCONJ
ejpam-4530	17	32	e	e	X
ejpam-4530	17	33	∈	∈	PROPN
ejpam-4530	17	34	idm(r	idm(r	PROPN
ejpam-4530	17	35	)	)	PUNCT
ejpam-4530	17	36	.	.	PUNCT
ejpam-4530	18	1	if	if	SCONJ
ejpam-4530	18	2	,	,	PUNCT
ejpam-4530	18	3	ue	ue	PROPN
ejpam-4530	18	4	=	=	SYM
ejpam-4530	18	5	eu	eu	PROPN
ejpam-4530	18	6	,	,	PUNCT
ejpam-4530	18	7	get	get	VERB
ejpam-4530	18	8	that	that	SCONJ
ejpam-4530	18	9	r	r	NOUN
ejpam-4530	18	10	is	be	AUX
ejpam-4530	18	11	strongly	strongly	ADV
ejpam-4530	18	12	invo-clean.which	invo-clean.which	PRON
ejpam-4530	18	13	was	be	AUX
ejpam-4530	18	14	first	first	ADV
ejpam-4530	18	15	defined	define	VERB
ejpam-4530	18	16	danchev	danchev	NOUN
ejpam-4530	18	17	see	see	VERB
ejpam-4530	18	18	[	[	X
ejpam-4530	18	19	6	6	NUM
ejpam-4530	18	20	]	]	PUNCT
ejpam-4530	18	21	.	.	PUNCT
ejpam-4530	19	1	∗corresponding	∗corresponde	VERB
ejpam-4530	19	2	author	author	NOUN
ejpam-4530	19	3	.	.	PUNCT
ejpam-4530	20	1	doi	doi	NOUN
ejpam-4530	20	2	:	:	PUNCT
ejpam-4530	20	3	https://doi.org/10.29020/nybg.ejpam.v15i4.4530	https://doi.org/10.29020/nybg.ejpam.v15i4.4530	PROPN
ejpam-4530	20	4	email	email	NOUN
ejpam-4530	20	5	addresses	address	VERB
ejpam-4530	20	6	:	:	PUNCT
ejpam-4530	20	7	shaymaahatim@uomosul.edu.iq	shaymaahatim@uomosul.edu.iq	ADJ
ejpam-4530	20	8	(	(	PUNCT
ejpam-4530	20	9	shaimaa	shaimaa	PROPN
ejpam-4530	20	10	h.	h.	PROPN
ejpam-4530	20	11	ahmad	ahmad	PROPN
ejpam-4530	20	12	)	)	PUNCT
ejpam-4530	20	13	,	,	PUNCT
ejpam-4530	20	14	mohammedmth@uomosul.edu.iq	mohammedmth@uomosul.edu.iq	NOUN
ejpam-4530	20	15	(	(	PUNCT
ejpam-4530	20	16	mohammed	mohammed	PROPN
ejpam-4530	20	17	al	al	PROPN
ejpam-4530	20	18	-	-	PUNCT
ejpam-4530	20	19	neima	neima	PROPN
ejpam-4530	20	20	)	)	PUNCT
ejpam-4530	20	21	,	,	PUNCT
ejpam-4530	20	22	ahmedgraph@uomosul.edu.iq	ahmedgraph@uomosul.edu.iq	NOUN
ejpam-4530	20	23	(	(	PUNCT
ejpam-4530	20	24	ahmed	ahmed	PROPN
ejpam-4530	20	25	ali	ali	PROPN
ejpam-4530	20	26	)	)	PUNCT
ejpam-4530	20	27	,	,	PUNCT
ejpam-4530	20	28	raida.1961@uomosul.edu.iq	raida.1961@uomosul.edu.iq	NOUN
ejpam-4530	20	29	(	(	PUNCT
ejpam-4530	20	30	raida	raida	PROPN
ejpam-4530	20	31	d.	d.	PROPN
ejpam-4530	20	32	mahmood	mahmood	PROPN
ejpam-4530	20	33	)	)	PUNCT
ejpam-4530	20	34	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4530	20	35	1637	1637	NUM
ejpam-4530	21	1	©	©	ADP
ejpam-4530	21	2	2022	2022	NUM
ejpam-4530	21	3	ejpam	ejpam	VERB
ejpam-4530	21	4	all	all	DET
ejpam-4530	21	5	rights	right	NOUN
ejpam-4530	21	6	reserved	reserve	VERB
ejpam-4530	21	7	.	.	PUNCT
ejpam-4530	22	1	mohammed	mohammed	PROPN
ejpam-4530	22	2	al	al	PROPN
ejpam-4530	22	3	-	-	PROPN
ejpam-4530	22	4	neima	neima	PROPN
ejpam-4530	22	5	et	et	PROPN
ejpam-4530	22	6	al	al	PROPN
ejpam-4530	22	7	.	.	PUNCT
ejpam-4530	22	8	/	/	SYM
ejpam-4530	22	9	eur	eur	PROPN
ejpam-4530	22	10	.	.	PUNCT
ejpam-4530	23	1	j.	j.	PROPN
ejpam-4530	23	2	pure	pure	PROPN
ejpam-4530	23	3	appl	appl	PROPN
ejpam-4530	23	4	.	.	PROPN
ejpam-4530	23	5	math	math	PROPN
ejpam-4530	23	6	,	,	PUNCT
ejpam-4530	23	7	15	15	NUM
ejpam-4530	23	8	(	(	PUNCT
ejpam-4530	23	9	4	4	NUM
ejpam-4530	23	10	)	)	PUNCT
ejpam-4530	23	11	(	(	PUNCT
ejpam-4530	23	12	2022	2022	NUM
ejpam-4530	23	13	)	)	PUNCT
ejpam-4530	23	14	,	,	PUNCT
ejpam-4530	23	15	1637	1637	NUM
ejpam-4530	23	16	-	-	SYM
ejpam-4530	23	17	1648	1648	NUM
ejpam-4530	23	18	1638	1638	NUM
ejpam-4530	23	19	every	every	DET
ejpam-4530	23	20	idempotent	idempotent	ADJ
ejpam-4530	23	21	element	element	NOUN
ejpam-4530	23	22	is	be	AUX
ejpam-4530	23	23	invo	invo	VERB
ejpam-4530	23	24	-	-	ADJ
ejpam-4530	23	25	clean	clean	ADJ
ejpam-4530	23	26	,	,	PUNCT
ejpam-4530	23	27	because	because	SCONJ
ejpam-4530	23	28	e	e	PROPN
ejpam-4530	23	29	=	=	PUNCT
ejpam-4530	23	30	(	(	PUNCT
ejpam-4530	23	31	2e−1)+(1−e	2e−1)+(1−e	NUM
ejpam-4530	23	32	)	)	PUNCT
ejpam-4530	23	33	,	,	PUNCT
ejpam-4530	23	34	where	where	SCONJ
ejpam-4530	23	35	(	(	PUNCT
ejpam-4530	23	36	2e−1)2	2e−1)2	NUM
ejpam-4530	23	37	=	=	SYM
ejpam-4530	23	38	1	1	NUM
ejpam-4530	23	39	and	and	CCONJ
ejpam-4530	23	40	(	(	PUNCT
ejpam-4530	23	41	1−	1−	NUM
ejpam-4530	23	42	e)2	e)2	NOUN
ejpam-4530	23	43	=	=	SYM
ejpam-4530	23	44	1−	1−	NUM
ejpam-4530	23	45	e.	e.	PROPN
ejpam-4530	23	46	moreover	moreover	ADV
ejpam-4530	23	47	,	,	PUNCT
ejpam-4530	23	48	z2	z2	PROPN
ejpam-4530	23	49	,	,	PUNCT
ejpam-4530	23	50	z3	z3	PROPN
ejpam-4530	23	51	,	,	PUNCT
ejpam-4530	23	52	z4	z4	PROPN
ejpam-4530	23	53	,	,	PUNCT
ejpam-4530	23	54	z6	z6	PROPN
ejpam-4530	23	55	,	,	PUNCT
ejpam-4530	23	56	z8	z8	PROPN
ejpam-4530	23	57	are	be	AUX
ejpam-4530	23	58	invo	invo	ADJ
ejpam-4530	23	59	-	-	ADJ
ejpam-4530	23	60	clean	clean	ADJ
ejpam-4530	23	61	rings	ring	NOUN
ejpam-4530	23	62	.	.	PUNCT
ejpam-4530	24	1	every	every	DET
ejpam-4530	24	2	invo	invo	ADJ
ejpam-4530	24	3	-	-	ADJ
ejpam-4530	24	4	clean	clean	ADJ
ejpam-4530	24	5	ring	ring	NOUN
ejpam-4530	24	6	is	be	AUX
ejpam-4530	24	7	clean	clean	ADJ
ejpam-4530	24	8	,	,	PUNCT
ejpam-4530	24	9	but	but	CCONJ
ejpam-4530	24	10	the	the	DET
ejpam-4530	24	11	opposite	opposite	NOUN
ejpam-4530	24	12	is	be	AUX
ejpam-4530	24	13	untrue	untrue	ADJ
ejpam-4530	24	14	.	.	PUNCT
ejpam-4530	25	1	(	(	PUNCT
ejpam-4530	25	2	examples	example	NOUN
ejpam-4530	25	3	z5	z5	PROPN
ejpam-4530	25	4	,	,	PUNCT
ejpam-4530	25	5	z10	z10	NOUN
ejpam-4530	25	6	)	)	PUNCT
ejpam-4530	25	7	.	.	PUNCT
ejpam-4530	26	1	as	as	ADP
ejpam-4530	26	2	usual	usual	ADJ
ejpam-4530	26	3	,	,	PUNCT
ejpam-4530	26	4	m2(r	m2(r	NOUN
ejpam-4530	26	5	)	)	PUNCT
ejpam-4530	26	6	stand	stand	VERB
ejpam-4530	26	7	for	for	ADP
ejpam-4530	26	8	the	the	DET
ejpam-4530	26	9	2×2	2×2	NUM
ejpam-4530	26	10	matrix	matrix	NOUN
ejpam-4530	26	11	ring	ring	NOUN
ejpam-4530	26	12	.	.	PUNCT
ejpam-4530	27	1	t2(r	t2(r	NOUN
ejpam-4530	27	2	)	)	PUNCT
ejpam-4530	27	3	is	be	AUX
ejpam-4530	27	4	2×2	2×2	NUM
ejpam-4530	27	5	upper	upper	ADJ
ejpam-4530	27	6	triangular	triangular	NOUN
ejpam-4530	27	7	matrix	matrix	NOUN
ejpam-4530	27	8	ring	ring	NOUN
ejpam-4530	27	9	.	.	PUNCT
ejpam-4530	28	1	we	we	PRON
ejpam-4530	28	2	write	write	VERB
ejpam-4530	28	3	zn	zn	PROPN
ejpam-4530	28	4	for	for	ADP
ejpam-4530	28	5	rings	ring	NOUN
ejpam-4530	28	6	of	of	ADP
ejpam-4530	28	7	integers	integer	NOUN
ejpam-4530	28	8	modulo	modulo	VERB
ejpam-4530	28	9	n.	n.	NOUN
ejpam-4530	28	10	in	in	ADP
ejpam-4530	28	11	[	[	PUNCT
ejpam-4530	28	12	11	11	NUM
ejpam-4530	28	13	]	]	PUNCT
ejpam-4530	28	14	,	,	PUNCT
ejpam-4530	28	15	the	the	DET
ejpam-4530	28	16	ring	ring	NOUN
ejpam-4530	28	17	r	r	NOUN
ejpam-4530	28	18	is	be	AUX
ejpam-4530	28	19	regular	regular	ADJ
ejpam-4530	28	20	if	if	SCONJ
ejpam-4530	28	21	every	every	DET
ejpam-4530	28	22	a	a	DET
ejpam-4530	28	23	∈	∈	PROPN
ejpam-4530	28	24	r	r	NOUN
ejpam-4530	28	25	,	,	PUNCT
ejpam-4530	28	26	a	a	DET
ejpam-4530	28	27	∈	∈	PROPN
ejpam-4530	28	28	ara	ara	NOUN
ejpam-4530	28	29	.	.	PUNCT
ejpam-4530	29	1	the	the	DET
ejpam-4530	29	2	ring	ring	NOUN
ejpam-4530	29	3	r	r	NOUN
ejpam-4530	29	4	is	be	AUX
ejpam-4530	29	5	called	call	VERB
ejpam-4530	29	6	r	r	NOUN
ejpam-4530	29	7	-	-	ADJ
ejpam-4530	29	8	clean	clean	ADJ
ejpam-4530	29	9	if	if	SCONJ
ejpam-4530	29	10	all	all	DET
ejpam-4530	29	11	elements	element	NOUN
ejpam-4530	29	12	of	of	ADP
ejpam-4530	29	13	r	r	NOUN
ejpam-4530	29	14	can	can	AUX
ejpam-4530	29	15	be	be	AUX
ejpam-4530	29	16	written	write	VERB
ejpam-4530	29	17	as	as	ADP
ejpam-4530	29	18	the	the	DET
ejpam-4530	29	19	summation	summation	NOUN
ejpam-4530	29	20	of	of	ADP
ejpam-4530	29	21	a	a	DET
ejpam-4530	29	22	regular	regular	ADJ
ejpam-4530	29	23	and	and	CCONJ
ejpam-4530	29	24	idempotent	idempotent	ADJ
ejpam-4530	29	25	elements	element	NOUN
ejpam-4530	29	26	[	[	X
ejpam-4530	29	27	2	2	NUM
ejpam-4530	29	28	]	]	PUNCT
ejpam-4530	29	29	.	.	PUNCT
ejpam-4530	30	1	zero	zero	NUM
ejpam-4530	30	2	divisor	divisor	NOUN
ejpam-4530	30	3	graph	graph	NOUN
ejpam-4530	30	4	is	be	AUX
ejpam-4530	30	5	concept	concept	NOUN
ejpam-4530	30	6	give	give	VERB
ejpam-4530	30	7	the	the	DET
ejpam-4530	30	8	relation	relation	NOUN
ejpam-4530	30	9	between	between	ADP
ejpam-4530	30	10	the	the	DET
ejpam-4530	30	11	commutative	commutative	ADJ
ejpam-4530	30	12	rings	ring	NOUN
ejpam-4530	30	13	and	and	CCONJ
ejpam-4530	30	14	graph	graph	NOUN
ejpam-4530	30	15	theory	theory	NOUN
ejpam-4530	30	16	,	,	PUNCT
ejpam-4530	30	17	which	which	PRON
ejpam-4530	30	18	was	be	AUX
ejpam-4530	30	19	first	first	ADV
ejpam-4530	30	20	defined	define	VERB
ejpam-4530	30	21	by	by	ADP
ejpam-4530	30	22	beck	beck	NOUN
ejpam-4530	30	23	in	in	ADP
ejpam-4530	30	24	[	[	X
ejpam-4530	30	25	4	4	NUM
ejpam-4530	30	26	]	]	PUNCT
ejpam-4530	30	27	.	.	PUNCT
ejpam-4530	31	1	in	in	ADP
ejpam-4530	31	2	the	the	DET
ejpam-4530	31	3	same	same	ADJ
ejpam-4530	31	4	way	way	NOUN
ejpam-4530	31	5	,	,	PUNCT
ejpam-4530	31	6	habibi	habibi	PROPN
ejpam-4530	31	7	,	,	PUNCT
ejpam-4530	31	8	celikel	celikel	NOUN
ejpam-4530	31	9	and	and	CCONJ
ejpam-4530	31	10	abdioglu	abdioglu	NOUN
ejpam-4530	31	11	in	in	ADP
ejpam-4530	31	12	[	[	X
ejpam-4530	31	13	8	8	NUM
ejpam-4530	31	14	]	]	PUNCT
ejpam-4530	31	15	start	start	NOUN
ejpam-4530	31	16	study	study	NOUN
ejpam-4530	31	17	of	of	ADP
ejpam-4530	31	18	clean	clean	ADJ
ejpam-4530	31	19	graph	graph	NOUN
ejpam-4530	31	20	defined	define	VERB
ejpam-4530	31	21	in	in	ADP
ejpam-4530	31	22	clean	clean	ADJ
ejpam-4530	31	23	ring	ring	NOUN
ejpam-4530	31	24	.	.	PUNCT
ejpam-4530	32	1	for	for	ADP
ejpam-4530	32	2	an	an	DET
ejpam-4530	32	3	application	application	NOUN
ejpam-4530	32	4	to	to	ADP
ejpam-4530	32	5	invo	invo	PROPN
ejpam-4530	32	6	-	-	PUNCT
ejpam-4530	32	7	t	t	NOUN
ejpam-4530	32	8	-	-	PUNCT
ejpam-4530	32	9	clean	clean	ADJ
ejpam-4530	32	10	ring	ring	NOUN
ejpam-4530	32	11	,	,	PUNCT
ejpam-4530	32	12	a	a	DET
ejpam-4530	32	13	new	new	ADJ
ejpam-4530	32	14	graph	graph	NOUN
ejpam-4530	32	15	is	be	AUX
ejpam-4530	32	16	defined	define	VERB
ejpam-4530	32	17	;	;	PUNCT
ejpam-4530	32	18	depended	depend	VERB
ejpam-4530	32	19	on	on	ADP
ejpam-4530	32	20	an	an	DET
ejpam-4530	32	21	involution	involution	NOUN
ejpam-4530	32	22	t	t	PROPN
ejpam-4530	32	23	-	-	PUNCT
ejpam-4530	32	24	clean	clean	ADJ
ejpam-4530	32	25	ring	ring	NOUN
ejpam-4530	32	26	.	.	PUNCT
ejpam-4530	33	1	in	in	ADP
ejpam-4530	33	2	graph	graph	NOUN
ejpam-4530	33	3	theory	theory	NOUN
ejpam-4530	33	4	,	,	PUNCT
ejpam-4530	33	5	the	the	DET
ejpam-4530	33	6	graph	graph	NOUN
ejpam-4530	33	7	is	be	AUX
ejpam-4530	33	8	an	an	DET
ejpam-4530	33	9	order	order	NOUN
ejpam-4530	33	10	pair	pair	NOUN
ejpam-4530	33	11	denoted	denote	VERB
ejpam-4530	33	12	by	by	ADP
ejpam-4530	33	13	g	g	PROPN
ejpam-4530	33	14	=	=	SYM
ejpam-4530	33	15	(	(	PUNCT
ejpam-4530	33	16	v	v	NOUN
ejpam-4530	33	17	,	,	PUNCT
ejpam-4530	33	18	f	f	PROPN
ejpam-4530	33	19	)	)	PUNCT
ejpam-4530	33	20	of	of	ADP
ejpam-4530	33	21	two	two	NUM
ejpam-4530	33	22	sets	set	NOUN
ejpam-4530	33	23	v	v	NOUN
ejpam-4530	33	24	(	(	PUNCT
ejpam-4530	33	25	is	be	AUX
ejpam-4530	33	26	non	non	ADJ
ejpam-4530	33	27	-	-	ADJ
ejpam-4530	33	28	empty	empty	ADJ
ejpam-4530	33	29	)	)	PUNCT
ejpam-4530	33	30	and	and	CCONJ
ejpam-4530	33	31	f	f	PROPN
ejpam-4530	33	32	(	(	PUNCT
ejpam-4530	33	33	may	may	AUX
ejpam-4530	33	34	be	be	AUX
ejpam-4530	33	35	empty	empty	ADJ
ejpam-4530	33	36	)	)	PUNCT
ejpam-4530	34	1	such	such	ADJ
ejpam-4530	34	2	that	that	SCONJ
ejpam-4530	34	3	f	f	PROPN
ejpam-4530	35	1	⊆	⊆	NUM
ejpam-4530	35	2	v	v	ADP
ejpam-4530	35	3	×	×	NOUN
ejpam-4530	35	4	v	v	ADP
ejpam-4530	35	5	.g	.g	NOUN
ejpam-4530	35	6	′	′	NUM
ejpam-4530	36	1	=	=	PUNCT
ejpam-4530	36	2	(	(	PUNCT
ejpam-4530	36	3	v	v	NOUN
ejpam-4530	36	4	′	′	NUM
ejpam-4530	36	5	,	,	PUNCT
ejpam-4530	36	6	f	f	PROPN
ejpam-4530	36	7	′	′	NUM
ejpam-4530	36	8	)	)	PUNCT
ejpam-4530	36	9	is	be	AUX
ejpam-4530	36	10	a	a	DET
ejpam-4530	36	11	sub	sub	NOUN
ejpam-4530	36	12	-	-	NOUN
ejpam-4530	36	13	graph	graph	NOUN
ejpam-4530	36	14	of	of	ADP
ejpam-4530	36	15	g	g	NOUN
ejpam-4530	36	16	=	=	SYM
ejpam-4530	36	17	(	(	PUNCT
ejpam-4530	36	18	v	v	NOUN
ejpam-4530	36	19	,	,	PUNCT
ejpam-4530	36	20	f	f	PROPN
ejpam-4530	36	21	)	)	PUNCT
ejpam-4530	36	22	written	write	VERB
ejpam-4530	36	23	as	as	ADP
ejpam-4530	36	24	g	g	NOUN
ejpam-4530	36	25	′	′	NUM
ejpam-4530	36	26	⊆	⊆	NUM
ejpam-4530	36	27	g	g	NOUN
ejpam-4530	36	28	if	if	SCONJ
ejpam-4530	36	29	v	v	ADP
ejpam-4530	36	30	′	′	NUM
ejpam-4530	36	31	⊆	⊆	NUM
ejpam-4530	36	32	v	v	NOUN
ejpam-4530	37	1	and	and	CCONJ
ejpam-4530	37	2	f	f	NOUN
ejpam-4530	38	1	′	′	NUM
ejpam-4530	39	1	⊆	⊆	NUM
ejpam-4530	39	2	f	f	NOUN
ejpam-4530	39	3	.	.	PUNCT
ejpam-4530	40	1	the	the	DET
ejpam-4530	40	2	order	order	NOUN
ejpam-4530	40	3	of	of	ADP
ejpam-4530	40	4	g	g	PROPN
ejpam-4530	40	5	is	be	AUX
ejpam-4530	40	6	the	the	DET
ejpam-4530	40	7	number	number	NOUN
ejpam-4530	40	8	of	of	ADP
ejpam-4530	40	9	vertices	vertex	NOUN
ejpam-4530	40	10	,	,	PUNCT
ejpam-4530	40	11	denoted	denote	VERB
ejpam-4530	40	12	by	by	ADP
ejpam-4530	40	13	|g|	|g|	PROPN
ejpam-4530	40	14	and	and	CCONJ
ejpam-4530	40	15	the	the	DET
ejpam-4530	40	16	number	number	NOUN
ejpam-4530	40	17	of	of	ADP
ejpam-4530	40	18	edges	edge	NOUN
ejpam-4530	40	19	is	be	AUX
ejpam-4530	40	20	denoted	denote	VERB
ejpam-4530	40	21	by	by	ADP
ejpam-4530	40	22	∥g∥.	∥g∥.	NOUN
ejpam-4530	40	23	the	the	DET
ejpam-4530	40	24	girth	girth	NOUN
ejpam-4530	40	25	is	be	AUX
ejpam-4530	40	26	the	the	DET
ejpam-4530	40	27	length	length	NOUN
ejpam-4530	40	28	of	of	ADP
ejpam-4530	40	29	the	the	DET
ejpam-4530	40	30	shortest	short	ADJ
ejpam-4530	40	31	cycle	cycle	NOUN
ejpam-4530	40	32	in	in	ADP
ejpam-4530	40	33	the	the	DET
ejpam-4530	40	34	graph	graph	NOUN
ejpam-4530	40	35	g	g	NOUN
ejpam-4530	40	36	,	,	PUNCT
ejpam-4530	40	37	denoted	denote	VERB
ejpam-4530	40	38	by	by	ADP
ejpam-4530	40	39	g(g	g(g	PROPN
ejpam-4530	40	40	)	)	PUNCT
ejpam-4530	40	41	.	.	PUNCT
ejpam-4530	41	1	each	each	DET
ejpam-4530	41	2	edge	edge	NOUN
ejpam-4530	41	3	incident	incident	NOUN
ejpam-4530	41	4	on	on	ADP
ejpam-4530	41	5	two	two	NUM
ejpam-4530	41	6	vertices	vertex	NOUN
ejpam-4530	41	7	,	,	PUNCT
ejpam-4530	41	8	the	the	DET
ejpam-4530	41	9	number	number	NOUN
ejpam-4530	41	10	of	of	ADP
ejpam-4530	41	11	the	the	DET
ejpam-4530	41	12	edges	edge	NOUN
ejpam-4530	41	13	incident	incident	NOUN
ejpam-4530	41	14	on	on	ADP
ejpam-4530	41	15	a	a	DET
ejpam-4530	41	16	vertex	vertex	NOUN
ejpam-4530	41	17	v	v	NOUN
ejpam-4530	41	18	is	be	AUX
ejpam-4530	41	19	said	say	VERB
ejpam-4530	41	20	to	to	PART
ejpam-4530	41	21	be	be	AUX
ejpam-4530	41	22	the	the	DET
ejpam-4530	41	23	degree	degree	NOUN
ejpam-4530	41	24	of	of	ADP
ejpam-4530	41	25	v	v	NOUN
ejpam-4530	41	26	and	and	CCONJ
ejpam-4530	41	27	it	it	PRON
ejpam-4530	41	28	’s	’s	AUX
ejpam-4530	41	29	denoted	denote	VERB
ejpam-4530	41	30	by	by	ADP
ejpam-4530	41	31	degg(v	degg(v	PROPN
ejpam-4530	41	32	)	)	PUNCT
ejpam-4530	41	33	or	or	CCONJ
ejpam-4530	41	34	deg(v	deg(v	PRON
ejpam-4530	41	35	)	)	PUNCT
ejpam-4530	41	36	.	.	PUNCT
ejpam-4530	42	1	the	the	DET
ejpam-4530	42	2	numbers	number	NOUN
ejpam-4530	42	3	δ(g	δ(g	ADV
ejpam-4530	42	4	)	)	PUNCT
ejpam-4530	42	5	and	and	CCONJ
ejpam-4530	42	6	∆(g	∆(g	NOUN
ejpam-4530	42	7	)	)	PUNCT
ejpam-4530	42	8	are	be	AUX
ejpam-4530	42	9	minimum	minimum	ADJ
ejpam-4530	42	10	and	and	CCONJ
ejpam-4530	42	11	maximum	maximum	ADJ
ejpam-4530	42	12	degrees	degree	NOUN
ejpam-4530	42	13	r	r	NOUN
ejpam-4530	42	14	of	of	ADP
ejpam-4530	42	15	a	a	DET
ejpam-4530	42	16	graph	graph	NOUN
ejpam-4530	42	17	g	g	NOUN
ejpam-4530	42	18	respectively	respectively	ADV
ejpam-4530	42	19	[	[	X
ejpam-4530	42	20	5	5	NUM
ejpam-4530	42	21	]	]	PUNCT
ejpam-4530	42	22	.	.	PUNCT
ejpam-4530	43	1	the	the	DET
ejpam-4530	43	2	average	average	ADJ
ejpam-4530	43	3	degree	degree	NOUN
ejpam-4530	43	4	of	of	ADP
ejpam-4530	43	5	g	g	PROPN
ejpam-4530	43	6	is	be	AUX
ejpam-4530	43	7	defined	define	VERB
ejpam-4530	43	8	by	by	ADP
ejpam-4530	43	9	:	:	PUNCT
ejpam-4530	43	10	ad(g	ad(g	X
ejpam-4530	43	11	)	)	PUNCT
ejpam-4530	43	12	=	=	SYM
ejpam-4530	43	13	1	1	NUM
ejpam-4530	43	14	|g|	|g|	PROPN
ejpam-4530	43	15	∑	∑	PUNCT
ejpam-4530	43	16	∀v∈v	∀v∈v	PROPN
ejpam-4530	43	17	deg(v	deg(v	PROPN
ejpam-4530	43	18	)	)	PUNCT
ejpam-4530	43	19	.	.	PUNCT
ejpam-4530	44	1	from	from	ADP
ejpam-4530	44	2	clearly	clearly	ADV
ejpam-4530	44	3	that	that	DET
ejpam-4530	44	4	δ(g	δ(g	ADP
ejpam-4530	44	5	)	)	PUNCT
ejpam-4530	44	6	≤	≤	NOUN
ejpam-4530	44	7	ad(g	ad(g	NOUN
ejpam-4530	44	8	)	)	PUNCT
ejpam-4530	44	9	≤	≤	NUM
ejpam-4530	44	10	∆(g	∆(g	NOUN
ejpam-4530	44	11	)	)	PUNCT
ejpam-4530	44	12	.	.	PUNCT
ejpam-4530	45	1	the	the	DET
ejpam-4530	45	2	distance	distance	NOUN
ejpam-4530	45	3	d(v	d(v	PROPN
ejpam-4530	45	4	,	,	PUNCT
ejpam-4530	45	5	u	u	NOUN
ejpam-4530	45	6	)	)	PUNCT
ejpam-4530	45	7	in	in	ADP
ejpam-4530	45	8	connected	connected	ADJ
ejpam-4530	45	9	graph	graph	NOUN
ejpam-4530	45	10	g	g	PROPN
ejpam-4530	45	11	is	be	AUX
ejpam-4530	45	12	positive	positive	ADJ
ejpam-4530	45	13	number	number	NOUN
ejpam-4530	45	14	represent	represent	NOUN
ejpam-4530	45	15	.	.	PUNCT
ejpam-4530	46	1	the	the	DET
ejpam-4530	46	2	length	length	NOUN
ejpam-4530	46	3	shortest	shortest	ADV
ejpam-4530	46	4	(	(	PUNCT
ejpam-4530	46	5	v	v	NOUN
ejpam-4530	46	6	−	−	NOUN
ejpam-4530	46	7	u)path	u)path	NOUN
ejpam-4530	46	8	in	in	ADP
ejpam-4530	46	9	g.	g.	PROPN
ejpam-4530	46	10	the	the	DET
ejpam-4530	46	11	maximum	maximum	ADJ
ejpam-4530	46	12	distance	distance	NOUN
ejpam-4530	46	13	between	between	ADP
ejpam-4530	46	14	any	any	DET
ejpam-4530	46	15	two	two	NUM
ejpam-4530	46	16	distinct	distinct	ADJ
ejpam-4530	46	17	vertices	vertex	NOUN
ejpam-4530	46	18	in	in	ADP
ejpam-4530	46	19	g	g	PROPN
ejpam-4530	46	20	is	be	AUX
ejpam-4530	46	21	the	the	DET
ejpam-4530	46	22	diameter	diameter	NOUN
ejpam-4530	46	23	of	of	ADP
ejpam-4530	46	24	g	g	PROPN
ejpam-4530	46	25	and	and	CCONJ
ejpam-4530	46	26	is	be	AUX
ejpam-4530	46	27	denoted	denote	VERB
ejpam-4530	46	28	by	by	ADP
ejpam-4530	46	29	diam(g	diam(g	PROPN
ejpam-4530	46	30	)	)	PUNCT
ejpam-4530	46	31	.	.	PUNCT
ejpam-4530	47	1	the	the	DET
ejpam-4530	47	2	sum	sum	NOUN
ejpam-4530	47	3	of	of	ADP
ejpam-4530	47	4	the	the	DET
ejpam-4530	47	5	lengths	length	NOUN
ejpam-4530	47	6	of	of	ADP
ejpam-4530	47	7	the	the	DET
ejpam-4530	47	8	shortest	short	ADJ
ejpam-4530	47	9	(	(	PUNCT
ejpam-4530	47	10	v	v	NOUN
ejpam-4530	47	11	−	−	NOUN
ejpam-4530	47	12	u)path	u)path	NOUN
ejpam-4530	47	13	in	in	ADP
ejpam-4530	47	14	g	g	PROPN
ejpam-4530	47	15	is	be	AUX
ejpam-4530	47	16	called	call	VERB
ejpam-4530	47	17	wiener	wiener	NOUN
ejpam-4530	47	18	index	index	NOUN
ejpam-4530	47	19	[	[	X
ejpam-4530	47	20	12	12	NUM
ejpam-4530	47	21	]	]	PUNCT
ejpam-4530	47	22	,	,	PUNCT
ejpam-4530	47	23	that	that	PRON
ejpam-4530	47	24	is	be	AUX
ejpam-4530	47	25	w	w	PROPN
ejpam-4530	47	26	(	(	PUNCT
ejpam-4530	47	27	g	g	NOUN
ejpam-4530	47	28	)	)	PUNCT
ejpam-4530	47	29	=	=	SYM
ejpam-4530	47	30	1	1	NUM
ejpam-4530	47	31	2	2	NUM
ejpam-4530	47	32	∑	∑	ADV
ejpam-4530	47	33	∀v	∀v	NOUN
ejpam-4530	47	34	,	,	PUNCT
ejpam-4530	47	35	u∈v	u∈v	NOUN
ejpam-4530	47	36	d(v	d(v	PROPN
ejpam-4530	47	37	,	,	PUNCT
ejpam-4530	47	38	u	u	NOUN
ejpam-4530	47	39	)	)	PUNCT
ejpam-4530	47	40	.	.	PUNCT
ejpam-4530	48	1	the	the	DET
ejpam-4530	48	2	average	average	ADJ
ejpam-4530	48	3	distance	distance	NOUN
ejpam-4530	48	4	is	be	AUX
ejpam-4530	48	5	define	define	VERB
ejpam-4530	48	6	by	by	ADP
ejpam-4530	48	7	:	:	PUNCT
ejpam-4530	48	8	d(g	d(g	PROPN
ejpam-4530	48	9	)	)	PUNCT
ejpam-4530	49	1	=	=	SYM
ejpam-4530	49	2	2w	2w	NUM
ejpam-4530	49	3	(	(	PUNCT
ejpam-4530	49	4	g	g	NOUN
ejpam-4530	49	5	)	)	PUNCT
ejpam-4530	49	6	|g|(|g|−1	|g|(|g|−1	NUM
ejpam-4530	49	7	)	)	PUNCT
ejpam-4530	49	8	.	.	PUNCT
ejpam-4530	50	1	let	let	VERB
ejpam-4530	50	2	d(g	d(g	PROPN
ejpam-4530	50	3	,	,	PUNCT
ejpam-4530	50	4	k	k	NOUN
ejpam-4530	50	5	)	)	PUNCT
ejpam-4530	50	6	be	be	VERB
ejpam-4530	50	7	the	the	DET
ejpam-4530	50	8	number	number	NOUN
ejpam-4530	50	9	of	of	ADP
ejpam-4530	50	10	vertex	vertex	NOUN
ejpam-4530	50	11	pairs	pair	NOUN
ejpam-4530	50	12	at	at	ADP
ejpam-4530	50	13	distance	distance	NOUN
ejpam-4530	50	14	k	k	PROPN
ejpam-4530	50	15	in	in	ADP
ejpam-4530	50	16	a	a	DET
ejpam-4530	50	17	connected	connected	ADJ
ejpam-4530	50	18	graph	graph	NOUN
ejpam-4530	50	19	g	g	NOUN
ejpam-4530	50	20	,	,	PUNCT
ejpam-4530	50	21	where	where	SCONJ
ejpam-4530	50	22	k	k	PROPN
ejpam-4530	50	23	=	=	SYM
ejpam-4530	50	24	0	0	NUM
ejpam-4530	50	25	,	,	PUNCT
ejpam-4530	50	26	1	1	NUM
ejpam-4530	50	27	,	,	PUNCT
ejpam-4530	50	28	·	·	PUNCT
ejpam-4530	50	29	·	·	PUNCT
ejpam-4530	50	30	·	·	PUNCT
ejpam-4530	50	31	,	,	PUNCT
ejpam-4530	50	32	diam(g	diam(g	NOUN
ejpam-4530	50	33	)	)	PUNCT
ejpam-4530	50	34	.	.	PUNCT
ejpam-4530	51	1	then	then	ADV
ejpam-4530	51	2	the	the	DET
ejpam-4530	51	3	hosoya	hosoya	ADJ
ejpam-4530	51	4	polynomial	polynomial	NOUN
ejpam-4530	51	5	[	[	X
ejpam-4530	51	6	7	7	NUM
ejpam-4530	51	7	]	]	PUNCT
ejpam-4530	51	8	of	of	ADP
ejpam-4530	51	9	g	g	PROPN
ejpam-4530	51	10	is	be	AUX
ejpam-4530	51	11	defined	define	VERB
ejpam-4530	51	12	as	as	ADP
ejpam-4530	51	13	:	:	PUNCT
ejpam-4530	51	14	h(g	h(g	PROPN
ejpam-4530	51	15	,	,	PUNCT
ejpam-4530	51	16	t	t	PROPN
ejpam-4530	51	17	)	)	PUNCT
ejpam-4530	51	18	=	=	SYM
ejpam-4530	51	19	∑diam(g	∑diam(g	PROPN
ejpam-4530	51	20	)	)	PUNCT
ejpam-4530	52	1	k=1	k=1	PROPN
ejpam-4530	53	1	d(g	d(g	PROPN
ejpam-4530	53	2	,	,	PUNCT
ejpam-4530	53	3	k)tk	k)tk	PROPN
ejpam-4530	53	4	.	.	PUNCT
ejpam-4530	54	1	from	from	ADP
ejpam-4530	54	2	clearly	clearly	ADV
ejpam-4530	54	3	that	that	PRON
ejpam-4530	54	4	:	:	PUNCT
ejpam-4530	54	5	w	w	X
ejpam-4530	54	6	(	(	PUNCT
ejpam-4530	54	7	g	g	NOUN
ejpam-4530	54	8	)	)	PUNCT
ejpam-4530	54	9	=	=	PUNCT
ejpam-4530	55	1	d	d	X
ejpam-4530	55	2	dth(g	dth(g	NOUN
ejpam-4530	55	3	,	,	PUNCT
ejpam-4530	55	4	t)|t=1	t)|t=1	NOUN
ejpam-4530	55	5	=	=	SYM
ejpam-4530	55	6	∑diam(g	∑diam(g	PROPN
ejpam-4530	55	7	)	)	PUNCT
ejpam-4530	55	8	k=0	k=0	PROPN
ejpam-4530	55	9	kd(g	kd(g	PROPN
ejpam-4530	55	10	,	,	PUNCT
ejpam-4530	55	11	k).∑diam(g	k).∑diam(g	NUM
ejpam-4530	55	12	)	)	PUNCT
ejpam-4530	55	13	k=0	k=0	PROPN
ejpam-4530	55	14	d(g	d(g	PROPN
ejpam-4530	55	15	,	,	PUNCT
ejpam-4530	55	16	k	k	NOUN
ejpam-4530	55	17	)	)	PUNCT
ejpam-4530	55	18	=	=	SYM
ejpam-4530	55	19	|g|(|g|+1	|g|(|g|+1	X
ejpam-4530	55	20	)	)	PUNCT
ejpam-4530	55	21	2∑diam(g	2∑diam(g	NUM
ejpam-4530	55	22	)	)	PUNCT
ejpam-4530	56	1	k=1	k=1	PROPN
ejpam-4530	57	1	d(g	d(g	PROPN
ejpam-4530	57	2	,	,	PUNCT
ejpam-4530	57	3	k	k	NOUN
ejpam-4530	57	4	)	)	PUNCT
ejpam-4530	57	5	=	=	PUNCT
ejpam-4530	57	6	|g|(|g|−1	|g|(|g|−1	NOUN
ejpam-4530	57	7	)	)	PUNCT
ejpam-4530	57	8	2	2	NUM
ejpam-4530	57	9	ad(g	ad(g	PUNCT
ejpam-4530	57	10	)	)	PUNCT
ejpam-4530	57	11	=	=	SYM
ejpam-4530	57	12	2∥g∥	2∥g∥	NUM
ejpam-4530	57	13	|g|	|g|	PROPN
ejpam-4530	57	14	,	,	PUNCT
ejpam-4530	57	15	d(g	d(g	PROPN
ejpam-4530	57	16	,	,	PUNCT
ejpam-4530	57	17	0	0	NUM
ejpam-4530	57	18	)	)	PUNCT
ejpam-4530	57	19	=	=	PUNCT
ejpam-4530	57	20	|g|	|g|	PROPN
ejpam-4530	57	21	andd(g	andd(g	PROPN
ejpam-4530	57	22	,	,	PUNCT
ejpam-4530	57	23	0	0	NUM
ejpam-4530	57	24	)	)	PUNCT
ejpam-4530	57	25	=	=	PRON
ejpam-4530	57	26	∥g∥.	∥g∥.	PROPN
ejpam-4530	57	27	mohammed	mohammed	PROPN
ejpam-4530	57	28	al	al	PROPN
ejpam-4530	57	29	-	-	PUNCT
ejpam-4530	57	30	neima	neima	PROPN
ejpam-4530	57	31	et	et	PROPN
ejpam-4530	57	32	al	al	PROPN
ejpam-4530	57	33	.	.	PUNCT
ejpam-4530	57	34	/	/	SYM
ejpam-4530	57	35	eur	eur	PROPN
ejpam-4530	57	36	.	.	PUNCT
ejpam-4530	58	1	j.	j.	PROPN
ejpam-4530	58	2	pure	pure	PROPN
ejpam-4530	58	3	appl	appl	PROPN
ejpam-4530	58	4	.	.	PROPN
ejpam-4530	58	5	math	math	PROPN
ejpam-4530	58	6	,	,	PUNCT
ejpam-4530	58	7	15	15	NUM
ejpam-4530	58	8	(	(	PUNCT
ejpam-4530	58	9	4	4	NUM
ejpam-4530	58	10	)	)	PUNCT
ejpam-4530	58	11	(	(	PUNCT
ejpam-4530	58	12	2022	2022	NUM
ejpam-4530	58	13	)	)	PUNCT
ejpam-4530	58	14	,	,	PUNCT
ejpam-4530	58	15	1637	1637	NUM
ejpam-4530	58	16	-	-	SYM
ejpam-4530	58	17	1648	1648	NUM
ejpam-4530	58	18	1639	1639	NUM
ejpam-4530	58	19	2	2	NUM
ejpam-4530	58	20	.	.	PUNCT
ejpam-4530	59	1	invo	invo	PROPN
ejpam-4530	59	2	-	-	PUNCT
ejpam-4530	59	3	t	t	PROPN
ejpam-4530	59	4	-	-	PUNCT
ejpam-4530	59	5	clean	clean	ADJ
ejpam-4530	59	6	rings	ring	NOUN
ejpam-4530	59	7	the	the	DET
ejpam-4530	59	8	section	section	NOUN
ejpam-4530	59	9	describes	describe	VERB
ejpam-4530	59	10	the	the	DET
ejpam-4530	59	11	structure	structure	NOUN
ejpam-4530	59	12	of	of	ADP
ejpam-4530	59	13	the	the	DET
ejpam-4530	59	14	invo	invo	PROPN
ejpam-4530	59	15	-	-	PUNCT
ejpam-4530	59	16	t	t	NOUN
ejpam-4530	59	17	-	-	PUNCT
ejpam-4530	59	18	clean	clean	ADJ
ejpam-4530	59	19	rings	ring	NOUN
ejpam-4530	59	20	.	.	PUNCT
ejpam-4530	60	1	definition	definition	NOUN
ejpam-4530	60	2	2.1	2.1	NUM
ejpam-4530	60	3	.	.	PUNCT
ejpam-4530	61	1	the	the	DET
ejpam-4530	61	2	ring	ring	NOUN
ejpam-4530	61	3	r	r	NOUN
ejpam-4530	61	4	is	be	AUX
ejpam-4530	61	5	called	call	VERB
ejpam-4530	61	6	involution	involution	NOUN
ejpam-4530	61	7	t	t	PROPN
ejpam-4530	61	8	-	-	PUNCT
ejpam-4530	61	9	clean	clean	ADJ
ejpam-4530	61	10	(	(	PUNCT
ejpam-4530	61	11	for	for	ADP
ejpam-4530	61	12	short	short	ADJ
ejpam-4530	61	13	invo	invo	VERB
ejpam-4530	61	14	-	-	PUNCT
ejpam-4530	61	15	t	t	NOUN
ejpam-4530	61	16	-	-	PUNCT
ejpam-4530	61	17	clean	clean	ADJ
ejpam-4530	61	18	)	)	PUNCT
ejpam-4530	61	19	,	,	PUNCT
ejpam-4530	61	20	if	if	SCONJ
ejpam-4530	61	21	all	all	DET
ejpam-4530	61	22	a	a	DET
ejpam-4530	61	23	∈	∈	NOUN
ejpam-4530	61	24	r	r	NOUN
ejpam-4530	61	25	can	can	AUX
ejpam-4530	61	26	be	be	AUX
ejpam-4530	61	27	expressed	express	VERB
ejpam-4530	61	28	as	as	ADP
ejpam-4530	61	29	a	a	DET
ejpam-4530	61	30	=	=	SYM
ejpam-4530	61	31	u+	u+	NOUN
ejpam-4530	61	32	t	t	PROPN
ejpam-4530	61	33	,	,	PUNCT
ejpam-4530	61	34	where	where	SCONJ
ejpam-4530	61	35	u	u	PROPN
ejpam-4530	61	36	∈	∈	PROPN
ejpam-4530	61	37	invo(r	invo(r	NOUN
ejpam-4530	61	38	)	)	PUNCT
ejpam-4530	61	39	and	and	CCONJ
ejpam-4530	61	40	t	t	PROPN
ejpam-4530	61	41	∈	∈	PROPN
ejpam-4530	61	42	tri(r	tri(r	PROPN
ejpam-4530	61	43	)	)	PUNCT
ejpam-4530	61	44	.	.	PUNCT
ejpam-4530	62	1	an	an	DET
ejpam-4530	62	2	invo	invo	PROPN
ejpam-4530	62	3	-	-	PUNCT
ejpam-4530	62	4	t	t	NOUN
ejpam-4530	62	5	-	-	PUNCT
ejpam-4530	62	6	clean	clean	ADJ
ejpam-4530	62	7	ring	ring	NOUN
ejpam-4530	62	8	with	with	ADP
ejpam-4530	62	9	ut	ut	PROPN
ejpam-4530	62	10	=	=	PROPN
ejpam-4530	62	11	tu	tu	PROPN
ejpam-4530	62	12	is	be	AUX
ejpam-4530	62	13	strongly	strongly	ADV
ejpam-4530	62	14	invo	invo	ADJ
ejpam-4530	62	15	-	-	PUNCT
ejpam-4530	62	16	t	t	NOUN
ejpam-4530	62	17	-	-	PUNCT
ejpam-4530	62	18	clean	clean	PROPN
ejpam-4530	62	19	.	.	PUNCT
ejpam-4530	62	20	example	example	NOUN
ejpam-4530	62	21	2.2	2.2	NUM
ejpam-4530	62	22	.	.	NOUN
ejpam-4530	63	1	1	1	X
ejpam-4530	63	2	.	.	X
ejpam-4530	63	3	let	let	VERB
ejpam-4530	63	4	n	n	PRON
ejpam-4530	63	5	≥	≥	X
ejpam-4530	63	6	2	2	NUM
ejpam-4530	63	7	and	and	CCONJ
ejpam-4530	63	8	integer	integer	NOUN
ejpam-4530	63	9	.	.	PUNCT
ejpam-4530	64	1	then	then	ADV
ejpam-4530	64	2	the	the	DET
ejpam-4530	64	3	ring	ring	NOUN
ejpam-4530	64	4	zn	zn	PROPN
ejpam-4530	64	5	is	be	AUX
ejpam-4530	64	6	invo	invo	ADJ
ejpam-4530	64	7	-	-	PUNCT
ejpam-4530	64	8	t	t	NOUN
ejpam-4530	64	9	-	-	PUNCT
ejpam-4530	64	10	clean	clean	ADJ
ejpam-4530	64	11	if	if	SCONJ
ejpam-4530	65	1	and	and	CCONJ
ejpam-4530	65	2	only	only	ADV
ejpam-4530	65	3	if	if	SCONJ
ejpam-4530	65	4	n	n	NOUN
ejpam-4530	65	5	=	=	SYM
ejpam-4530	65	6	2	2	NUM
ejpam-4530	65	7	,	,	PUNCT
ejpam-4530	65	8	3	3	NUM
ejpam-4530	65	9	,	,	PUNCT
ejpam-4530	65	10	4	4	NUM
ejpam-4530	65	11	,	,	PUNCT
ejpam-4530	65	12	5	5	NUM
ejpam-4530	65	13	,	,	PUNCT
ejpam-4530	65	14	6	6	NUM
ejpam-4530	65	15	,	,	PUNCT
ejpam-4530	65	16	8	8	NUM
ejpam-4530	65	17	,	,	PUNCT
ejpam-4530	65	18	10	10	NUM
ejpam-4530	65	19	,	,	PUNCT
ejpam-4530	65	20	12	12	NUM
ejpam-4530	65	21	,	,	PUNCT
ejpam-4530	65	22	15	15	NUM
ejpam-4530	65	23	,	,	PUNCT
ejpam-4530	65	24	20	20	NUM
ejpam-4530	65	25	,	,	PUNCT
ejpam-4530	65	26	24	24	NUM
ejpam-4530	65	27	,	,	PUNCT
ejpam-4530	65	28	30	30	NUM
ejpam-4530	65	29	,	,	PUNCT
ejpam-4530	65	30	40	40	NUM
ejpam-4530	65	31	,	,	PUNCT
ejpam-4530	65	32	60	60	NUM
ejpam-4530	65	33	,	,	PUNCT
ejpam-4530	65	34	120	120	NUM
ejpam-4530	65	35	.	.	NOUN
ejpam-4530	65	36	2	2	X
ejpam-4530	65	37	.	.	X
ejpam-4530	66	1	let	let	VERB
ejpam-4530	66	2	m2(z2),m2(z3	m2(z2),m2(z3	ADJ
ejpam-4530	66	3	)	)	PUNCT
ejpam-4530	66	4	and	and	CCONJ
ejpam-4530	66	5	the	the	DET
ejpam-4530	66	6	upper	upper	ADJ
ejpam-4530	66	7	triangular	triangular	NOUN
ejpam-4530	66	8	matrices	matrice	VERB
ejpam-4530	66	9	t2(z2	t2(z2	NOUN
ejpam-4530	66	10	)	)	PUNCT
ejpam-4530	66	11	,	,	PUNCT
ejpam-4530	66	12	t2(z3	t2(z3	NOUN
ejpam-4530	66	13	)	)	PUNCT
ejpam-4530	66	14	are	be	AUX
ejpam-4530	66	15	invo	invo	ADJ
ejpam-4530	66	16	-	-	ADJ
ejpam-4530	66	17	tclean	tclean	ADJ
ejpam-4530	66	18	rings	ring	NOUN
ejpam-4530	66	19	.	.	PUNCT
ejpam-4530	67	1	remark	remark	VERB
ejpam-4530	67	2	2.3	2.3	NUM
ejpam-4530	67	3	.	.	PUNCT
ejpam-4530	68	1	1	1	NUM
ejpam-4530	68	2	.	.	X
ejpam-4530	69	1	every	every	DET
ejpam-4530	69	2	invo	invo	PROPN
ejpam-4530	69	3	-	-	PUNCT
ejpam-4530	69	4	t	t	NOUN
ejpam-4530	69	5	-	-	PUNCT
ejpam-4530	69	6	clean	clean	ADJ
ejpam-4530	69	7	ring	ring	NOUN
ejpam-4530	69	8	is	be	AUX
ejpam-4530	69	9	also	also	ADV
ejpam-4530	69	10	clean	clean	ADJ
ejpam-4530	69	11	,	,	PUNCT
ejpam-4530	69	12	but	but	CCONJ
ejpam-4530	69	13	the	the	DET
ejpam-4530	69	14	reverse	reverse	NOUN
ejpam-4530	69	15	is	be	AUX
ejpam-4530	69	16	not	not	PART
ejpam-4530	69	17	true	true	ADJ
ejpam-4530	69	18	,	,	PUNCT
ejpam-4530	69	19	for	for	ADP
ejpam-4530	69	20	a	a	DET
ejpam-4530	69	21	commutative	commutative	ADJ
ejpam-4530	69	22	example	example	NOUN
ejpam-4530	69	23	z7	z7	PROPN
ejpam-4530	69	24	.	.	PUNCT
ejpam-4530	70	1	for	for	ADP
ejpam-4530	70	2	non	non	ADJ
ejpam-4530	70	3	-	-	ADJ
ejpam-4530	70	4	commutative	commutative	ADJ
ejpam-4530	70	5	example	example	NOUN
ejpam-4530	70	6	m2(z4	m2(z4	PROPN
ejpam-4530	70	7	)	)	PUNCT
ejpam-4530	70	8	,	,	PUNCT
ejpam-4530	70	9	t2(z4	t2(z4	NOUN
ejpam-4530	70	10	)	)	PUNCT
ejpam-4530	70	11	.	.	PUNCT
ejpam-4530	71	1	the	the	DET
ejpam-4530	71	2	elements	element	NOUN
ejpam-4530	71	3	[	[	PUNCT
ejpam-4530	71	4	2	2	NUM
ejpam-4530	71	5	3	3	NUM
ejpam-4530	71	6	0	0	NUM
ejpam-4530	71	7	2	2	NUM
ejpam-4530	71	8	]	]	PUNCT
ejpam-4530	71	9	,	,	PUNCT
ejpam-4530	71	10	[	[	PUNCT
ejpam-4530	71	11	2	2	NUM
ejpam-4530	71	12	1	1	NUM
ejpam-4530	71	13	0	0	NUM
ejpam-4530	71	14	2	2	NUM
ejpam-4530	71	15	]	]	PUNCT
ejpam-4530	71	16	,	,	PUNCT
ejpam-4530	71	17	[	[	PUNCT
ejpam-4530	71	18	0	0	NUM
ejpam-4530	71	19	1	1	NUM
ejpam-4530	71	20	0	0	NUM
ejpam-4530	71	21	0	0	NUM
ejpam-4530	71	22	]	]	PUNCT
ejpam-4530	71	23	,	,	PUNCT
ejpam-4530	71	24	[	[	PUNCT
ejpam-4530	71	25	0	0	NUM
ejpam-4530	71	26	3	3	NUM
ejpam-4530	71	27	0	0	NUM
ejpam-4530	71	28	0	0	NUM
ejpam-4530	71	29	]	]	PUNCT
ejpam-4530	71	30	are	be	AUX
ejpam-4530	71	31	not	not	PART
ejpam-4530	71	32	invo	invo	VERB
ejpam-4530	71	33	-	-	PUNCT
ejpam-4530	71	34	t	t	NOUN
ejpam-4530	71	35	-	-	PUNCT
ejpam-4530	71	36	clean	clean	ADJ
ejpam-4530	71	37	in	in	ADP
ejpam-4530	71	38	,	,	PUNCT
ejpam-4530	71	39	t2(z4	t2(z4	NOUN
ejpam-4530	71	40	)	)	PUNCT
ejpam-4530	71	41	,	,	PUNCT
ejpam-4530	71	42	where	where	SCONJ
ejpam-4530	71	43	u2(t2(z4	u2(t2(z4	NOUN
ejpam-4530	71	44	)	)	PUNCT
ejpam-4530	71	45	)	)	PUNCT
ejpam-4530	72	1	=	=	PUNCT
ejpam-4530	72	2			PUNCT
ejpam-4530	72	3	[	[	PUNCT
ejpam-4530	72	4	1	1	NUM
ejpam-4530	72	5	0	0	NUM
ejpam-4530	72	6	0	0	NUM
ejpam-4530	72	7	1	1	NUM
ejpam-4530	72	8	]	]	PUNCT
ejpam-4530	72	9	,	,	PUNCT
ejpam-4530	72	10	[	[	PUNCT
ejpam-4530	72	11	1	1	NUM
ejpam-4530	72	12	0	0	NUM
ejpam-4530	72	13	0	0	NUM
ejpam-4530	72	14	3	3	NUM
ejpam-4530	72	15	]	]	PUNCT
ejpam-4530	72	16	,	,	PUNCT
ejpam-4530	72	17	[	[	PUNCT
ejpam-4530	72	18	1	1	NUM
ejpam-4530	72	19	1	1	NUM
ejpam-4530	72	20	0	0	NUM
ejpam-4530	72	21	3	3	NUM
ejpam-4530	72	22	]	]	PUNCT
ejpam-4530	72	23	,	,	PUNCT
ejpam-4530	72	24	[	[	PUNCT
ejpam-4530	72	25	1	1	NUM
ejpam-4530	72	26	2	2	NUM
ejpam-4530	72	27	0	0	NUM
ejpam-4530	72	28	1	1	NUM
ejpam-4530	72	29	]	]	PUNCT
ejpam-4530	72	30	,	,	PUNCT
ejpam-4530	72	31	[	[	PUNCT
ejpam-4530	72	32	1	1	NUM
ejpam-4530	72	33	2	2	NUM
ejpam-4530	72	34	0	0	NUM
ejpam-4530	72	35	3	3	NUM
ejpam-4530	72	36	]	]	PUNCT
ejpam-4530	72	37	,	,	PUNCT
ejpam-4530	72	38	[	[	PUNCT
ejpam-4530	72	39	1	1	NUM
ejpam-4530	72	40	3	3	NUM
ejpam-4530	72	41	0	0	NUM
ejpam-4530	72	42	3	3	NUM
ejpam-4530	72	43	]	]	PUNCT
ejpam-4530	72	44	,	,	PUNCT
ejpam-4530	72	45	[	[	PUNCT
ejpam-4530	72	46	3	3	NUM
ejpam-4530	72	47	0	0	NUM
ejpam-4530	72	48	0	0	NUM
ejpam-4530	72	49	1	1	NUM
ejpam-4530	72	50	]	]	PUNCT
ejpam-4530	72	51	,	,	PUNCT
ejpam-4530	72	52	[	[	PUNCT
ejpam-4530	72	53	3	3	NUM
ejpam-4530	72	54	0	0	NUM
ejpam-4530	72	55	0	0	NUM
ejpam-4530	72	56	3	3	NUM
ejpam-4530	72	57	]	]	PUNCT
ejpam-4530	72	58	,	,	PUNCT
ejpam-4530	72	59	[	[	PUNCT
ejpam-4530	72	60	3	3	NUM
ejpam-4530	72	61	1	1	NUM
ejpam-4530	72	62	0	0	NUM
ejpam-4530	72	63	1	1	NUM
ejpam-4530	72	64	]	]	PUNCT
ejpam-4530	72	65	,	,	PUNCT
ejpam-4530	72	66	[	[	PUNCT
ejpam-4530	72	67	3	3	NUM
ejpam-4530	72	68	2	2	NUM
ejpam-4530	72	69	0	0	NUM
ejpam-4530	72	70	1	1	NUM
ejpam-4530	72	71	]	]	PUNCT
ejpam-4530	72	72	,	,	PUNCT
ejpam-4530	72	73	[	[	PUNCT
ejpam-4530	72	74	3	3	NUM
ejpam-4530	72	75	2	2	NUM
ejpam-4530	72	76	0	0	NUM
ejpam-4530	72	77	3	3	NUM
ejpam-4530	72	78	]	]	PUNCT
ejpam-4530	72	79	,	,	PUNCT
ejpam-4530	72	80	[	[	PUNCT
ejpam-4530	72	81	3	3	NUM
ejpam-4530	72	82	3	3	NUM
ejpam-4530	72	83	0	0	NUM
ejpam-4530	72	84	1	1	NUM
ejpam-4530	72	85	]	]	PUNCT
ejpam-4530	72	86			PROPN
ejpam-4530	72	87	tri(t2(z4	tri(t2(z4	PROPN
ejpam-4530	72	88	)	)	PUNCT
ejpam-4530	72	89	)	)	PUNCT
ejpam-4530	73	1	=	=	SYM
ejpam-4530	73	2			PUNCT
ejpam-4530	73	3	[	[	PUNCT
ejpam-4530	73	4	0	0	NUM
ejpam-4530	73	5	0	0	NUM
ejpam-4530	73	6	0	0	NUM
ejpam-4530	73	7	0	0	NUM
ejpam-4530	73	8	]	]	PUNCT
ejpam-4530	73	9	,	,	PUNCT
ejpam-4530	73	10	[	[	PUNCT
ejpam-4530	73	11	0	0	NUM
ejpam-4530	73	12	0	0	NUM
ejpam-4530	73	13	0	0	NUM
ejpam-4530	73	14	1	1	NUM
ejpam-4530	73	15	]	]	PUNCT
ejpam-4530	73	16	,	,	PUNCT
ejpam-4530	73	17	[	[	PUNCT
ejpam-4530	73	18	0	0	NUM
ejpam-4530	73	19	0	0	NUM
ejpam-4530	73	20	0	0	NUM
ejpam-4530	73	21	3	3	NUM
ejpam-4530	73	22	]	]	PUNCT
ejpam-4530	73	23	,	,	PUNCT
ejpam-4530	73	24	[	[	PUNCT
ejpam-4530	73	25	0	0	NUM
ejpam-4530	73	26	1	1	NUM
ejpam-4530	73	27	0	0	NUM
ejpam-4530	73	28	1	1	NUM
ejpam-4530	73	29	]	]	PUNCT
ejpam-4530	73	30	,	,	PUNCT
ejpam-4530	73	31	[	[	PUNCT
ejpam-4530	73	32	0	0	NUM
ejpam-4530	73	33	1	1	NUM
ejpam-4530	73	34	0	0	NUM
ejpam-4530	73	35	3	3	NUM
ejpam-4530	73	36	]	]	PUNCT
ejpam-4530	73	37	,	,	PUNCT
ejpam-4530	73	38	[	[	PUNCT
ejpam-4530	73	39	0	0	NUM
ejpam-4530	73	40	2	2	NUM
ejpam-4530	73	41	0	0	NUM
ejpam-4530	73	42	1	1	NUM
ejpam-4530	73	43	]	]	PUNCT
ejpam-4530	73	44	,	,	PUNCT
ejpam-4530	73	45	[	[	PUNCT
ejpam-4530	73	46	0	0	NUM
ejpam-4530	73	47	2	2	NUM
ejpam-4530	73	48	0	0	NUM
ejpam-4530	73	49	3	3	NUM
ejpam-4530	73	50	]	]	PUNCT
ejpam-4530	73	51	,	,	PUNCT
ejpam-4530	73	52	[	[	PUNCT
ejpam-4530	73	53	0	0	NUM
ejpam-4530	73	54	3	3	NUM
ejpam-4530	73	55	0	0	NUM
ejpam-4530	73	56	1	1	NUM
ejpam-4530	73	57	]	]	PUNCT
ejpam-4530	73	58	,	,	PUNCT
ejpam-4530	73	59	[	[	PUNCT
ejpam-4530	73	60	0	0	NUM
ejpam-4530	73	61	3	3	NUM
ejpam-4530	73	62	0	0	NUM
ejpam-4530	73	63	3	3	NUM
ejpam-4530	73	64	]	]	PUNCT
ejpam-4530	73	65	,	,	PUNCT
ejpam-4530	73	66	[	[	PUNCT
ejpam-4530	73	67	1	1	NUM
ejpam-4530	73	68	0	0	NUM
ejpam-4530	73	69	0	0	NUM
ejpam-4530	73	70	0	0	NUM
ejpam-4530	73	71	]	]	PUNCT
ejpam-4530	73	72	,	,	PUNCT
ejpam-4530	73	73	[	[	PUNCT
ejpam-4530	73	74	1	1	NUM
ejpam-4530	73	75	0	0	NUM
ejpam-4530	73	76	0	0	NUM
ejpam-4530	73	77	1	1	NUM
ejpam-4530	73	78	]	]	PUNCT
ejpam-4530	73	79	,	,	PUNCT
ejpam-4530	73	80	[	[	PUNCT
ejpam-4530	73	81	1	1	NUM
ejpam-4530	73	82	0	0	NUM
ejpam-4530	73	83	0	0	NUM
ejpam-4530	73	84	3	3	NUM
ejpam-4530	73	85	]	]	PUNCT
ejpam-4530	73	86	,	,	PUNCT
ejpam-4530	73	87	[	[	PUNCT
ejpam-4530	73	88	1	1	NUM
ejpam-4530	73	89	1	1	NUM
ejpam-4530	73	90	0	0	NUM
ejpam-4530	73	91	0	0	NUM
ejpam-4530	73	92	]	]	PUNCT
ejpam-4530	73	93	,	,	PUNCT
ejpam-4530	73	94	[	[	PUNCT
ejpam-4530	73	95	1	1	NUM
ejpam-4530	73	96	1	1	NUM
ejpam-4530	73	97	0	0	NUM
ejpam-4530	73	98	3	3	NUM
ejpam-4530	73	99	]	]	PUNCT
ejpam-4530	73	100	,	,	PUNCT
ejpam-4530	73	101	[	[	PUNCT
ejpam-4530	73	102	1	1	NUM
ejpam-4530	73	103	2	2	NUM
ejpam-4530	73	104	0	0	NUM
ejpam-4530	73	105	0	0	NUM
ejpam-4530	73	106	]	]	PUNCT
ejpam-4530	73	107	,	,	PUNCT
ejpam-4530	73	108	[	[	PUNCT
ejpam-4530	73	109	1	1	NUM
ejpam-4530	73	110	2	2	NUM
ejpam-4530	73	111	0	0	NUM
ejpam-4530	73	112	1	1	NUM
ejpam-4530	73	113	]	]	PUNCT
ejpam-4530	73	114	,	,	PUNCT
ejpam-4530	73	115	[	[	PUNCT
ejpam-4530	73	116	1	1	NUM
ejpam-4530	73	117	2	2	NUM
ejpam-4530	73	118	0	0	NUM
ejpam-4530	73	119	3	3	NUM
ejpam-4530	73	120	]	]	PUNCT
ejpam-4530	73	121	,	,	PUNCT
ejpam-4530	73	122	[	[	PUNCT
ejpam-4530	73	123	1	1	NUM
ejpam-4530	73	124	3	3	NUM
ejpam-4530	73	125	0	0	NUM
ejpam-4530	73	126	0	0	NUM
ejpam-4530	73	127	]	]	PUNCT
ejpam-4530	73	128	,	,	PUNCT
ejpam-4530	73	129	[	[	PUNCT
ejpam-4530	73	130	1	1	NUM
ejpam-4530	73	131	3	3	NUM
ejpam-4530	73	132	0	0	NUM
ejpam-4530	73	133	3	3	NUM
ejpam-4530	73	134	]	]	PUNCT
ejpam-4530	73	135	,	,	PUNCT
ejpam-4530	73	136	[	[	PUNCT
ejpam-4530	73	137	3	3	NUM
ejpam-4530	73	138	0	0	NUM
ejpam-4530	73	139	0	0	NUM
ejpam-4530	73	140	0	0	NUM
ejpam-4530	73	141	]	]	PUNCT
ejpam-4530	73	142	,	,	PUNCT
ejpam-4530	73	143	[	[	PUNCT
ejpam-4530	73	144	3	3	NUM
ejpam-4530	73	145	0	0	NUM
ejpam-4530	73	146	0	0	NUM
ejpam-4530	73	147	1	1	NUM
ejpam-4530	73	148	]	]	PUNCT
ejpam-4530	73	149	,	,	PUNCT
ejpam-4530	73	150	[	[	PUNCT
ejpam-4530	73	151	3	3	NUM
ejpam-4530	73	152	0	0	NUM
ejpam-4530	73	153	0	0	NUM
ejpam-4530	73	154	3	3	NUM
ejpam-4530	73	155	]	]	PUNCT
ejpam-4530	73	156	,	,	PUNCT
ejpam-4530	73	157	[	[	PUNCT
ejpam-4530	73	158	3	3	NUM
ejpam-4530	73	159	1	1	NUM
ejpam-4530	73	160	0	0	NUM
ejpam-4530	73	161	0	0	NUM
ejpam-4530	73	162	]	]	PUNCT
ejpam-4530	73	163	,	,	PUNCT
ejpam-4530	73	164	[	[	PUNCT
ejpam-4530	73	165	3	3	NUM
ejpam-4530	73	166	1	1	NUM
ejpam-4530	73	167	0	0	NUM
ejpam-4530	73	168	1	1	NUM
ejpam-4530	73	169	]	]	PUNCT
ejpam-4530	73	170	,	,	PUNCT
ejpam-4530	73	171	[	[	PUNCT
ejpam-4530	73	172	3	3	NUM
ejpam-4530	73	173	2	2	NUM
ejpam-4530	73	174	0	0	NUM
ejpam-4530	73	175	0	0	NUM
ejpam-4530	73	176	]	]	PUNCT
ejpam-4530	73	177	,	,	PUNCT
ejpam-4530	73	178	[	[	PUNCT
ejpam-4530	73	179	3	3	NUM
ejpam-4530	73	180	2	2	NUM
ejpam-4530	73	181	0	0	NUM
ejpam-4530	73	182	1	1	NUM
ejpam-4530	73	183	]	]	PUNCT
ejpam-4530	73	184	,	,	PUNCT
ejpam-4530	73	185	[	[	PUNCT
ejpam-4530	73	186	3	3	NUM
ejpam-4530	73	187	2	2	NUM
ejpam-4530	73	188	0	0	NUM
ejpam-4530	73	189	3	3	NUM
ejpam-4530	73	190	]	]	PUNCT
ejpam-4530	73	191	,	,	PUNCT
ejpam-4530	73	192	[	[	PUNCT
ejpam-4530	73	193	3	3	NUM
ejpam-4530	73	194	3	3	NUM
ejpam-4530	73	195	0	0	NUM
ejpam-4530	73	196	0	0	NUM
ejpam-4530	73	197	]	]	PUNCT
ejpam-4530	73	198	,	,	PUNCT
ejpam-4530	73	199	[	[	PUNCT
ejpam-4530	73	200	3	3	NUM
ejpam-4530	73	201	3	3	NUM
ejpam-4530	73	202	0	0	NUM
ejpam-4530	73	203	1	1	NUM
ejpam-4530	73	204	]	]	PUNCT
ejpam-4530	73	205			NOUN
ejpam-4530	73	206	2	2	NUM
ejpam-4530	73	207	.	.	PUNCT
ejpam-4530	74	1	every	every	DET
ejpam-4530	74	2	invo	invo	ADJ
ejpam-4530	74	3	-	-	ADJ
ejpam-4530	74	4	clean	clean	ADJ
ejpam-4530	74	5	ring	ring	NOUN
ejpam-4530	74	6	is	be	AUX
ejpam-4530	74	7	invo	invo	ADJ
ejpam-4530	74	8	-	-	PUNCT
ejpam-4530	74	9	t	t	NOUN
ejpam-4530	74	10	-	-	PUNCT
ejpam-4530	74	11	clean	clean	ADJ
ejpam-4530	74	12	,	,	PUNCT
ejpam-4530	74	13	but	but	CCONJ
ejpam-4530	74	14	the	the	DET
ejpam-4530	74	15	reverse	reverse	NOUN
ejpam-4530	74	16	is	be	AUX
ejpam-4530	74	17	not	not	PART
ejpam-4530	74	18	true	true	ADJ
ejpam-4530	74	19	.	.	PUNCT
ejpam-4530	75	1	for	for	ADP
ejpam-4530	75	2	commutative	commutative	ADJ
ejpam-4530	75	3	example	example	NOUN
ejpam-4530	75	4	z5	z5	PROPN
ejpam-4530	75	5	,	,	PUNCT
ejpam-4530	75	6	the	the	DET
ejpam-4530	75	7	element	element	NOUN
ejpam-4530	75	8	3	3	NUM
ejpam-4530	75	9	is	be	AUX
ejpam-4530	75	10	not	not	PART
ejpam-4530	75	11	invo	invo	ADJ
ejpam-4530	75	12	-	-	ADJ
ejpam-4530	75	13	clean	clean	ADJ
ejpam-4530	75	14	.	.	PUNCT
ejpam-4530	76	1	for	for	ADP
ejpam-4530	76	2	non	non	ADJ
ejpam-4530	76	3	-	-	ADJ
ejpam-4530	76	4	commutative	commutative	ADJ
ejpam-4530	76	5	example	example	NOUN
ejpam-4530	76	6	m2(z3	m2(z3	NUM
ejpam-4530	76	7	)	)	PUNCT
ejpam-4530	76	8	,	,	PUNCT
ejpam-4530	76	9	t2(z3	t2(z3	NOUN
ejpam-4530	76	10	)	)	PUNCT
ejpam-4530	76	11	.	.	PUNCT
ejpam-4530	77	1	the	the	DET
ejpam-4530	77	2	elements	element	NOUN
ejpam-4530	77	3	[	[	PUNCT
ejpam-4530	77	4	0	0	NUM
ejpam-4530	77	5	2	2	NUM
ejpam-4530	77	6	0	0	NUM
ejpam-4530	77	7	0	0	NUM
ejpam-4530	77	8	]	]	PUNCT
ejpam-4530	77	9	,	,	PUNCT
ejpam-4530	77	10	[	[	PUNCT
ejpam-4530	77	11	0	0	NUM
ejpam-4530	77	12	1	1	NUM
ejpam-4530	77	13	0	0	NUM
ejpam-4530	77	14	0	0	NUM
ejpam-4530	77	15	]	]	PUNCT
ejpam-4530	77	16	,	,	PUNCT
ejpam-4530	77	17	[	[	PUNCT
ejpam-4530	77	18	1	1	NUM
ejpam-4530	77	19	2	2	NUM
ejpam-4530	77	20	0	0	NUM
ejpam-4530	77	21	1	1	NUM
ejpam-4530	77	22	]	]	PUNCT
ejpam-4530	77	23	,	,	PUNCT
ejpam-4530	77	24	[	[	PUNCT
ejpam-4530	77	25	1	1	NUM
ejpam-4530	77	26	1	1	NUM
ejpam-4530	77	27	0	0	NUM
ejpam-4530	77	28	1	1	NUM
ejpam-4530	77	29	]	]	PUNCT
ejpam-4530	77	30	are	be	AUX
ejpam-4530	77	31	not	not	PART
ejpam-4530	77	32	invo	invo	ADJ
ejpam-4530	77	33	-	-	ADJ
ejpam-4530	77	34	clean	clean	ADJ
ejpam-4530	77	35	in	in	ADP
ejpam-4530	77	36	t2(z3	t2(z3	NUM
ejpam-4530	77	37	)	)	PUNCT
ejpam-4530	77	38	,	,	PUNCT
ejpam-4530	77	39	where	where	SCONJ
ejpam-4530	77	40	u2(t2(z3	u2(t2(z3	VERB
ejpam-4530	77	41	)	)	PUNCT
ejpam-4530	77	42	)	)	PUNCT
ejpam-4530	78	1	=	=	PUNCT
ejpam-4530	78	2			PUNCT
ejpam-4530	78	3	[	[	PUNCT
ejpam-4530	78	4	1	1	NUM
ejpam-4530	78	5	0	0	NUM
ejpam-4530	78	6	0	0	NUM
ejpam-4530	78	7	1	1	NUM
ejpam-4530	78	8	]	]	PUNCT
ejpam-4530	78	9	,	,	PUNCT
ejpam-4530	78	10	[	[	PUNCT
ejpam-4530	78	11	1	1	NUM
ejpam-4530	78	12	0	0	NUM
ejpam-4530	78	13	0	0	NUM
ejpam-4530	78	14	2	2	NUM
ejpam-4530	78	15	]	]	PUNCT
ejpam-4530	78	16	,	,	PUNCT
ejpam-4530	78	17	[	[	PUNCT
ejpam-4530	78	18	1	1	NUM
ejpam-4530	78	19	1	1	NUM
ejpam-4530	78	20	0	0	NUM
ejpam-4530	78	21	2	2	NUM
ejpam-4530	78	22	]	]	PUNCT
ejpam-4530	78	23	,	,	PUNCT
ejpam-4530	78	24	[	[	PUNCT
ejpam-4530	78	25	1	1	NUM
ejpam-4530	78	26	2	2	NUM
ejpam-4530	78	27	0	0	NUM
ejpam-4530	78	28	2	2	NUM
ejpam-4530	78	29	]	]	PUNCT
ejpam-4530	78	30	,	,	PUNCT
ejpam-4530	78	31	[	[	PUNCT
ejpam-4530	78	32	2	2	NUM
ejpam-4530	78	33	0	0	NUM
ejpam-4530	78	34	0	0	NUM
ejpam-4530	78	35	1	1	NUM
ejpam-4530	78	36	]	]	PUNCT
ejpam-4530	78	37	,	,	PUNCT
ejpam-4530	78	38	[	[	PUNCT
ejpam-4530	78	39	2	2	NUM
ejpam-4530	78	40	0	0	NUM
ejpam-4530	78	41	0	0	NUM
ejpam-4530	78	42	2	2	NUM
ejpam-4530	78	43	]	]	PUNCT
ejpam-4530	78	44	,	,	PUNCT
ejpam-4530	78	45	[	[	PUNCT
ejpam-4530	78	46	2	2	NUM
ejpam-4530	78	47	1	1	NUM
ejpam-4530	78	48	0	0	NUM
ejpam-4530	78	49	1	1	NUM
ejpam-4530	78	50	]	]	PUNCT
ejpam-4530	78	51	,	,	PUNCT
ejpam-4530	78	52	[	[	PUNCT
ejpam-4530	78	53	2	2	NUM
ejpam-4530	78	54	2	2	NUM
ejpam-4530	78	55	0	0	NUM
ejpam-4530	78	56	1	1	NUM
ejpam-4530	78	57	]	]	PUNCT
ejpam-4530	79	1			PROPN
ejpam-4530	79	2	mohammed	mohammed	PROPN
ejpam-4530	79	3	al	al	PROPN
ejpam-4530	79	4	-	-	PUNCT
ejpam-4530	79	5	neima	neima	PROPN
ejpam-4530	79	6	et	et	PROPN
ejpam-4530	79	7	al	al	PROPN
ejpam-4530	79	8	.	.	PUNCT
ejpam-4530	79	9	/	/	SYM
ejpam-4530	79	10	eur	eur	PROPN
ejpam-4530	79	11	.	.	PUNCT
ejpam-4530	80	1	j.	j.	PROPN
ejpam-4530	80	2	pure	pure	PROPN
ejpam-4530	80	3	appl	appl	PROPN
ejpam-4530	80	4	.	.	PROPN
ejpam-4530	80	5	math	math	PROPN
ejpam-4530	80	6	,	,	PUNCT
ejpam-4530	80	7	15	15	NUM
ejpam-4530	80	8	(	(	PUNCT
ejpam-4530	80	9	4	4	NUM
ejpam-4530	80	10	)	)	PUNCT
ejpam-4530	80	11	(	(	PUNCT
ejpam-4530	80	12	2022	2022	NUM
ejpam-4530	80	13	)	)	PUNCT
ejpam-4530	80	14	,	,	PUNCT
ejpam-4530	80	15	1637	1637	NUM
ejpam-4530	80	16	-	-	SYM
ejpam-4530	80	17	1648	1648	NUM
ejpam-4530	80	18	1640	1640	NUM
ejpam-4530	80	19	id(t2(z3	id(t2(z3	NOUN
ejpam-4530	80	20	)	)	PUNCT
ejpam-4530	80	21	)	)	PUNCT
ejpam-4530	81	1	=	=	PUNCT
ejpam-4530	81	2			PUNCT
ejpam-4530	82	1	[	[	PUNCT
ejpam-4530	82	2	0	0	NUM
ejpam-4530	82	3	0	0	NUM
ejpam-4530	82	4	0	0	NUM
ejpam-4530	82	5	0	0	NUM
ejpam-4530	82	6	]	]	PUNCT
ejpam-4530	82	7	,	,	PUNCT
ejpam-4530	82	8	[	[	PUNCT
ejpam-4530	82	9	0	0	NUM
ejpam-4530	82	10	0	0	NUM
ejpam-4530	82	11	0	0	NUM
ejpam-4530	82	12	1	1	NUM
ejpam-4530	82	13	]	]	PUNCT
ejpam-4530	82	14	,	,	PUNCT
ejpam-4530	82	15	[	[	PUNCT
ejpam-4530	82	16	0	0	NUM
ejpam-4530	82	17	1	1	NUM
ejpam-4530	82	18	0	0	NUM
ejpam-4530	82	19	1	1	NUM
ejpam-4530	82	20	]	]	PUNCT
ejpam-4530	82	21	,	,	PUNCT
ejpam-4530	82	22	[	[	PUNCT
ejpam-4530	82	23	0	0	NUM
ejpam-4530	82	24	2	2	NUM
ejpam-4530	82	25	0	0	NUM
ejpam-4530	82	26	1	1	NUM
ejpam-4530	82	27	]	]	PUNCT
ejpam-4530	82	28	,	,	PUNCT
ejpam-4530	82	29	[	[	PUNCT
ejpam-4530	82	30	1	1	NUM
ejpam-4530	82	31	0	0	NUM
ejpam-4530	82	32	0	0	NUM
ejpam-4530	82	33	0	0	NUM
ejpam-4530	82	34	]	]	PUNCT
ejpam-4530	82	35	,	,	PUNCT
ejpam-4530	82	36	[	[	PUNCT
ejpam-4530	82	37	1	1	NUM
ejpam-4530	82	38	0	0	NUM
ejpam-4530	82	39	0	0	NUM
ejpam-4530	82	40	1	1	NUM
ejpam-4530	82	41	]	]	PUNCT
ejpam-4530	82	42	,	,	PUNCT
ejpam-4530	82	43	[	[	PUNCT
ejpam-4530	82	44	1	1	NUM
ejpam-4530	82	45	1	1	NUM
ejpam-4530	82	46	0	0	NUM
ejpam-4530	82	47	0	0	NUM
ejpam-4530	82	48	]	]	PUNCT
ejpam-4530	82	49	,	,	PUNCT
ejpam-4530	82	50	[	[	PUNCT
ejpam-4530	82	51	1	1	NUM
ejpam-4530	82	52	2	2	NUM
ejpam-4530	82	53	0	0	NUM
ejpam-4530	82	54	0	0	NUM
ejpam-4530	82	55	]	]	PUNCT
ejpam-4530	83	1			NOUN
ejpam-4530	83	2	we	we	PRON
ejpam-4530	83	3	begin	begin	VERB
ejpam-4530	83	4	with	with	ADP
ejpam-4530	83	5	two	two	NUM
ejpam-4530	83	6	useful	useful	ADJ
ejpam-4530	83	7	technicalities	technicality	NOUN
ejpam-4530	83	8	.	.	PUNCT
ejpam-4530	84	1	proposition	proposition	NOUN
ejpam-4530	84	2	2.4	2.4	NUM
ejpam-4530	84	3	.	.	PUNCT
ejpam-4530	85	1	let	let	VERB
ejpam-4530	85	2	3	3	NUM
ejpam-4530	85	3	be	be	AUX
ejpam-4530	85	4	an	an	DET
ejpam-4530	85	5	invo	invo	NOUN
ejpam-4530	85	6	-	-	PUNCT
ejpam-4530	85	7	t	t	NOUN
ejpam-4530	85	8	-	-	PUNCT
ejpam-4530	85	9	clean	clean	ADJ
ejpam-4530	85	10	element	element	NOUN
ejpam-4530	85	11	in	in	ADP
ejpam-4530	85	12	a	a	DET
ejpam-4530	85	13	ring	ring	NOUN
ejpam-4530	85	14	r.	r.	PROPN
ejpam-4530	85	15	then	then	ADV
ejpam-4530	85	16	15	15	NUM
ejpam-4530	85	17	t	t	NOUN
ejpam-4530	85	18	=	=	SYM
ejpam-4530	85	19	0	0	NUM
ejpam-4530	85	20	and	and	CCONJ
ejpam-4530	85	21	120	120	NUM
ejpam-4530	85	22	=	=	SYM
ejpam-4530	85	23	0	0	NUM
ejpam-4530	85	24	.	.	PUNCT
ejpam-4530	86	1	proof	proof	NOUN
ejpam-4530	86	2	.	.	PUNCT
ejpam-4530	87	1	since	since	SCONJ
ejpam-4530	87	2	3	3	NUM
ejpam-4530	87	3	=	=	SYM
ejpam-4530	87	4	u+	u+	NOUN
ejpam-4530	87	5	t	t	PROPN
ejpam-4530	87	6	,	,	PUNCT
ejpam-4530	87	7	where	where	SCONJ
ejpam-4530	87	8	u	u	PROPN
ejpam-4530	87	9	∈	∈	PROPN
ejpam-4530	87	10	invo(r	invo(r	NOUN
ejpam-4530	87	11	)	)	PUNCT
ejpam-4530	87	12	and	and	CCONJ
ejpam-4530	87	13	t	t	PROPN
ejpam-4530	87	14	∈	∈	PROPN
ejpam-4530	87	15	tri(r).thus	tri(r).thus	PROPN
ejpam-4530	87	16	ut	ut	PROPN
ejpam-4530	87	17	=	=	PRON
ejpam-4530	87	18	(	(	PUNCT
ejpam-4530	87	19	3−	3−	X
ejpam-4530	87	20	t)t	t)t	X
ejpam-4530	87	21	=	=	PUNCT
ejpam-4530	87	22	3t−	3t−	NUM
ejpam-4530	87	23	t2	t2	NOUN
ejpam-4530	87	24	=	=	SYM
ejpam-4530	87	25	t(3−	t(3−	PROPN
ejpam-4530	87	26	t	t	PROPN
ejpam-4530	87	27	)	)	PUNCT
ejpam-4530	87	28	=	=	SYM
ejpam-4530	87	29	tu	tu	PROPN
ejpam-4530	87	30	,	,	PUNCT
ejpam-4530	87	31	so	so	ADV
ejpam-4530	87	32	ut	ut	PROPN
ejpam-4530	87	33	=	=	PROPN
ejpam-4530	87	34	tu	tu	PROPN
ejpam-4530	87	35	.	.	PUNCT
ejpam-4530	88	1	now	now	ADV
ejpam-4530	88	2	24	24	NUM
ejpam-4530	88	3	=	=	SYM
ejpam-4530	88	4	33	33	NUM
ejpam-4530	88	5	−	−	NOUN
ejpam-4530	88	6	3	3	NUM
ejpam-4530	88	7	=	=	SYM
ejpam-4530	88	8	(	(	PUNCT
ejpam-4530	88	9	u+	u+	NUM
ejpam-4530	88	10	t)3	t)3	NOUN
ejpam-4530	88	11	−	−	PROPN
ejpam-4530	88	12	(	(	PUNCT
ejpam-4530	88	13	u+	u+	NOUN
ejpam-4530	88	14	t	t	PROPN
ejpam-4530	88	15	)	)	PUNCT
ejpam-4530	88	16	=	=	SYM
ejpam-4530	88	17	8	8	NUM
ejpam-4530	88	18	·	·	SYM
ejpam-4530	88	19	3	3	NUM
ejpam-4530	88	20	=	=	SYM
ejpam-4530	88	21	8(u+	8(u+	NUM
ejpam-4530	88	22	t	t	PROPN
ejpam-4530	88	23	)	)	PUNCT
ejpam-4530	88	24	,	,	PUNCT
ejpam-4530	88	25	u3	u3	NOUN
ejpam-4530	88	26	+	+	CCONJ
ejpam-4530	88	27	3u2t+	3u2t+	NUM
ejpam-4530	88	28	3ut2	3ut2	NUM
ejpam-4530	88	29	+	+	CCONJ
ejpam-4530	88	30	t3	t3	PROPN
ejpam-4530	88	31	−	−	PROPN
ejpam-4530	88	32	ut	ut	PROPN
ejpam-4530	88	33	=	=	NOUN
ejpam-4530	88	34	8(u+	8(u+	PROPN
ejpam-4530	88	35	t	t	PROPN
ejpam-4530	88	36	)	)	PUNCT
ejpam-4530	88	37	u+	u+	NOUN
ejpam-4530	88	38	3t+	3t+	NUM
ejpam-4530	88	39	3ut2	3ut2	NUM
ejpam-4530	88	40	+	+	CCONJ
ejpam-4530	88	41	t−	t−	PROPN
ejpam-4530	88	42	u−	u−	PROPN
ejpam-4530	88	43	t	t	NOUN
ejpam-4530	88	44	=	=	SYM
ejpam-4530	88	45	8(u+	8(u+	NUM
ejpam-4530	88	46	t	t	PROPN
ejpam-4530	88	47	)	)	PUNCT
ejpam-4530	88	48	.	.	PUNCT
ejpam-4530	89	1	−3t−	−3t−	NOUN
ejpam-4530	89	2	3ut2	3ut2	NUM
ejpam-4530	89	3	+	+	CCONJ
ejpam-4530	89	4	8u+	8u+	NUM
ejpam-4530	89	5	8	8	NUM
ejpam-4530	89	6	t	t	NOUN
ejpam-4530	89	7	=	=	SYM
ejpam-4530	89	8	0	0	X
ejpam-4530	89	9	.	.	PUNCT
ejpam-4530	90	1	multiply	multiply	AUX
ejpam-4530	90	2	both	both	PRON
ejpam-4530	90	3	sided	side	VERB
ejpam-4530	90	4	from	from	ADP
ejpam-4530	90	5	the	the	DET
ejpam-4530	90	6	right	right	NOUN
ejpam-4530	90	7	by	by	ADP
ejpam-4530	90	8	t	t	PROPN
ejpam-4530	90	9	−3t2	−3t2	PUNCT
ejpam-4530	90	10	−	−	PROPN
ejpam-4530	90	11	3ut3	3ut3	NUM
ejpam-4530	90	12	+	+	CCONJ
ejpam-4530	90	13	8ut+	8ut+	NUM
ejpam-4530	90	14	8t2	8t2	NUM
ejpam-4530	91	1	=	=	SYM
ejpam-4530	91	2	5t(t+	5t(t+	NUM
ejpam-4530	91	3	u	u	NOUN
ejpam-4530	91	4	)	)	PUNCT
ejpam-4530	91	5	=	=	SYM
ejpam-4530	92	1	0	0	X
ejpam-4530	92	2	.	.	PUNCT
ejpam-4530	93	1	hence	hence	ADV
ejpam-4530	93	2	15	15	NUM
ejpam-4530	93	3	t	t	NOUN
ejpam-4530	93	4	=	=	SYM
ejpam-4530	93	5	0	0	NUM
ejpam-4530	93	6	in	in	ADP
ejpam-4530	93	7	addition	addition	NOUN
ejpam-4530	93	8	,	,	PUNCT
ejpam-4530	93	9	24	24	NUM
ejpam-4530	93	10	=	=	SYM
ejpam-4530	93	11	3t+	3t+	NUM
ejpam-4530	93	12	3ut2	3ut2	NUM
ejpam-4530	93	13	=	=	NOUN
ejpam-4530	93	14	3t+	3t+	NUM
ejpam-4530	93	15	3(3−	3(3−	NUM
ejpam-4530	93	16	t)t2	t)t2	PROPN
ejpam-4530	94	1	=	=	PUNCT
ejpam-4530	95	1	3t+	3t+	NUM
ejpam-4530	95	2	9t2	9t2	NUM
ejpam-4530	95	3	−	−	ADP
ejpam-4530	95	4	3t3	3t3	NUM
ejpam-4530	95	5	=	=	NOUN
ejpam-4530	95	6	9t2	9t2	NUM
ejpam-4530	95	7	.	.	PUNCT
ejpam-4530	96	1	so	so	ADV
ejpam-4530	96	2	120	120	NUM
ejpam-4530	96	3	=	=	SYM
ejpam-4530	96	4	5	5	NUM
ejpam-4530	96	5	·	·	SYM
ejpam-4530	96	6	24	24	NUM
ejpam-4530	96	7	=	=	SYM
ejpam-4530	96	8	5	5	NUM
ejpam-4530	96	9	·	·	PUNCT
ejpam-4530	96	10	9t2	9t2	NUM
ejpam-4530	97	1	=	=	SYM
ejpam-4530	97	2	3(15t)t	3(15t)t	NUM
ejpam-4530	97	3	=	=	SYM
ejpam-4530	97	4	0	0	NUM
ejpam-4530	97	5	.	.	PUNCT
ejpam-4530	98	1	■	■	PUNCT
ejpam-4530	98	2	proposition	proposition	NOUN
ejpam-4530	98	3	2.5	2.5	NUM
ejpam-4530	98	4	.	.	PUNCT
ejpam-4530	99	1	the	the	DET
ejpam-4530	99	2	homomorphic	homomorphic	ADJ
ejpam-4530	99	3	image	image	NOUN
ejpam-4530	99	4	of	of	ADP
ejpam-4530	99	5	invo	invo	PROPN
ejpam-4530	99	6	-	-	PUNCT
ejpam-4530	99	7	t	t	PROPN
ejpam-4530	99	8	-	-	PUNCT
ejpam-4530	99	9	clean	clean	ADJ
ejpam-4530	99	10	rings	ring	NOUN
ejpam-4530	99	11	are	be	AUX
ejpam-4530	99	12	invo	invo	ADJ
ejpam-4530	99	13	-	-	PUNCT
ejpam-4530	99	14	t	t	NOUN
ejpam-4530	99	15	-	-	PUNCT
ejpam-4530	99	16	clean	clean	ADJ
ejpam-4530	99	17	.	.	PUNCT
ejpam-4530	100	1	proof	proof	NOUN
ejpam-4530	100	2	.	.	PUNCT
ejpam-4530	101	1	let	let	VERB
ejpam-4530	101	2	f	f	NOUN
ejpam-4530	101	3	:	:	PUNCT
ejpam-4530	101	4	r	r	VERB
ejpam-4530	101	5	−→	−→	NOUN
ejpam-4530	101	6	s	s	AUX
ejpam-4530	101	7	be	be	AUX
ejpam-4530	101	8	a	a	DET
ejpam-4530	101	9	homomorphic	homomorphic	ADJ
ejpam-4530	101	10	mapping	mapping	NOUN
ejpam-4530	101	11	from	from	ADP
ejpam-4530	101	12	an	an	DET
ejpam-4530	101	13	invo	invo	PROPN
ejpam-4530	101	14	-	-	PUNCT
ejpam-4530	101	15	t	t	NOUN
ejpam-4530	101	16	-	-	PUNCT
ejpam-4530	101	17	clean	clean	ADJ
ejpam-4530	101	18	ring	ring	NOUN
ejpam-4530	101	19	r	r	NOUN
ejpam-4530	101	20	into	into	ADP
ejpam-4530	101	21	s.	s.	PROPN
ejpam-4530	101	22	then	then	ADV
ejpam-4530	101	23	for	for	SCONJ
ejpam-4530	101	24	all	all	DET
ejpam-4530	101	25	y	y	PROPN
ejpam-4530	101	26	∈	∈	PROPN
ejpam-4530	101	27	s	s	VERB
ejpam-4530	101	28	there	there	ADV
ejpam-4530	101	29	x	x	SYM
ejpam-4530	101	30	∈	∈	NOUN
ejpam-4530	101	31	r	r	NOUN
ejpam-4530	101	32	with	with	ADP
ejpam-4530	101	33	y	y	PROPN
ejpam-4530	101	34	=	=	SYM
ejpam-4530	101	35	f(x	f(x	PROPN
ejpam-4530	101	36	)	)	PUNCT
ejpam-4530	101	37	and	and	CCONJ
ejpam-4530	101	38	x	x	X
ejpam-4530	101	39	=	=	SYM
ejpam-4530	101	40	u	u	PROPN
ejpam-4530	101	41	+	+	X
ejpam-4530	101	42	t	t	NOUN
ejpam-4530	101	43	where	where	SCONJ
ejpam-4530	101	44	u	u	PROPN
ejpam-4530	101	45	∈	∈	PROPN
ejpam-4530	101	46	invo(r	invo(r	NOUN
ejpam-4530	101	47	)	)	PUNCT
ejpam-4530	101	48	and	and	CCONJ
ejpam-4530	101	49	t	t	PROPN
ejpam-4530	101	50	∈	∈	PROPN
ejpam-4530	101	51	tri(r	tri(r	PROPN
ejpam-4530	101	52	)	)	PUNCT
ejpam-4530	101	53	.	.	PUNCT
ejpam-4530	102	1	now	now	ADV
ejpam-4530	102	2	y	y	PROPN
ejpam-4530	102	3	=	=	SYM
ejpam-4530	102	4	f(x	f(x	PROPN
ejpam-4530	102	5	)	)	PUNCT
ejpam-4530	102	6	=	=	PUNCT
ejpam-4530	102	7	f(u+t	f(u+t	NOUN
ejpam-4530	102	8	)	)	PUNCT
ejpam-4530	102	9	=	=	SYM
ejpam-4530	102	10	f(u)+f(t	f(u)+f(t	PROPN
ejpam-4530	102	11	)	)	PUNCT
ejpam-4530	102	12	,	,	PUNCT
ejpam-4530	102	13	(	(	PUNCT
ejpam-4530	102	14	f(t))3	f(t))3	VERB
ejpam-4530	102	15	=	=	SYM
ejpam-4530	102	16	f(t3	f(t3	X
ejpam-4530	102	17	)	)	PUNCT
ejpam-4530	102	18	=	=	SYM
ejpam-4530	102	19	f(t	f(t	NOUN
ejpam-4530	102	20	)	)	PUNCT
ejpam-4530	102	21	∈	∈	PROPN
ejpam-4530	102	22	tri(r	tri(r	PROPN
ejpam-4530	102	23	)	)	PUNCT
ejpam-4530	102	24	.	.	PUNCT
ejpam-4530	103	1	since	since	SCONJ
ejpam-4530	103	2	u	u	NOUN
ejpam-4530	103	3	∈	∈	PROPN
ejpam-4530	103	4	u2(r),then	u2(r),then	ADV
ejpam-4530	103	5	(	(	PUNCT
ejpam-4530	103	6	f(u))2	f(u))2	PROPN
ejpam-4530	103	7	=	=	SYM
ejpam-4530	103	8	f(u2	f(u2	NOUN
ejpam-4530	103	9	)	)	PUNCT
ejpam-4530	103	10	=	=	PUNCT
ejpam-4530	104	1	f(1	f(1	PROPN
ejpam-4530	104	2	)	)	PUNCT
ejpam-4530	104	3	=	=	SYM
ejpam-4530	104	4	1	1	NUM
ejpam-4530	104	5	,	,	PUNCT
ejpam-4530	104	6	so	so	ADV
ejpam-4530	104	7	f(u	f(u	PROPN
ejpam-4530	104	8	)	)	PUNCT
ejpam-4530	104	9	∈	∈	PROPN
ejpam-4530	104	10	u2(r	u2(r	SYM
ejpam-4530	104	11	)	)	PUNCT
ejpam-4530	104	12	y	y	PROPN
ejpam-4530	104	13	=	=	SYM
ejpam-4530	104	14	f(x	f(x	PROPN
ejpam-4530	104	15	)	)	PUNCT
ejpam-4530	104	16	=	=	SYM
ejpam-4530	104	17	f(u	f(u	PROPN
ejpam-4530	104	18	)	)	PUNCT
ejpam-4530	104	19	+	+	CCONJ
ejpam-4530	104	20	f(t	f(t	NOUN
ejpam-4530	104	21	)	)	PUNCT
ejpam-4530	104	22	.	.	PUNCT
ejpam-4530	105	1	therefore	therefore	ADV
ejpam-4530	105	2	s	s	VERB
ejpam-4530	105	3	is	be	AUX
ejpam-4530	105	4	invo	invo	ADJ
ejpam-4530	105	5	-	-	PUNCT
ejpam-4530	105	6	t	t	NOUN
ejpam-4530	105	7	-	-	PUNCT
ejpam-4530	105	8	clean	clean	ADJ
ejpam-4530	105	9	ring	ring	NOUN
ejpam-4530	105	10	.	.	PUNCT
ejpam-4530	106	1	■	■	PUNCT
ejpam-4530	106	2	corollary	corollary	ADJ
ejpam-4530	106	3	2.6	2.6	NUM
ejpam-4530	106	4	.	.	PUNCT
ejpam-4530	107	1	let	let	VERB
ejpam-4530	107	2	r	r	PRON
ejpam-4530	107	3	be	be	AUX
ejpam-4530	107	4	an	an	DET
ejpam-4530	107	5	invo	invo	NOUN
ejpam-4530	107	6	-	-	PUNCT
ejpam-4530	107	7	t	t	NOUN
ejpam-4530	107	8	-	-	PUNCT
ejpam-4530	107	9	clean	clean	ADJ
ejpam-4530	107	10	ring	ring	NOUN
ejpam-4530	108	1	and	and	CCONJ
ejpam-4530	108	2	i	i	PRON
ejpam-4530	108	3	is	be	AUX
ejpam-4530	108	4	an	an	DET
ejpam-4530	108	5	ideal	ideal	NOUN
ejpam-4530	108	6	of	of	ADP
ejpam-4530	108	7	r.	r.	PROPN
ejpam-4530	108	8	then	then	ADV
ejpam-4530	108	9	r	r	PROPN
ejpam-4530	108	10	/	/	SYM
ejpam-4530	108	11	i	i	PRON
ejpam-4530	108	12	is	be	AUX
ejpam-4530	108	13	an	an	DET
ejpam-4530	108	14	invo	invo	PROPN
ejpam-4530	108	15	-	-	PUNCT
ejpam-4530	108	16	t	t	NOUN
ejpam-4530	108	17	-	-	PUNCT
ejpam-4530	108	18	clean	clean	ADJ
ejpam-4530	108	19	.	.	PUNCT
ejpam-4530	109	1	since	since	SCONJ
ejpam-4530	109	2	the	the	DET
ejpam-4530	109	3	involution	involution	NOUN
ejpam-4530	109	4	element	element	NOUN
ejpam-4530	109	5	is	be	AUX
ejpam-4530	109	6	also	also	ADV
ejpam-4530	109	7	a	a	DET
ejpam-4530	109	8	tripotent	tripotent	ADJ
ejpam-4530	109	9	element	element	NOUN
ejpam-4530	109	10	.	.	PUNCT
ejpam-4530	110	1	the	the	DET
ejpam-4530	110	2	following	follow	VERB
ejpam-4530	110	3	proposition	proposition	NOUN
ejpam-4530	110	4	explains	explain	VERB
ejpam-4530	110	5	that	that	SCONJ
ejpam-4530	110	6	the	the	DET
ejpam-4530	110	7	nilpotent	nilpotent	ADJ
ejpam-4530	110	8	element	element	NOUN
ejpam-4530	110	9	of	of	ADP
ejpam-4530	110	10	index	index	NOUN
ejpam-4530	110	11	2	2	NUM
ejpam-4530	110	12	will	will	AUX
ejpam-4530	110	13	be	be	AUX
ejpam-4530	110	14	a	a	DET
ejpam-4530	110	15	sum	sum	NOUN
ejpam-4530	110	16	of	of	ADP
ejpam-4530	110	17	two	two	NUM
ejpam-4530	110	18	involution	involution	NOUN
ejpam-4530	110	19	elements	element	NOUN
ejpam-4530	110	20	if	if	SCONJ
ejpam-4530	110	21	it	it	PRON
ejpam-4530	110	22	is	be	AUX
ejpam-4530	110	23	invo	invo	ADJ
ejpam-4530	110	24	-	-	PUNCT
ejpam-4530	110	25	t	t	NOUN
ejpam-4530	110	26	-	-	PUNCT
ejpam-4530	110	27	clean	clean	ADJ
ejpam-4530	110	28	.	.	PUNCT
ejpam-4530	111	1	proposition	proposition	NOUN
ejpam-4530	111	2	2.7	2.7	NUM
ejpam-4530	111	3	.	.	PUNCT
ejpam-4530	112	1	for	for	ADP
ejpam-4530	112	2	a	a	DET
ejpam-4530	112	3	ring	ring	NOUN
ejpam-4530	112	4	r.	r.	PROPN
ejpam-4530	112	5	let	let	VERB
ejpam-4530	112	6	a	a	DET
ejpam-4530	112	7	∈	∈	PROPN
ejpam-4530	112	8	n2(r	n2(r	PROPN
ejpam-4530	112	9	)	)	PUNCT
ejpam-4530	112	10	.	.	PUNCT
ejpam-4530	113	1	1	1	X
ejpam-4530	113	2	.	.	X
ejpam-4530	113	3	if	if	SCONJ
ejpam-4530	113	4	a	a	PRON
ejpam-4530	113	5	is	be	AUX
ejpam-4530	113	6	an	an	DET
ejpam-4530	113	7	invo	invo	VERB
ejpam-4530	113	8	-	-	PUNCT
ejpam-4530	113	9	t	t	NOUN
ejpam-4530	113	10	-	-	PUNCT
ejpam-4530	113	11	clean	clean	ADJ
ejpam-4530	113	12	element	element	NOUN
ejpam-4530	113	13	,	,	PUNCT
ejpam-4530	113	14	then	then	ADV
ejpam-4530	113	15	t	t	PROPN
ejpam-4530	113	16	∈	∈	PROPN
ejpam-4530	113	17	invo(r	invo(r	PROPN
ejpam-4530	113	18	)	)	PUNCT
ejpam-4530	113	19	.	.	PUNCT
ejpam-4530	114	1	2	2	X
ejpam-4530	114	2	.	.	X
ejpam-4530	114	3	if	if	SCONJ
ejpam-4530	114	4	a	a	PRON
ejpam-4530	114	5	is	be	AUX
ejpam-4530	114	6	a	a	DET
ejpam-4530	114	7	strongly	strongly	ADV
ejpam-4530	114	8	invo	invo	VERB
ejpam-4530	114	9	-	-	PUNCT
ejpam-4530	114	10	t	t	NOUN
ejpam-4530	114	11	-	-	PUNCT
ejpam-4530	114	12	clean	clean	ADJ
ejpam-4530	114	13	element	element	NOUN
ejpam-4530	114	14	,	,	PUNCT
ejpam-4530	114	15	then	then	ADV
ejpam-4530	114	16	2a	2a	NUM
ejpam-4530	114	17	=	=	SYM
ejpam-4530	114	18	0	0	X
ejpam-4530	114	19	.	.	PUNCT
ejpam-4530	114	20	proof	proof	NOUN
ejpam-4530	114	21	.	.	PUNCT
ejpam-4530	115	1	(	(	PUNCT
ejpam-4530	115	2	1	1	X
ejpam-4530	115	3	)	)	PUNCT
ejpam-4530	115	4	since	since	SCONJ
ejpam-4530	115	5	a	a	DET
ejpam-4530	115	6	∈	∈	PROPN
ejpam-4530	115	7	n2(r	n2(r	PROPN
ejpam-4530	115	8	)	)	PUNCT
ejpam-4530	115	9	,	,	PUNCT
ejpam-4530	115	10	then	then	ADV
ejpam-4530	115	11	a2	a2	PROPN
ejpam-4530	115	12	=	=	SYM
ejpam-4530	115	13	0	0	PROPN
ejpam-4530	115	14	and	and	CCONJ
ejpam-4530	115	15	a	a	DET
ejpam-4530	115	16	=	=	SYM
ejpam-4530	115	17	u	u	PROPN
ejpam-4530	115	18	+	+	PROPN
ejpam-4530	115	19	t	t	PROPN
ejpam-4530	115	20	,	,	PUNCT
ejpam-4530	115	21	where	where	SCONJ
ejpam-4530	115	22	u	u	PROPN
ejpam-4530	115	23	∈	∈	PROPN
ejpam-4530	115	24	invo(r	invo(r	NOUN
ejpam-4530	115	25	)	)	PUNCT
ejpam-4530	115	26	and	and	CCONJ
ejpam-4530	115	27	t	t	PROPN
ejpam-4530	115	28	∈	∈	PROPN
ejpam-4530	115	29	tri(r	tri(r	PROPN
ejpam-4530	115	30	)	)	PUNCT
ejpam-4530	115	31	.	.	PUNCT
ejpam-4530	115	32	0	0	NUM
ejpam-4530	116	1	=	=	SYM
ejpam-4530	116	2	a2	a2	PROPN
ejpam-4530	116	3	=	=	SYM
ejpam-4530	116	4	(	(	PUNCT
ejpam-4530	116	5	u+	u+	NUM
ejpam-4530	116	6	t)2	t)2	PROPN
ejpam-4530	116	7	=	=	SYM
ejpam-4530	116	8	1+ut+	1+ut+	NUM
ejpam-4530	116	9	tu+	tu+	NOUN
ejpam-4530	116	10	t2	t2	NOUN
ejpam-4530	116	11	.	.	PUNCT
ejpam-4530	117	1	multiply	multiply	AUX
ejpam-4530	117	2	both	both	PRON
ejpam-4530	117	3	sided	side	VERB
ejpam-4530	117	4	from	from	ADP
ejpam-4530	117	5	the	the	DET
ejpam-4530	117	6	right	right	NOUN
ejpam-4530	117	7	and	and	CCONJ
ejpam-4530	117	8	left	leave	VERB
ejpam-4530	117	9	by	by	ADP
ejpam-4530	117	10	t.	t.	PROPN
ejpam-4530	117	11	2t2	2t2	PROPN
ejpam-4530	118	1	+	+	CCONJ
ejpam-4530	118	2	tut2	tut2	NOUN
ejpam-4530	118	3	+	+	CCONJ
ejpam-4530	118	4	t2ut	t2ut	PUNCT
ejpam-4530	118	5	=	=	SYM
ejpam-4530	118	6	0	0	NUM
ejpam-4530	118	7	since	since	SCONJ
ejpam-4530	118	8	a2	a2	PROPN
ejpam-4530	118	9	=	=	SYM
ejpam-4530	118	10	0	0	PROPN
ejpam-4530	118	11	,	,	PUNCT
ejpam-4530	118	12	then	then	ADV
ejpam-4530	118	13	0	0	NUM
ejpam-4530	119	1	=	=	SYM
ejpam-4530	119	2	(	(	PUNCT
ejpam-4530	119	3	ua)2u+	ua)2u+	PROPN
ejpam-4530	119	4	ta2	ta2	PROPN
ejpam-4530	119	5	t	t	PROPN
ejpam-4530	119	6	=	=	SYM
ejpam-4530	119	7	u(u+	u(u+	PROPN
ejpam-4530	119	8	t)2u+	t)2u+	PROPN
ejpam-4530	119	9	t(u+	t(u+	PUNCT
ejpam-4530	119	10	t)2u	t)2u	NOUN
ejpam-4530	119	11	=	=	NOUN
ejpam-4530	120	1	1	1	NUM
ejpam-4530	120	2	+	+	NUM
ejpam-4530	120	3	tu+	tu+	ADJ
ejpam-4530	120	4	ut+	ut+	ADJ
ejpam-4530	120	5	ut2u+	ut2u+	PROPN
ejpam-4530	120	6	t2	t2	NOUN
ejpam-4530	120	7	+	+	CCONJ
ejpam-4530	120	8	tut2	tut2	NOUN
ejpam-4530	120	9	+	+	CCONJ
ejpam-4530	120	10	t2ut+	t2ut+	PROPN
ejpam-4530	120	11	t2	t2	NOUN
ejpam-4530	120	12	=	=	SYM
ejpam-4530	120	13	−t2	−t2	PROPN
ejpam-4530	120	14	+	+	PROPN
ejpam-4530	120	15	ut2u	ut2u	PROPN
ejpam-4530	120	16	.	.	PUNCT
ejpam-4530	121	1	so	so	ADV
ejpam-4530	121	2	t2	t2	PROPN
ejpam-4530	121	3	=	=	PUNCT
ejpam-4530	121	4	ut2u	ut2u	PROPN
ejpam-4530	121	5	implies	imply	VERB
ejpam-4530	121	6	ut2	ut2	NOUN
ejpam-4530	121	7	=	=	SYM
ejpam-4530	121	8	t2u	t2u	PROPN
ejpam-4530	121	9	.	.	PROPN
ejpam-4530	121	10	1	1	NUM
ejpam-4530	122	1	+	+	CCONJ
ejpam-4530	122	2	ut+	ut+	ADJ
ejpam-4530	122	3	tu+	tu+	NOUN
ejpam-4530	122	4	t2	t2	NOUN
ejpam-4530	122	5	=	=	SYM
ejpam-4530	122	6	0	0	PUNCT
ejpam-4530	122	7	=	=	SYM
ejpam-4530	122	8	2t2	2t2	NUM
ejpam-4530	122	9	+	+	CCONJ
ejpam-4530	122	10	tut2	tut2	NOUN
ejpam-4530	122	11	+	+	CCONJ
ejpam-4530	122	12	t2ut	t2ut	PUNCT
ejpam-4530	122	13	=	=	SYM
ejpam-4530	122	14	2t2	2t2	NUM
ejpam-4530	122	15	+	+	CCONJ
ejpam-4530	122	16	tu+	tu+	ADJ
ejpam-4530	122	17	ut	ut	PROPN
ejpam-4530	122	18	t2	t2	PROPN
ejpam-4530	122	19	=	=	SYM
ejpam-4530	122	20	1	1	X
ejpam-4530	122	21	.	.	PUNCT
ejpam-4530	122	22	(	(	PUNCT
ejpam-4530	122	23	2	2	NUM
ejpam-4530	122	24	):	):	PUNCT
ejpam-4530	122	25	0	0	NUM
ejpam-4530	122	26	=	=	SYM
ejpam-4530	122	27	a2	a2	PROPN
ejpam-4530	122	28	=	=	SYM
ejpam-4530	122	29	(	(	PUNCT
ejpam-4530	122	30	u	u	NOUN
ejpam-4530	122	31	+	+	X
ejpam-4530	122	32	t)2	t)2	NOUN
ejpam-4530	122	33	=	=	NOUN
ejpam-4530	122	34	1	1	NUM
ejpam-4530	122	35	+	+	NUM
ejpam-4530	122	36	2ut	2ut	NOUN
ejpam-4530	122	37	+	+	CCONJ
ejpam-4530	122	38	t2	t2	NOUN
ejpam-4530	122	39	.	.	PUNCT
ejpam-4530	123	1	multiply	multiply	AUX
ejpam-4530	123	2	both	both	PRON
ejpam-4530	123	3	sided	side	VERB
ejpam-4530	123	4	from	from	ADP
ejpam-4530	123	5	the	the	DET
ejpam-4530	123	6	right	right	NOUN
ejpam-4530	123	7	by	by	ADP
ejpam-4530	123	8	t	t	PROPN
ejpam-4530	123	9	,	,	PUNCT
ejpam-4530	123	10	0	0	NUM
ejpam-4530	124	1	=	=	SYM
ejpam-4530	124	2	2ut2	2ut2	NUM
ejpam-4530	125	1	+	+	CCONJ
ejpam-4530	125	2	2	2	NUM
ejpam-4530	125	3	t	t	NOUN
ejpam-4530	125	4	=	=	SYM
ejpam-4530	125	5	2t(u+	2t(u+	PROPN
ejpam-4530	125	6	t	t	PROPN
ejpam-4530	125	7	)	)	PUNCT
ejpam-4530	125	8	=	=	SYM
ejpam-4530	126	1	2ta	2ta	ADJ
ejpam-4530	126	2	=	=	PUNCT
ejpam-4530	126	3	2t2a	2t2a	NUM
ejpam-4530	126	4	=	=	SYM
ejpam-4530	126	5	2a	2a	NUM
ejpam-4530	126	6	from(1	from(1	NOUN
ejpam-4530	126	7	)	)	PUNCT
ejpam-4530	126	8	.	.	PUNCT
ejpam-4530	127	1	■	■	PUNCT
ejpam-4530	127	2	mohammed	mohammed	PROPN
ejpam-4530	127	3	al	al	PROPN
ejpam-4530	127	4	-	-	PUNCT
ejpam-4530	127	5	neima	neima	PROPN
ejpam-4530	127	6	et	et	PROPN
ejpam-4530	127	7	al	al	PROPN
ejpam-4530	127	8	.	.	PUNCT
ejpam-4530	127	9	/	/	SYM
ejpam-4530	127	10	eur	eur	PROPN
ejpam-4530	127	11	.	.	PUNCT
ejpam-4530	128	1	j.	j.	PROPN
ejpam-4530	128	2	pure	pure	PROPN
ejpam-4530	128	3	appl	appl	PROPN
ejpam-4530	128	4	.	.	PROPN
ejpam-4530	128	5	math	math	PROPN
ejpam-4530	128	6	,	,	PUNCT
ejpam-4530	128	7	15	15	NUM
ejpam-4530	128	8	(	(	PUNCT
ejpam-4530	128	9	4	4	NUM
ejpam-4530	128	10	)	)	PUNCT
ejpam-4530	128	11	(	(	PUNCT
ejpam-4530	128	12	2022	2022	NUM
ejpam-4530	128	13	)	)	PUNCT
ejpam-4530	128	14	,	,	PUNCT
ejpam-4530	128	15	1637	1637	NUM
ejpam-4530	128	16	-	-	SYM
ejpam-4530	128	17	1648	1648	NUM
ejpam-4530	128	18	1641	1641	NUM
ejpam-4530	128	19	remark	remark	NOUN
ejpam-4530	128	20	2.8	2.8	NUM
ejpam-4530	128	21	.	.	PUNCT
ejpam-4530	129	1	the	the	DET
ejpam-4530	129	2	invo	invo	PROPN
ejpam-4530	129	3	-	-	PUNCT
ejpam-4530	129	4	t	t	NOUN
ejpam-4530	129	5	-	-	PUNCT
ejpam-4530	129	6	clean	clean	ADJ
ejpam-4530	129	7	elements	element	NOUN
ejpam-4530	129	8	in	in	ADP
ejpam-4530	129	9	n2(zn	n2(zn	PROPN
ejpam-4530	129	10	)	)	PUNCT
ejpam-4530	129	11	is	be	AUX
ejpam-4530	129	12	either	either	PRON
ejpam-4530	129	13	0	0	NUM
ejpam-4530	129	14	or	or	CCONJ
ejpam-4530	129	15	0	0	NUM
ejpam-4530	129	16	,	,	PUNCT
ejpam-4530	129	17	n2	n2	NOUN
ejpam-4530	129	18	.for	.for	PUNCT
ejpam-4530	129	19	example	example	NOUN
ejpam-4530	129	20	1	1	NUM
ejpam-4530	129	21	.	.	X
ejpam-4530	129	22	for	for	SCONJ
ejpam-4530	129	23	an	an	DET
ejpam-4530	129	24	invo	invo	VERB
ejpam-4530	129	25	-	-	PUNCT
ejpam-4530	129	26	t	t	NOUN
ejpam-4530	129	27	-	-	PUNCT
ejpam-4530	129	28	clean	clean	ADJ
ejpam-4530	129	29	ring	ring	NOUN
ejpam-4530	129	30	take	take	VERB
ejpam-4530	129	31	z12	z12	NUM
ejpam-4530	129	32	,	,	PUNCT
ejpam-4530	129	33	then	then	ADV
ejpam-4530	129	34	every	every	DET
ejpam-4530	129	35	elements	element	NOUN
ejpam-4530	129	36	in	in	ADP
ejpam-4530	129	37	n2(z12	n2(z12	NOUN
ejpam-4530	129	38	)	)	PUNCT
ejpam-4530	130	1	=	=	SYM
ejpam-4530	130	2	0	0	NUM
ejpam-4530	130	3	,	,	PUNCT
ejpam-4530	130	4	6	6	NUM
ejpam-4530	130	5	is	be	AUX
ejpam-4530	130	6	invot	invot	NOUN
ejpam-4530	130	7	-	-	PUNCT
ejpam-4530	130	8	clean	clean	ADJ
ejpam-4530	130	9	where	where	SCONJ
ejpam-4530	130	10	6	6	NUM
ejpam-4530	130	11	=	=	SYM
ejpam-4530	130	12	1	1	NUM
ejpam-4530	130	13	+	+	NUM
ejpam-4530	130	14	5	5	NUM
ejpam-4530	130	15	=	=	SYM
ejpam-4530	130	16	7	7	NUM
ejpam-4530	130	17	+	+	NUM
ejpam-4530	130	18	11	11	NUM
ejpam-4530	130	19	,	,	PUNCT
ejpam-4530	130	20	where	where	SCONJ
ejpam-4530	130	21	invo(z12	invo(z12	NOUN
ejpam-4530	130	22	)	)	PUNCT
ejpam-4530	130	23	=	=	PUNCT
ejpam-4530	131	1	{	{	PUNCT
ejpam-4530	131	2	1	1	NUM
ejpam-4530	131	3	,	,	PUNCT
ejpam-4530	131	4	5	5	NUM
ejpam-4530	131	5	,	,	PUNCT
ejpam-4530	131	6	7	7	NUM
ejpam-4530	131	7	,	,	PUNCT
ejpam-4530	131	8	11	11	NUM
ejpam-4530	131	9	}	}	PUNCT
ejpam-4530	131	10	,	,	PUNCT
ejpam-4530	131	11	tri(z12	tri(z12	NUM
ejpam-4530	131	12	)	)	PUNCT
ejpam-4530	131	13	=	=	PUNCT
ejpam-4530	131	14	{	{	PUNCT
ejpam-4530	131	15	0	0	NUM
ejpam-4530	131	16	,	,	PUNCT
ejpam-4530	131	17	1	1	NUM
ejpam-4530	131	18	,	,	PUNCT
ejpam-4530	131	19	3	3	NUM
ejpam-4530	131	20	,	,	PUNCT
ejpam-4530	131	21	4	4	NUM
ejpam-4530	131	22	,	,	PUNCT
ejpam-4530	131	23	5	5	NUM
ejpam-4530	131	24	,	,	PUNCT
ejpam-4530	131	25	7	7	NUM
ejpam-4530	131	26	,	,	PUNCT
ejpam-4530	131	27	8	8	NUM
ejpam-4530	131	28	,	,	PUNCT
ejpam-4530	131	29	9	9	NUM
ejpam-4530	131	30	,	,	PUNCT
ejpam-4530	131	31	11	11	NUM
ejpam-4530	131	32	}	}	PUNCT
ejpam-4530	131	33	.	.	PUNCT
ejpam-4530	132	1	2	2	X
ejpam-4530	132	2	.	.	X
ejpam-4530	132	3	for	for	ADP
ejpam-4530	132	4	a	a	DET
ejpam-4530	132	5	ring	ring	NOUN
ejpam-4530	132	6	which	which	PRON
ejpam-4530	132	7	is	be	AUX
ejpam-4530	132	8	not	not	PART
ejpam-4530	132	9	invo	invo	ADJ
ejpam-4530	132	10	-	-	PUNCT
ejpam-4530	132	11	t	t	NOUN
ejpam-4530	132	12	-	-	PUNCT
ejpam-4530	132	13	clean	clean	ADJ
ejpam-4530	132	14	take	take	PROPN
ejpam-4530	132	15	z36	z36	PROPN
ejpam-4530	132	16	,	,	PUNCT
ejpam-4530	132	17	n2(z36	n2(z36	NOUN
ejpam-4530	132	18	)	)	PUNCT
ejpam-4530	132	19	=	=	SYM
ejpam-4530	132	20	0	0	NUM
ejpam-4530	132	21	,	,	PUNCT
ejpam-4530	132	22	6	6	NUM
ejpam-4530	132	23	,	,	PUNCT
ejpam-4530	132	24	12	12	NUM
ejpam-4530	132	25	,	,	PUNCT
ejpam-4530	132	26	24	24	NUM
ejpam-4530	132	27	,	,	PUNCT
ejpam-4530	132	28	30	30	NUM
ejpam-4530	132	29	the	the	DET
ejpam-4530	132	30	only	only	ADJ
ejpam-4530	132	31	invo	invo	VERB
ejpam-4530	132	32	-	-	PUNCT
ejpam-4530	132	33	t	t	NOUN
ejpam-4530	132	34	-	-	PUNCT
ejpam-4530	132	35	clean	clean	ADJ
ejpam-4530	132	36	elements	element	NOUN
ejpam-4530	132	37	in	in	ADP
ejpam-4530	132	38	n2(z36	n2(z36	PROPN
ejpam-4530	132	39	)	)	PUNCT
ejpam-4530	132	40	is	be	AUX
ejpam-4530	132	41	0	0	NUM
ejpam-4530	132	42	,	,	PUNCT
ejpam-4530	132	43	18	18	NUM
ejpam-4530	132	44	,	,	PUNCT
ejpam-4530	132	45	18	18	NUM
ejpam-4530	132	46	=	=	SYM
ejpam-4530	132	47	1	1	NUM
ejpam-4530	132	48	+	+	NUM
ejpam-4530	132	49	17	17	NUM
ejpam-4530	132	50	=	=	SYM
ejpam-4530	132	51	19	19	NUM
ejpam-4530	132	52	+	+	NUM
ejpam-4530	132	53	35	35	NUM
ejpam-4530	132	54	,	,	PUNCT
ejpam-4530	132	55	where	where	SCONJ
ejpam-4530	132	56	invo(z36	invo(z36	NOUN
ejpam-4530	132	57	)	)	PUNCT
ejpam-4530	132	58	=	=	SYM
ejpam-4530	132	59	{	{	PUNCT
ejpam-4530	132	60	1	1	NUM
ejpam-4530	132	61	,	,	PUNCT
ejpam-4530	132	62	17	17	NUM
ejpam-4530	132	63	,	,	PUNCT
ejpam-4530	132	64	19	19	NUM
ejpam-4530	132	65	,	,	PUNCT
ejpam-4530	132	66	35	35	NUM
ejpam-4530	132	67	}	}	PUNCT
ejpam-4530	132	68	,	,	PUNCT
ejpam-4530	132	69	tri(z36	tri(z36	NOUN
ejpam-4530	132	70	)	)	PUNCT
ejpam-4530	132	71	=	=	SYM
ejpam-4530	132	72	{	{	PUNCT
ejpam-4530	132	73	0	0	NUM
ejpam-4530	132	74	,	,	PUNCT
ejpam-4530	132	75	1	1	NUM
ejpam-4530	132	76	,	,	PUNCT
ejpam-4530	132	77	8	8	NUM
ejpam-4530	132	78	,	,	PUNCT
ejpam-4530	132	79	9	9	NUM
ejpam-4530	132	80	,	,	PUNCT
ejpam-4530	132	81	17	17	NUM
ejpam-4530	132	82	,	,	PUNCT
ejpam-4530	132	83	19	19	NUM
ejpam-4530	132	84	,	,	PUNCT
ejpam-4530	132	85	27	27	NUM
ejpam-4530	132	86	,	,	PUNCT
ejpam-4530	132	87	28	28	NUM
ejpam-4530	132	88	,	,	PUNCT
ejpam-4530	132	89	35	35	NUM
ejpam-4530	132	90	}	}	PUNCT
ejpam-4530	132	91	.	.	PUNCT
ejpam-4530	133	1	in	in	ADP
ejpam-4530	133	2	noncommutative	noncommutative	ADJ
ejpam-4530	133	3	ring	ring	PROPN
ejpam-4530	133	4	r	r	NOUN
ejpam-4530	133	5	,	,	PUNCT
ejpam-4530	133	6	the	the	DET
ejpam-4530	133	7	invo	invo	PROPN
ejpam-4530	133	8	-	-	PUNCT
ejpam-4530	133	9	t	t	NOUN
ejpam-4530	133	10	-	-	PUNCT
ejpam-4530	133	11	clean	clean	ADJ
ejpam-4530	133	12	elements	element	NOUN
ejpam-4530	133	13	in	in	ADP
ejpam-4530	133	14	n2(r	n2(r	NOUN
ejpam-4530	133	15	)	)	PUNCT
ejpam-4530	133	16	need	need	VERB
ejpam-4530	133	17	not	not	PART
ejpam-4530	133	18	strongly	strongly	ADV
ejpam-4530	133	19	invot	invot	NOUN
ejpam-4530	133	20	-	-	PUNCT
ejpam-4530	133	21	clean	clean	ADJ
ejpam-4530	133	22	elements	element	NOUN
ejpam-4530	133	23	,	,	PUNCT
ejpam-4530	133	24	but	but	CCONJ
ejpam-4530	133	25	it	it	PRON
ejpam-4530	133	26	is	be	AUX
ejpam-4530	133	27	still	still	ADV
ejpam-4530	133	28	satisfies	satisfy	VERB
ejpam-4530	133	29	the	the	DET
ejpam-4530	133	30	proposition	proposition	NOUN
ejpam-4530	133	31	2.7	2.7	NUM
ejpam-4530	133	32	,	,	PUNCT
ejpam-4530	133	33	which	which	PRON
ejpam-4530	133	34	every	every	DET
ejpam-4530	133	35	elements	element	NOUN
ejpam-4530	133	36	in	in	ADP
ejpam-4530	133	37	n2(r	n2(r	PROPN
ejpam-4530	133	38	)	)	PUNCT
ejpam-4530	133	39	is	be	AUX
ejpam-4530	133	40	sum	sum	NOUN
ejpam-4530	133	41	of	of	ADP
ejpam-4530	133	42	two	two	NUM
ejpam-4530	133	43	involution	involution	NOUN
ejpam-4530	133	44	elements	element	NOUN
ejpam-4530	133	45	,	,	PUNCT
ejpam-4530	133	46	for	for	ADP
ejpam-4530	133	47	example	example	NOUN
ejpam-4530	133	48	the	the	DET
ejpam-4530	133	49	ring	ring	NOUN
ejpam-4530	133	50	t2(z3	t2(z3	NOUN
ejpam-4530	133	51	)	)	PUNCT
ejpam-4530	133	52	n2(t2(z3	n2(t2(z3	NOUN
ejpam-4530	133	53	)	)	PUNCT
ejpam-4530	133	54	)	)	PUNCT
ejpam-4530	134	1	=	=	PRON
ejpam-4530	134	2	{	{	PUNCT
ejpam-4530	135	1	[	[	PUNCT
ejpam-4530	135	2	0	0	NUM
ejpam-4530	135	3	0	0	NUM
ejpam-4530	135	4	0	0	NUM
ejpam-4530	135	5	0	0	NUM
ejpam-4530	135	6	]	]	PUNCT
ejpam-4530	135	7	,	,	PUNCT
ejpam-4530	135	8	[	[	PUNCT
ejpam-4530	135	9	0	0	NUM
ejpam-4530	135	10	1	1	NUM
ejpam-4530	135	11	0	0	NUM
ejpam-4530	135	12	0	0	NUM
ejpam-4530	135	13	]	]	PUNCT
ejpam-4530	135	14	,	,	PUNCT
ejpam-4530	135	15	[	[	PUNCT
ejpam-4530	135	16	0	0	NUM
ejpam-4530	135	17	2	2	NUM
ejpam-4530	135	18	0	0	NUM
ejpam-4530	135	19	1	1	NUM
ejpam-4530	135	20	]	]	PUNCT
ejpam-4530	135	21	}	}	PUNCT
ejpam-4530	135	22	where	where	SCONJ
ejpam-4530	135	23	[	[	PUNCT
ejpam-4530	135	24	0	0	NUM
ejpam-4530	135	25	0	0	NUM
ejpam-4530	135	26	0	0	NUM
ejpam-4530	135	27	0	0	NUM
ejpam-4530	135	28	]	]	PUNCT
ejpam-4530	136	1	=	=	PUNCT
ejpam-4530	136	2	[	[	PUNCT
ejpam-4530	136	3	1	1	NUM
ejpam-4530	136	4	0	0	NUM
ejpam-4530	136	5	0	0	NUM
ejpam-4530	136	6	1	1	NUM
ejpam-4530	136	7	]	]	PUNCT
ejpam-4530	137	1	+	+	CCONJ
ejpam-4530	137	2	[	[	PUNCT
ejpam-4530	137	3	2	2	NUM
ejpam-4530	137	4	0	0	NUM
ejpam-4530	137	5	0	0	NUM
ejpam-4530	137	6	2	2	NUM
ejpam-4530	137	7	]	]	PUNCT
ejpam-4530	137	8	,	,	PUNCT
ejpam-4530	137	9	[	[	PUNCT
ejpam-4530	137	10	0	0	NUM
ejpam-4530	137	11	1	1	NUM
ejpam-4530	137	12	0	0	NUM
ejpam-4530	137	13	0	0	NUM
ejpam-4530	137	14	]	]	PUNCT
ejpam-4530	137	15	=[	=[	NOUN
ejpam-4530	137	16	1	1	NUM
ejpam-4530	137	17	1	1	NUM
ejpam-4530	137	18	0	0	NUM
ejpam-4530	137	19	2	2	NUM
ejpam-4530	137	20	]	]	PUNCT
ejpam-4530	138	1	+	+	CCONJ
ejpam-4530	138	2	[	[	PUNCT
ejpam-4530	138	3	2	2	NUM
ejpam-4530	138	4	0	0	NUM
ejpam-4530	138	5	0	0	NUM
ejpam-4530	138	6	1	1	NUM
ejpam-4530	138	7	]	]	PUNCT
ejpam-4530	138	8	,	,	PUNCT
ejpam-4530	138	9	[	[	PUNCT
ejpam-4530	138	10	0	0	NUM
ejpam-4530	138	11	2	2	NUM
ejpam-4530	138	12	0	0	NUM
ejpam-4530	138	13	0	0	NUM
ejpam-4530	138	14	]	]	PUNCT
ejpam-4530	139	1	=	=	PUNCT
ejpam-4530	139	2	[	[	PUNCT
ejpam-4530	139	3	1	1	NUM
ejpam-4530	139	4	2	2	NUM
ejpam-4530	139	5	0	0	NUM
ejpam-4530	139	6	2	2	NUM
ejpam-4530	139	7	]	]	PUNCT
ejpam-4530	140	1	+	+	CCONJ
ejpam-4530	140	2	[	[	PUNCT
ejpam-4530	140	3	2	2	NUM
ejpam-4530	140	4	0	0	NUM
ejpam-4530	140	5	0	0	NUM
ejpam-4530	140	6	1	1	NUM
ejpam-4530	140	7	]	]	PUNCT
ejpam-4530	140	8	.	.	PUNCT
ejpam-4530	141	1	proposition	proposition	NOUN
ejpam-4530	141	2	2.9	2.9	NUM
ejpam-4530	141	3	.	.	PUNCT
ejpam-4530	142	1	let	let	VERB
ejpam-4530	142	2	a	a	PRON
ejpam-4530	142	3	is	be	AUX
ejpam-4530	142	4	a	a	DET
ejpam-4530	142	5	strongly	strongly	ADV
ejpam-4530	142	6	invo	invo	VERB
ejpam-4530	142	7	-	-	PUNCT
ejpam-4530	142	8	t	t	NOUN
ejpam-4530	142	9	-	-	PUNCT
ejpam-4530	142	10	clean	clean	ADJ
ejpam-4530	142	11	element	element	NOUN
ejpam-4530	142	12	in	in	ADP
ejpam-4530	142	13	r.	r.	PROPN
ejpam-4530	142	14	then	then	ADV
ejpam-4530	142	15	1	1	X
ejpam-4530	142	16	.	.	X
ejpam-4530	142	17	−a	−a	NOUN
ejpam-4530	142	18	is	be	AUX
ejpam-4530	142	19	strongly	strongly	ADV
ejpam-4530	142	20	invo	invo	ADJ
ejpam-4530	142	21	-	-	PUNCT
ejpam-4530	142	22	t	t	NOUN
ejpam-4530	142	23	-	-	PUNCT
ejpam-4530	142	24	clean	clean	ADJ
ejpam-4530	142	25	element	element	NOUN
ejpam-4530	142	26	.	.	PUNCT
ejpam-4530	143	1	2	2	X
ejpam-4530	143	2	.	.	X
ejpam-4530	143	3	au	au	PROPN
ejpam-4530	143	4	is	be	AUX
ejpam-4530	143	5	strongly	strongly	ADV
ejpam-4530	143	6	invo	invo	VERB
ejpam-4530	143	7	-	-	PUNCT
ejpam-4530	143	8	t	t	NOUN
ejpam-4530	143	9	-	-	PUNCT
ejpam-4530	143	10	clean	clean	ADJ
ejpam-4530	143	11	element	element	NOUN
ejpam-4530	143	12	.	.	PUNCT
ejpam-4530	144	1	3	3	X
ejpam-4530	144	2	.	.	X
ejpam-4530	145	1	at	at	ADP
ejpam-4530	145	2	is	be	AUX
ejpam-4530	145	3	a	a	DET
ejpam-4530	145	4	sum	sum	NOUN
ejpam-4530	145	5	of	of	ADP
ejpam-4530	145	6	idempotent	idempotent	NOUN
ejpam-4530	145	7	and	and	CCONJ
ejpam-4530	145	8	tripotent	tripotent	ADJ
ejpam-4530	145	9	elements	element	NOUN
ejpam-4530	145	10	.	.	PUNCT
ejpam-4530	146	1	4	4	X
ejpam-4530	146	2	.	.	X
ejpam-4530	146	3	if	if	SCONJ
ejpam-4530	146	4	2	2	NUM
ejpam-4530	146	5	is	be	AUX
ejpam-4530	146	6	invertible	invertible	ADJ
ejpam-4530	146	7	.	.	PUNCT
ejpam-4530	147	1	then	then	ADV
ejpam-4530	147	2	a2	a2	PROPN
ejpam-4530	147	3	−	−	PROPN
ejpam-4530	147	4	1	1	NUM
ejpam-4530	147	5	is	be	AUX
ejpam-4530	147	6	r	r	NOUN
ejpam-4530	147	7	-	-	PUNCT
ejpam-4530	147	8	clean	clean	ADJ
ejpam-4530	147	9	element	element	NOUN
ejpam-4530	147	10	.	.	PUNCT
ejpam-4530	148	1	5	5	X
ejpam-4530	148	2	.	.	X
ejpam-4530	148	3	if	if	SCONJ
ejpam-4530	148	4	char(r	char(r	NOUN
ejpam-4530	148	5	)	)	PUNCT
ejpam-4530	148	6	=	=	SYM
ejpam-4530	149	1	4	4	X
ejpam-4530	149	2	.	.	PUNCT
ejpam-4530	149	3	then	then	ADV
ejpam-4530	149	4	a	a	PRON
ejpam-4530	149	5	=	=	PUNCT
ejpam-4530	149	6	(	(	PUNCT
ejpam-4530	149	7	u−	u−	PROPN
ejpam-4530	149	8	2	2	NUM
ejpam-4530	149	9	t	t	NOUN
ejpam-4530	149	10	)	)	PUNCT
ejpam-4530	149	11	+	+	CCONJ
ejpam-4530	149	12	3	3	NUM
ejpam-4530	149	13	t	t	NOUN
ejpam-4530	149	14	,	,	PUNCT
ejpam-4530	149	15	u−	u−	PROPN
ejpam-4530	149	16	2	2	NUM
ejpam-4530	149	17	t	t	NOUN
ejpam-4530	149	18	∈	∈	PROPN
ejpam-4530	149	19	invo(r	invo(r	NOUN
ejpam-4530	149	20	)	)	PUNCT
ejpam-4530	149	21	and	and	CCONJ
ejpam-4530	149	22	3	3	NUM
ejpam-4530	149	23	t	t	NOUN
ejpam-4530	149	24	∈	∈	PROPN
ejpam-4530	149	25	tri(r	tri(r	PROPN
ejpam-4530	149	26	)	)	PUNCT
ejpam-4530	149	27	.	.	PUNCT
ejpam-4530	150	1	6	6	X
ejpam-4530	150	2	.	.	X
ejpam-4530	150	3	if	if	SCONJ
ejpam-4530	150	4	char(r	char(r	NOUN
ejpam-4530	150	5	)	)	PUNCT
ejpam-4530	150	6	=	=	SYM
ejpam-4530	151	1	6	6	X
ejpam-4530	151	2	.	.	PUNCT
ejpam-4530	151	3	then	then	ADV
ejpam-4530	151	4	a2	a2	PROPN
ejpam-4530	151	5	∈	∈	PROPN
ejpam-4530	151	6	idm(r	idm(r	PROPN
ejpam-4530	151	7	)	)	PUNCT
ejpam-4530	151	8	.	.	PUNCT
ejpam-4530	152	1	proof	proof	NOUN
ejpam-4530	152	2	.	.	PUNCT
ejpam-4530	153	1	(	(	PUNCT
ejpam-4530	153	2	1	1	NUM
ejpam-4530	153	3	)	)	PUNCT
ejpam-4530	153	4	,	,	PUNCT
ejpam-4530	153	5	(	(	PUNCT
ejpam-4530	153	6	2	2	X
ejpam-4530	153	7	)	)	PUNCT
ejpam-4530	153	8	and	and	CCONJ
ejpam-4530	153	9	(	(	PUNCT
ejpam-4530	153	10	3	3	X
ejpam-4530	153	11	)	)	PUNCT
ejpam-4530	153	12	is	be	AUX
ejpam-4530	153	13	clearly	clearly	ADV
ejpam-4530	153	14	.	.	PUNCT
ejpam-4530	154	1	(	(	PUNCT
ejpam-4530	154	2	4	4	NUM
ejpam-4530	154	3	)	)	PUNCT
ejpam-4530	154	4	since	since	SCONJ
ejpam-4530	154	5	a	a	PRON
ejpam-4530	154	6	is	be	AUX
ejpam-4530	154	7	strongly	strongly	ADV
ejpam-4530	154	8	invo	invo	VERB
ejpam-4530	154	9	-	-	PUNCT
ejpam-4530	154	10	t	t	NOUN
ejpam-4530	154	11	-	-	PUNCT
ejpam-4530	154	12	clean	clean	ADJ
ejpam-4530	154	13	element	element	NOUN
ejpam-4530	154	14	,	,	PUNCT
ejpam-4530	154	15	then	then	ADV
ejpam-4530	154	16	there	there	PRON
ejpam-4530	154	17	exists	exist	VERB
ejpam-4530	154	18	u	u	PROPN
ejpam-4530	154	19	∈	∈	PROPN
ejpam-4530	154	20	invo(r	invo(r	NOUN
ejpam-4530	154	21	)	)	PUNCT
ejpam-4530	154	22	and	and	CCONJ
ejpam-4530	154	23	t	t	PROPN
ejpam-4530	154	24	∈	∈	PROPN
ejpam-4530	154	25	tri(r	tri(r	PROPN
ejpam-4530	154	26	)	)	PUNCT
ejpam-4530	155	1	such	such	ADJ
ejpam-4530	155	2	that	that	SCONJ
ejpam-4530	155	3	a	a	DET
ejpam-4530	155	4	=	=	PUNCT
ejpam-4530	155	5	u+	u+	NOUN
ejpam-4530	155	6	t	t	PROPN
ejpam-4530	155	7	and	and	CCONJ
ejpam-4530	155	8	ut	ut	PROPN
ejpam-4530	155	9	=	=	PROPN
ejpam-4530	155	10	tu	tu	PROPN
ejpam-4530	155	11	,	,	PUNCT
ejpam-4530	155	12	a2	a2	PROPN
ejpam-4530	155	13	−	−	PROPN
ejpam-4530	155	14	1	1	NUM
ejpam-4530	155	15	=	=	SYM
ejpam-4530	155	16	(	(	PUNCT
ejpam-4530	155	17	u+	u+	NOUN
ejpam-4530	155	18	t)2	t)2	PROPN
ejpam-4530	155	19	−	−	PROPN
ejpam-4530	155	20	1	1	NUM
ejpam-4530	155	21	=	=	SYM
ejpam-4530	155	22	1	1	NUM
ejpam-4530	155	23	+	+	NUM
ejpam-4530	155	24	2ut+	2ut+	NUM
ejpam-4530	155	25	t2	t2	NOUN
ejpam-4530	155	26	−	−	NOUN
ejpam-4530	155	27	1	1	NUM
ejpam-4530	155	28	=	=	SYM
ejpam-4530	155	29	2ut+	2ut+	NUM
ejpam-4530	155	30	t2	t2	NOUN
ejpam-4530	155	31	.	.	PUNCT
ejpam-4530	156	1	for	for	ADP
ejpam-4530	156	2	proving	prove	VERB
ejpam-4530	156	3	2ut	2ut	NOUN
ejpam-4530	156	4	is	be	AUX
ejpam-4530	156	5	regular	regular	ADJ
ejpam-4530	156	6	.	.	PUNCT
ejpam-4530	157	1	set	set	PROPN
ejpam-4530	157	2	b	b	NOUN
ejpam-4530	157	3	=	=	NOUN
ejpam-4530	157	4	ut2−1	ut2−1	NOUN
ejpam-4530	157	5	,	,	PUNCT
ejpam-4530	157	6	(	(	PUNCT
ejpam-4530	157	7	2ut)b(2ut	2ut)b(2ut	NUM
ejpam-4530	157	8	)	)	PUNCT
ejpam-4530	157	9	=	=	PUNCT
ejpam-4530	157	10	(	(	PUNCT
ejpam-4530	157	11	2ut)(ut2−1)(2ut	2ut)(ut2−1)(2ut	NUM
ejpam-4530	157	12	)	)	PUNCT
ejpam-4530	157	13	=	=	SYM
ejpam-4530	158	1	2ututut	2ututut	NUM
ejpam-4530	158	2	=	=	SYM
ejpam-4530	158	3	2ut	2ut	NOUN
ejpam-4530	158	4	.	.	PUNCT
ejpam-4530	159	1	therefore	therefore	ADV
ejpam-4530	159	2	,	,	PUNCT
ejpam-4530	159	3	a2−1	a2−1	PRON
ejpam-4530	159	4	is	be	AUX
ejpam-4530	159	5	a	a	DET
ejpam-4530	159	6	r	r	NOUN
ejpam-4530	159	7	-	-	PUNCT
ejpam-4530	159	8	clean	clean	ADJ
ejpam-4530	159	9	element	element	NOUN
ejpam-4530	159	10	.	.	PUNCT
ejpam-4530	160	1	(	(	PUNCT
ejpam-4530	160	2	5	5	NUM
ejpam-4530	160	3	)	)	PUNCT
ejpam-4530	160	4	since	since	SCONJ
ejpam-4530	160	5	a	a	DET
ejpam-4530	160	6	=	=	SYM
ejpam-4530	160	7	u	u	NOUN
ejpam-4530	160	8	+	+	NOUN
ejpam-4530	160	9	t	t	NOUN
ejpam-4530	160	10	=	=	SYM
ejpam-4530	160	11	(	(	PUNCT
ejpam-4530	160	12	u	u	NOUN
ejpam-4530	160	13	−	−	PROPN
ejpam-4530	160	14	2	2	NUM
ejpam-4530	160	15	t	t	NOUN
ejpam-4530	160	16	)	)	PUNCT
ejpam-4530	160	17	+	+	CCONJ
ejpam-4530	160	18	3	3	NUM
ejpam-4530	160	19	t	t	NOUN
ejpam-4530	160	20	,	,	PUNCT
ejpam-4530	160	21	(	(	PUNCT
ejpam-4530	160	22	u	u	NOUN
ejpam-4530	161	1	−	−	NOUN
ejpam-4530	161	2	2t)2	2t)2	NUM
ejpam-4530	161	3	=	=	SYM
ejpam-4530	161	4	u2	u2	PROPN
ejpam-4530	161	5	−	−	PROPN
ejpam-4530	161	6	4ut	4ut	NOUN
ejpam-4530	162	1	+	+	CCONJ
ejpam-4530	162	2	4t2	4t2	NUM
ejpam-4530	162	3	=	=	SYM
ejpam-4530	162	4	1	1	NUM
ejpam-4530	162	5	,	,	PUNCT
ejpam-4530	162	6	u	u	NOUN
ejpam-4530	162	7	−	−	PROPN
ejpam-4530	162	8	2	2	NUM
ejpam-4530	162	9	t	t	NOUN
ejpam-4530	162	10	∈	∈	PROPN
ejpam-4530	162	11	invo(r	invo(r	NOUN
ejpam-4530	162	12	)	)	PUNCT
ejpam-4530	162	13	,	,	PUNCT
ejpam-4530	162	14	(	(	PUNCT
ejpam-4530	162	15	3t)3	3t)3	NUM
ejpam-4530	162	16	=	=	SYM
ejpam-4530	163	1	27t3	27t3	NUM
ejpam-4530	163	2	=	=	SYM
ejpam-4530	163	3	3	3	NUM
ejpam-4530	163	4	t	t	NOUN
ejpam-4530	163	5	∈	∈	PROPN
ejpam-4530	163	6	tri(r	tri(r	PROPN
ejpam-4530	163	7	)	)	PUNCT
ejpam-4530	163	8	.	.	PUNCT
ejpam-4530	164	1	(	(	PUNCT
ejpam-4530	164	2	6	6	NUM
ejpam-4530	164	3	)	)	PUNCT
ejpam-4530	164	4	since	since	SCONJ
ejpam-4530	164	5	a	a	DET
ejpam-4530	164	6	=	=	SYM
ejpam-4530	164	7	u	u	PROPN
ejpam-4530	164	8	+	+	PROPN
ejpam-4530	164	9	t	t	PROPN
ejpam-4530	164	10	,	,	PUNCT
ejpam-4530	164	11	a	a	DET
ejpam-4530	164	12	−	−	PROPN
ejpam-4530	164	13	t	t	NOUN
ejpam-4530	164	14	=	=	SYM
ejpam-4530	164	15	u	u	PROPN
ejpam-4530	164	16	,	,	PUNCT
ejpam-4530	164	17	(	(	PUNCT
ejpam-4530	164	18	a	a	DET
ejpam-4530	164	19	−	−	NOUN
ejpam-4530	164	20	t)2	t)2	NOUN
ejpam-4530	164	21	=	=	PROPN
ejpam-4530	164	22	u2	u2	NOUN
ejpam-4530	164	23	=	=	SYM
ejpam-4530	164	24	1	1	NUM
ejpam-4530	164	25	,	,	PUNCT
ejpam-4530	164	26	a2	a2	NOUN
ejpam-4530	164	27	−	−	PROPN
ejpam-4530	164	28	2at	2at	NOUN
ejpam-4530	164	29	+	+	CCONJ
ejpam-4530	164	30	t2	t2	NOUN
ejpam-4530	164	31	=	=	SYM
ejpam-4530	164	32	1	1	NUM
ejpam-4530	164	33	,	,	PUNCT
ejpam-4530	164	34	multiply	multiply	ADV
ejpam-4530	164	35	by	by	ADP
ejpam-4530	164	36	t	t	PROPN
ejpam-4530	164	37	,	,	PUNCT
ejpam-4530	164	38	a2	a2	PROPN
ejpam-4530	164	39	t	t	PROPN
ejpam-4530	164	40	−	−	NOUN
ejpam-4530	164	41	2at2	2at2	NUM
ejpam-4530	164	42	+	+	CCONJ
ejpam-4530	164	43	t3	t3	PROPN
ejpam-4530	164	44	=	=	SYM
ejpam-4530	164	45	t	t	PROPN
ejpam-4530	164	46	,	,	PUNCT
ejpam-4530	164	47	a2	a2	PROPN
ejpam-4530	164	48	t	t	NOUN
ejpam-4530	164	49	=	=	PUNCT
ejpam-4530	164	50	2at2	2at2	NUM
ejpam-4530	164	51	multiply	multiply	ADV
ejpam-4530	164	52	by	by	ADP
ejpam-4530	164	53	t	t	PROPN
ejpam-4530	164	54	,	,	PUNCT
ejpam-4530	164	55	a2t2	a2t2	PROPN
ejpam-4530	164	56	=	=	SYM
ejpam-4530	164	57	2at	2at	NOUN
ejpam-4530	164	58	,	,	PUNCT
ejpam-4530	164	59	a2	a2	PROPN
ejpam-4530	164	60	−	−	PROPN
ejpam-4530	164	61	2at	2at	NOUN
ejpam-4530	164	62	=	=	NOUN
ejpam-4530	164	63	1	1	NUM
ejpam-4530	164	64	−	−	PROPN
ejpam-4530	164	65	t2	t2	NOUN
ejpam-4530	164	66	,	,	PUNCT
ejpam-4530	164	67	(	(	PUNCT
ejpam-4530	164	68	a2	a2	PROPN
ejpam-4530	164	69	−	−	PROPN
ejpam-4530	164	70	2at)2	2at)2	NUM
ejpam-4530	164	71	=	=	SYM
ejpam-4530	164	72	(	(	PUNCT
ejpam-4530	164	73	1	1	NUM
ejpam-4530	164	74	−	−	NOUN
ejpam-4530	164	75	t2)2	t2)2	ADP
ejpam-4530	164	76	,	,	PUNCT
ejpam-4530	164	77	a4	a4	NOUN
ejpam-4530	164	78	−	−	NOUN
ejpam-4530	164	79	4a3	4a3	NUM
ejpam-4530	164	80	t	t	NOUN
ejpam-4530	164	81	+	+	NOUN
ejpam-4530	164	82	4a2t2	4a2t2	NOUN
ejpam-4530	164	83	=	=	SYM
ejpam-4530	164	84	1	1	NUM
ejpam-4530	164	85	−	−	PROPN
ejpam-4530	164	86	t2	t2	NOUN
ejpam-4530	164	87	,	,	PUNCT
ejpam-4530	164	88	a4	a4	NOUN
ejpam-4530	164	89	−	−	PROPN
ejpam-4530	164	90	4a(t(a)2t2	4a(t(a)2t2	NUM
ejpam-4530	164	91	)	)	PUNCT
ejpam-4530	165	1	+	+	NUM
ejpam-4530	165	2	4a2t2	4a2t2	NUM
ejpam-4530	165	3	=	=	SYM
ejpam-4530	166	1	1	1	NUM
ejpam-4530	166	2	−	−	PROPN
ejpam-4530	166	3	t2	t2	NOUN
ejpam-4530	166	4	,	,	PUNCT
ejpam-4530	166	5	a4	a4	NOUN
ejpam-4530	166	6	−	−	PROPN
ejpam-4530	166	7	4at(2at	4at(2at	NUM
ejpam-4530	166	8	)	)	PUNCT
ejpam-4530	167	1	+	+	CCONJ
ejpam-4530	167	2	4(2at	4(2at	X
ejpam-4530	167	3	)	)	PUNCT
ejpam-4530	167	4	=	=	SYM
ejpam-4530	167	5	1	1	NUM
ejpam-4530	167	6	−	−	PROPN
ejpam-4530	167	7	t2	t2	NOUN
ejpam-4530	167	8	,	,	PUNCT
ejpam-4530	167	9	a4	a4	NOUN
ejpam-4530	167	10	−	−	NOUN
ejpam-4530	167	11	8a2t2	8a2t2	NUM
ejpam-4530	168	1	+	+	CCONJ
ejpam-4530	168	2	8at	8at	ADJ
ejpam-4530	168	3	=	=	SYM
ejpam-4530	168	4	1	1	NUM
ejpam-4530	168	5	−	−	NOUN
ejpam-4530	168	6	t2	t2	NOUN
ejpam-4530	168	7	,	,	PUNCT
ejpam-4530	168	8	a4	a4	NOUN
ejpam-4530	168	9	−	−	PROPN
ejpam-4530	168	10	16at	16at	NOUN
ejpam-4530	168	11	+	+	CCONJ
ejpam-4530	168	12	8at	8at	ADJ
ejpam-4530	168	13	=	=	SYM
ejpam-4530	168	14	a2	a2	PROPN
ejpam-4530	168	15	−	−	PROPN
ejpam-4530	168	16	2at	2at	NOUN
ejpam-4530	168	17	,	,	PUNCT
ejpam-4530	168	18	a4	a4	NOUN
ejpam-4530	168	19	−	−	PRON
ejpam-4530	168	20	6at	6at	NOUN
ejpam-4530	168	21	=	=	SYM
ejpam-4530	168	22	a2	a2	PROPN
ejpam-4530	168	23	,	,	PUNCT
ejpam-4530	168	24	soa4	soa4	NOUN
ejpam-4530	168	25	=	=	SYM
ejpam-4530	168	26	a2	a2	PROPN
ejpam-4530	168	27	.	.	PUNCT
ejpam-4530	169	1	■	■	PUNCT
ejpam-4530	169	2	mohammed	mohammed	PROPN
ejpam-4530	169	3	al	al	PROPN
ejpam-4530	169	4	-	-	PUNCT
ejpam-4530	169	5	neima	neima	PROPN
ejpam-4530	169	6	et	et	PROPN
ejpam-4530	169	7	al	al	PROPN
ejpam-4530	169	8	.	.	PUNCT
ejpam-4530	169	9	/	/	SYM
ejpam-4530	169	10	eur	eur	PROPN
ejpam-4530	169	11	.	.	PUNCT
ejpam-4530	170	1	j.	j.	PROPN
ejpam-4530	170	2	pure	pure	PROPN
ejpam-4530	170	3	appl	appl	PROPN
ejpam-4530	170	4	.	.	PROPN
ejpam-4530	170	5	math	math	PROPN
ejpam-4530	170	6	,	,	PUNCT
ejpam-4530	170	7	15	15	NUM
ejpam-4530	170	8	(	(	PUNCT
ejpam-4530	170	9	4	4	NUM
ejpam-4530	170	10	)	)	PUNCT
ejpam-4530	170	11	(	(	PUNCT
ejpam-4530	170	12	2022	2022	NUM
ejpam-4530	170	13	)	)	PUNCT
ejpam-4530	170	14	,	,	PUNCT
ejpam-4530	170	15	1637	1637	NUM
ejpam-4530	170	16	-	-	SYM
ejpam-4530	170	17	1648	1648	NUM
ejpam-4530	170	18	1642	1642	NUM
ejpam-4530	170	19	proposition	proposition	NOUN
ejpam-4530	170	20	2.10	2.10	NUM
ejpam-4530	170	21	.	.	PUNCT
ejpam-4530	171	1	if	if	SCONJ
ejpam-4530	171	2	r	r	NOUN
ejpam-4530	171	3	is	be	AUX
ejpam-4530	171	4	a	a	DET
ejpam-4530	171	5	ring	ring	NOUN
ejpam-4530	171	6	with	with	ADP
ejpam-4530	171	7	j(r	j(r	PROPN
ejpam-4530	171	8	)	)	PUNCT
ejpam-4530	171	9	is	be	AUX
ejpam-4530	171	10	strongly	strongly	ADV
ejpam-4530	171	11	invo	invo	ADJ
ejpam-4530	171	12	-	-	PUNCT
ejpam-4530	171	13	t	t	NOUN
ejpam-4530	171	14	-	-	PUNCT
ejpam-4530	171	15	clean	clean	ADJ
ejpam-4530	171	16	.	.	PUNCT
ejpam-4530	172	1	then	then	ADV
ejpam-4530	172	2	j(r	j(r	PROPN
ejpam-4530	172	3	)	)	PUNCT
ejpam-4530	172	4	is	be	AUX
ejpam-4530	172	5	nil	nil	NOUN
ejpam-4530	172	6	with	with	ADP
ejpam-4530	172	7	index	index	NOUN
ejpam-4530	172	8	of	of	ADP
ejpam-4530	172	9	nilpotent	nilpotent	NOUN
ejpam-4530	172	10	at	at	ADP
ejpam-4530	172	11	most	most	ADJ
ejpam-4530	172	12	3	3	NUM
ejpam-4530	172	13	,	,	PUNCT
ejpam-4530	172	14	and	and	CCONJ
ejpam-4530	172	15	char(j(r	char(j(r	PROPN
ejpam-4530	172	16	)	)	PUNCT
ejpam-4530	172	17	)	)	PUNCT
ejpam-4530	173	1	=	=	PUNCT
ejpam-4530	173	2	4	4	X
ejpam-4530	173	3	.	.	X
ejpam-4530	173	4	proof	proof	NOUN
ejpam-4530	173	5	.	.	PUNCT
ejpam-4530	174	1	let	let	VERB
ejpam-4530	174	2	a	a	DET
ejpam-4530	174	3	∈	∈	PROPN
ejpam-4530	174	4	j(r	j(r	PROPN
ejpam-4530	174	5	)	)	PUNCT
ejpam-4530	174	6	,	,	PUNCT
ejpam-4530	174	7	since	since	SCONJ
ejpam-4530	174	8	j(r	j(r	PROPN
ejpam-4530	174	9	)	)	PUNCT
ejpam-4530	174	10	is	be	AUX
ejpam-4530	174	11	strongly	strongly	ADV
ejpam-4530	174	12	invo	invo	ADJ
ejpam-4530	174	13	-	-	PUNCT
ejpam-4530	174	14	t	t	NOUN
ejpam-4530	174	15	-	-	PUNCT
ejpam-4530	174	16	clean	clean	ADJ
ejpam-4530	174	17	,	,	PUNCT
ejpam-4530	174	18	then	then	ADV
ejpam-4530	174	19	there	there	PRON
ejpam-4530	174	20	exists	exist	VERB
ejpam-4530	174	21	u	u	PROPN
ejpam-4530	174	22	∈	∈	PROPN
ejpam-4530	174	23	invo(r	invo(r	NOUN
ejpam-4530	174	24	)	)	PUNCT
ejpam-4530	174	25	and	and	CCONJ
ejpam-4530	174	26	t	t	PROPN
ejpam-4530	174	27	∈	∈	PROPN
ejpam-4530	174	28	tri(r	tri(r	PROPN
ejpam-4530	174	29	)	)	PUNCT
ejpam-4530	175	1	such	such	ADJ
ejpam-4530	175	2	that	that	SCONJ
ejpam-4530	175	3	a	a	DET
ejpam-4530	175	4	=	=	SYM
ejpam-4530	175	5	u	u	NOUN
ejpam-4530	175	6	+	+	PROPN
ejpam-4530	175	7	t	t	PROPN
ejpam-4530	175	8	,	,	PUNCT
ejpam-4530	175	9	−u	−u	PRON
ejpam-4530	175	10	+	+	CCONJ
ejpam-4530	175	11	a	a	DET
ejpam-4530	175	12	=	=	SYM
ejpam-4530	175	13	t	t	PROPN
ejpam-4530	175	14	∈	∈	PROPN
ejpam-4530	175	15	u(r	u(r	PROPN
ejpam-4530	175	16	)	)	PUNCT
ejpam-4530	176	1	+	+	CCONJ
ejpam-4530	176	2	j(r	j(r	NOUN
ejpam-4530	176	3	)	)	PUNCT
ejpam-4530	176	4	=	=	SYM
ejpam-4530	176	5	u(r	u(r	NOUN
ejpam-4530	176	6	)	)	PUNCT
ejpam-4530	176	7	,	,	PUNCT
ejpam-4530	176	8	so	so	SCONJ
ejpam-4530	176	9	t	t	PROPN
ejpam-4530	176	10	∈	∈	PROPN
ejpam-4530	176	11	u(r	u(r	PROPN
ejpam-4530	176	12	)	)	PUNCT
ejpam-4530	176	13	∩	∩	NOUN
ejpam-4530	176	14	j(r	j(r	NOUN
ejpam-4530	176	15	)	)	PUNCT
ejpam-4530	177	1	=	=	SYM
ejpam-4530	177	2	u2(r	u2(r	X
ejpam-4530	177	3	)	)	PUNCT
ejpam-4530	177	4	,	,	PUNCT
ejpam-4530	177	5	t2	t2	NOUN
ejpam-4530	177	6	=	=	SYM
ejpam-4530	177	7	1	1	X
ejpam-4530	177	8	.	.	PUNCT
ejpam-4530	177	9	now	now	ADV
ejpam-4530	177	10	a2	a2	PROPN
ejpam-4530	177	11	=	=	SYM
ejpam-4530	177	12	(	(	PUNCT
ejpam-4530	177	13	u+	u+	NUM
ejpam-4530	177	14	t)2	t)2	PROPN
ejpam-4530	177	15	=	=	PROPN
ejpam-4530	177	16	2	2	NUM
ejpam-4530	177	17	+	+	NOUN
ejpam-4530	177	18	2ut	2ut	NOUN
ejpam-4530	177	19	=	=	SYM
ejpam-4530	177	20	2u(u+	2u(u+	PROPN
ejpam-4530	177	21	t	t	PROPN
ejpam-4530	177	22	)	)	PUNCT
ejpam-4530	177	23	=	=	SYM
ejpam-4530	177	24	2ua	2ua	NOUN
ejpam-4530	177	25	,	,	PUNCT
ejpam-4530	177	26	multiply	multiply	NOUN
ejpam-4530	177	27	a2	a2	PROPN
ejpam-4530	177	28	=	=	SYM
ejpam-4530	177	29	2ua	2ua	NOUN
ejpam-4530	177	30	both	both	DET
ejpam-4530	177	31	side	side	NOUN
ejpam-4530	177	32	by	by	ADP
ejpam-4530	177	33	a	a	DET
ejpam-4530	177	34	,	,	PUNCT
ejpam-4530	177	35	a3	a3	NOUN
ejpam-4530	177	36	=	=	SYM
ejpam-4530	177	37	2ua2	2ua2	NUM
ejpam-4530	177	38	=	=	SYM
ejpam-4530	177	39	2u(2ua	2u(2ua	X
ejpam-4530	177	40	)	)	PUNCT
ejpam-4530	177	41	=	=	SYM
ejpam-4530	177	42	4a	4a	NOUN
ejpam-4530	177	43	,	,	PUNCT
ejpam-4530	177	44	replacing	replace	VERB
ejpam-4530	177	45	a	a	PRON
ejpam-4530	177	46	by	by	ADP
ejpam-4530	177	47	2a	2a	NUM
ejpam-4530	177	48	,	,	PUNCT
ejpam-4530	177	49	(	(	PUNCT
ejpam-4530	177	50	8a)3	8a)3	NUM
ejpam-4530	177	51	=	=	SYM
ejpam-4530	177	52	8a	8a	NUM
ejpam-4530	177	53	,	,	PUNCT
ejpam-4530	177	54	8a(1−	8a(1−	NUM
ejpam-4530	177	55	a2	a2	NOUN
ejpam-4530	177	56	)	)	PUNCT
ejpam-4530	177	57	=	=	SYM
ejpam-4530	177	58	0	0	NUM
ejpam-4530	177	59	,	,	PUNCT
ejpam-4530	177	60	since	since	SCONJ
ejpam-4530	177	61	a	a	DET
ejpam-4530	177	62	∈	∈	PROPN
ejpam-4530	177	63	j(r	j(r	PROPN
ejpam-4530	177	64	)	)	PUNCT
ejpam-4530	177	65	,	,	PUNCT
ejpam-4530	177	66	1−a2	1−a2	NUM
ejpam-4530	177	67	∈	∈	PROPN
ejpam-4530	177	68	u(r	u(r	NOUN
ejpam-4530	177	69	)	)	PUNCT
ejpam-4530	177	70	,	,	PUNCT
ejpam-4530	177	71	get	get	VERB
ejpam-4530	177	72	that	that	PRON
ejpam-4530	177	73	8a	8a	NUM
ejpam-4530	177	74	=	=	SYM
ejpam-4530	177	75	0	0	PROPN
ejpam-4530	177	76	.	.	PUNCT
ejpam-4530	177	77	for	for	ADP
ejpam-4530	177	78	a2	a2	PROPN
ejpam-4530	177	79	=	=	SYM
ejpam-4530	177	80	2ua	2ua	PROPN
ejpam-4530	177	81	replacing	replace	VERB
ejpam-4530	177	82	a	a	PRON
ejpam-4530	177	83	by	by	ADP
ejpam-4530	177	84	2a	2a	NUM
ejpam-4530	177	85	,	,	PUNCT
ejpam-4530	177	86	4a2	4a2	NUM
ejpam-4530	177	87	=	=	SYM
ejpam-4530	177	88	4ua	4ua	NOUN
ejpam-4530	177	89	.	.	PUNCT
ejpam-4530	178	1	by	by	ADP
ejpam-4530	178	2	multiply	multiply	PROPN
ejpam-4530	178	3	a2	a2	PROPN
ejpam-4530	178	4	=	=	PUNCT
ejpam-4530	178	5	2ua	2ua	NOUN
ejpam-4530	178	6	by	by	ADP
ejpam-4530	178	7	4	4	NUM
ejpam-4530	178	8	get	get	NOUN
ejpam-4530	178	9	(	(	PUNCT
ejpam-4530	178	10	4a)2	4a)2	NOUN
ejpam-4530	178	11	=	=	SYM
ejpam-4530	178	12	8ua	8ua	PROPN
ejpam-4530	178	13	.	.	PUNCT
ejpam-4530	179	1	so	so	ADV
ejpam-4530	179	2	8ua	8ua	PROPN
ejpam-4530	179	3	=	=	SYM
ejpam-4530	179	4	4ua	4ua	ADJ
ejpam-4530	179	5	,	,	PUNCT
ejpam-4530	179	6	4ua	4ua	ADJ
ejpam-4530	179	7	=	=	SYM
ejpam-4530	179	8	0	0	NUM
ejpam-4530	179	9	,	,	PUNCT
ejpam-4530	179	10	4a	4a	NOUN
ejpam-4530	179	11	=	=	SYM
ejpam-4530	179	12	0	0	PROPN
ejpam-4530	179	13	.	.	PUNCT
ejpam-4530	179	14	a3	a3	NOUN
ejpam-4530	179	15	=	=	SYM
ejpam-4530	179	16	4a	4a	X
ejpam-4530	179	17	=	=	SYM
ejpam-4530	179	18	0	0	NUM
ejpam-4530	179	19	.	.	PUNCT
ejpam-4530	180	1	■	■	PUNCT
ejpam-4530	180	2	3	3	X
ejpam-4530	180	3	.	.	PUNCT
ejpam-4530	180	4	applications	application	NOUN
ejpam-4530	180	5	in	in	ADP
ejpam-4530	180	6	graph	graph	NOUN
ejpam-4530	180	7	theory	theory	NOUN
ejpam-4530	180	8	definition	definition	NOUN
ejpam-4530	180	9	3.1	3.1	NUM
ejpam-4530	180	10	.	.	PUNCT
ejpam-4530	181	1	the	the	DET
ejpam-4530	181	2	graph	graph	NOUN
ejpam-4530	181	3	of	of	ADP
ejpam-4530	181	4	invo	invo	PROPN
ejpam-4530	181	5	-	-	PUNCT
ejpam-4530	181	6	t	t	NOUN
ejpam-4530	181	7	-	-	PUNCT
ejpam-4530	181	8	clean	clean	ADJ
ejpam-4530	181	9	ring	ring	NOUN
ejpam-4530	181	10	r	r	NOUN
ejpam-4530	181	11	,	,	PUNCT
ejpam-4530	181	12	which	which	PRON
ejpam-4530	181	13	is	be	AUX
ejpam-4530	181	14	denoted	denote	VERB
ejpam-4530	181	15	by	by	ADP
ejpam-4530	181	16	clt(r	clt(r	PROPN
ejpam-4530	181	17	)	)	PUNCT
ejpam-4530	181	18	has	have	VERB
ejpam-4530	181	19	vertex	vertex	NOUN
ejpam-4530	181	20	set	set	VERB
ejpam-4530	181	21	v	v	NOUN
ejpam-4530	181	22	(	(	PUNCT
ejpam-4530	181	23	clt(r	clt(r	PROPN
ejpam-4530	181	24	)	)	PUNCT
ejpam-4530	181	25	)	)	PUNCT
ejpam-4530	182	1	=	=	PRON
ejpam-4530	182	2	{	{	PUNCT
ejpam-4530	182	3	(	(	PUNCT
ejpam-4530	182	4	u	u	NOUN
ejpam-4530	182	5	,	,	PUNCT
ejpam-4530	182	6	t	t	PROPN
ejpam-4530	182	7	)	)	PUNCT
ejpam-4530	182	8	:	:	PUNCT
ejpam-4530	182	9	u	u	PROPN
ejpam-4530	182	10	∈	∈	PROPN
ejpam-4530	182	11	invo(r)&t	invo(r)&t	CCONJ
ejpam-4530	182	12	∈	∈	PROPN
ejpam-4530	182	13	tri(r	tri(r	PROPN
ejpam-4530	182	14	)	)	PUNCT
ejpam-4530	182	15	}	}	PUNCT
ejpam-4530	182	16	and	and	CCONJ
ejpam-4530	182	17	has	have	AUX
ejpam-4530	182	18	the	the	DET
ejpam-4530	182	19	edge	edge	NOUN
ejpam-4530	182	20	set	set	VERB
ejpam-4530	182	21	f	f	PROPN
ejpam-4530	182	22	(	(	PUNCT
ejpam-4530	182	23	clt(r	clt(r	PROPN
ejpam-4530	182	24	)	)	PUNCT
ejpam-4530	182	25	)	)	PUNCT
ejpam-4530	183	1	=	=	PRON
ejpam-4530	183	2	{	{	PUNCT
ejpam-4530	183	3	h1h2	h1h2	X
ejpam-4530	183	4	:	:	PUNCT
ejpam-4530	183	5	h1	h1	PROPN
ejpam-4530	183	6	=	=	SYM
ejpam-4530	183	7	(	(	PUNCT
ejpam-4530	183	8	u1	u1	PROPN
ejpam-4530	183	9	,	,	PUNCT
ejpam-4530	183	10	t1	t1	NOUN
ejpam-4530	183	11	)	)	PUNCT
ejpam-4530	183	12	,	,	PUNCT
ejpam-4530	183	13	h2	h2	NOUN
ejpam-4530	183	14	=	=	SYM
ejpam-4530	183	15	(	(	PUNCT
ejpam-4530	183	16	u2	u2	PROPN
ejpam-4530	183	17	,	,	PUNCT
ejpam-4530	183	18	t2),u1+u2	t2),u1+u2	NOUN
ejpam-4530	183	19	=	=	SYM
ejpam-4530	183	20	0	0	NUM
ejpam-4530	183	21	or	or	CCONJ
ejpam-4530	183	22	t1	t1	NOUN
ejpam-4530	183	23	·	·	PUNCT
ejpam-4530	183	24	t2	t2	NOUN
ejpam-4530	183	25	=	=	SYM
ejpam-4530	183	26	0	0	NUM
ejpam-4530	183	27	,	,	PUNCT
ejpam-4530	183	28	ui	ui	PROPN
ejpam-4530	183	29	∈	∈	PROPN
ejpam-4530	183	30	invo(r	invo(r	NOUN
ejpam-4530	183	31	)	)	PUNCT
ejpam-4530	183	32	,	,	PUNCT
ejpam-4530	183	33	ti	ti	NOUN
ejpam-4530	183	34	∈	∈	PROPN
ejpam-4530	183	35	tri(r	tri(r	PROPN
ejpam-4530	183	36	)	)	PUNCT
ejpam-4530	183	37	,	,	PUNCT
ejpam-4530	183	38	ui	ui	PROPN
ejpam-4530	184	1	+	+	CCONJ
ejpam-4530	184	2	ti	ti	NOUN
ejpam-4530	184	3	is	be	AUX
ejpam-4530	184	4	an	an	DET
ejpam-4530	184	5	invo	invo	PROPN
ejpam-4530	184	6	-	-	PUNCT
ejpam-4530	184	7	t	t	NOUN
ejpam-4530	184	8	-	-	PUNCT
ejpam-4530	184	9	clean	clean	ADJ
ejpam-4530	184	10	element	element	NOUN
ejpam-4530	184	11	i	i	NOUN
ejpam-4530	184	12	=	=	NOUN
ejpam-4530	184	13	1	1	NUM
ejpam-4530	184	14	,	,	PUNCT
ejpam-4530	184	15	2	2	NUM
ejpam-4530	184	16	}	}	PUNCT
ejpam-4530	184	17	.	.	PUNCT
ejpam-4530	185	1	for	for	ADP
ejpam-4530	185	2	example	example	NOUN
ejpam-4530	185	3	,	,	PUNCT
ejpam-4530	185	4	let	let	VERB
ejpam-4530	185	5	v	v	X
ejpam-4530	185	6	(	(	PUNCT
ejpam-4530	185	7	clt(z4	clt(z4	PROPN
ejpam-4530	185	8	)	)	PUNCT
ejpam-4530	185	9	)	)	PUNCT
ejpam-4530	186	1	=	=	PRON
ejpam-4530	186	2	{	{	PUNCT
ejpam-4530	187	1	[	[	X
ejpam-4530	187	2	1	1	NUM
ejpam-4530	187	3	,	,	PUNCT
ejpam-4530	187	4	0	0	NUM
ejpam-4530	187	5	]	]	PUNCT
ejpam-4530	187	6	,	,	PUNCT
ejpam-4530	187	7	[	[	X
ejpam-4530	187	8	3	3	NUM
ejpam-4530	187	9	,	,	PUNCT
ejpam-4530	187	10	0	0	NUM
ejpam-4530	187	11	]	]	PUNCT
ejpam-4530	187	12	,	,	PUNCT
ejpam-4530	188	1	[	[	X
ejpam-4530	188	2	1	1	NUM
ejpam-4530	188	3	,	,	PUNCT
ejpam-4530	188	4	1	1	NUM
ejpam-4530	188	5	]	]	PUNCT
ejpam-4530	188	6	,	,	PUNCT
ejpam-4530	188	7	[	[	X
ejpam-4530	188	8	1	1	NUM
ejpam-4530	188	9	,	,	PUNCT
ejpam-4530	188	10	3	3	NUM
ejpam-4530	188	11	]	]	PUNCT
ejpam-4530	188	12	,	,	PUNCT
ejpam-4530	188	13	[	[	X
ejpam-4530	188	14	3	3	NUM
ejpam-4530	188	15	,	,	PUNCT
ejpam-4530	188	16	1	1	NUM
ejpam-4530	188	17	]	]	PUNCT
ejpam-4530	188	18	,	,	PUNCT
ejpam-4530	188	19	[	[	X
ejpam-4530	188	20	3	3	NUM
ejpam-4530	188	21	,	,	PUNCT
ejpam-4530	188	22	3	3	NUM
ejpam-4530	188	23	]	]	PUNCT
ejpam-4530	188	24	}	}	PUNCT
ejpam-4530	188	25	then	then	ADV
ejpam-4530	188	26	,	,	PUNCT
ejpam-4530	188	27	f	f	PROPN
ejpam-4530	188	28	(	(	PUNCT
ejpam-4530	188	29	clt(z4	clt(z4	PROPN
ejpam-4530	188	30	)	)	PUNCT
ejpam-4530	188	31	)	)	PUNCT
ejpam-4530	189	1	=	=	PRON
ejpam-4530	189	2	{	{	PUNCT
ejpam-4530	190	1	[	[	X
ejpam-4530	190	2	1	1	NUM
ejpam-4530	190	3	,	,	PUNCT
ejpam-4530	190	4	0][1	0][1	NUM
ejpam-4530	190	5	,	,	PUNCT
ejpam-4530	190	6	0	0	NUM
ejpam-4530	190	7	]	]	PUNCT
ejpam-4530	190	8	,	,	PUNCT
ejpam-4530	191	1	[	[	X
ejpam-4530	191	2	1	1	NUM
ejpam-4530	191	3	,	,	PUNCT
ejpam-4530	191	4	0][3	0][3	NUM
ejpam-4530	191	5	,	,	PUNCT
ejpam-4530	191	6	0	0	NUM
ejpam-4530	191	7	]	]	PUNCT
ejpam-4530	191	8	,	,	PUNCT
ejpam-4530	191	9	[	[	X
ejpam-4530	191	10	1	1	NUM
ejpam-4530	191	11	,	,	PUNCT
ejpam-4530	191	12	0][1	0][1	NUM
ejpam-4530	191	13	,	,	PUNCT
ejpam-4530	191	14	1	1	NUM
ejpam-4530	191	15	]	]	PUNCT
ejpam-4530	191	16	,	,	PUNCT
ejpam-4530	191	17	[	[	X
ejpam-4530	191	18	1	1	NUM
ejpam-4530	191	19	,	,	PUNCT
ejpam-4530	191	20	0][3	0][3	NUM
ejpam-4530	191	21	,	,	PUNCT
ejpam-4530	191	22	1	1	NUM
ejpam-4530	191	23	]	]	PUNCT
ejpam-4530	191	24	,	,	PUNCT
ejpam-4530	191	25	[	[	X
ejpam-4530	191	26	1	1	NUM
ejpam-4530	191	27	,	,	PUNCT
ejpam-4530	191	28	0][1	0][1	NUM
ejpam-4530	191	29	,	,	PUNCT
ejpam-4530	191	30	3	3	NUM
ejpam-4530	191	31	]	]	PUNCT
ejpam-4530	191	32	,	,	PUNCT
ejpam-4530	191	33	[	[	X
ejpam-4530	191	34	1	1	NUM
ejpam-4530	191	35	,	,	PUNCT
ejpam-4530	191	36	0][3	0][3	NUM
ejpam-4530	191	37	,	,	PUNCT
ejpam-4530	191	38	3	3	NUM
ejpam-4530	191	39	]	]	PUNCT
ejpam-4530	191	40	,	,	PUNCT
ejpam-4530	191	41	[	[	X
ejpam-4530	191	42	3	3	NUM
ejpam-4530	191	43	,	,	PUNCT
ejpam-4530	191	44	0][3	0][3	NUM
ejpam-4530	191	45	,	,	PUNCT
ejpam-4530	191	46	0	0	NUM
ejpam-4530	191	47	]	]	PUNCT
ejpam-4530	191	48	,	,	PUNCT
ejpam-4530	191	49	[	[	X
ejpam-4530	191	50	3	3	NUM
ejpam-4530	191	51	,	,	PUNCT
ejpam-4530	191	52	0][1	0][1	NUM
ejpam-4530	191	53	,	,	PUNCT
ejpam-4530	191	54	1	1	NUM
ejpam-4530	191	55	]	]	PUNCT
ejpam-4530	191	56	,	,	PUNCT
ejpam-4530	191	57	[	[	X
ejpam-4530	191	58	3	3	NUM
ejpam-4530	191	59	,	,	PUNCT
ejpam-4530	191	60	0][3	0][3	NUM
ejpam-4530	191	61	,	,	PUNCT
ejpam-4530	191	62	1	1	NUM
ejpam-4530	191	63	]	]	PUNCT
ejpam-4530	191	64	,	,	PUNCT
ejpam-4530	191	65	[	[	X
ejpam-4530	191	66	3	3	NUM
ejpam-4530	191	67	,	,	PUNCT
ejpam-4530	191	68	0][1	0][1	NUM
ejpam-4530	191	69	,	,	PUNCT
ejpam-4530	191	70	3	3	NUM
ejpam-4530	191	71	]	]	PUNCT
ejpam-4530	191	72	,	,	PUNCT
ejpam-4530	191	73	[	[	X
ejpam-4530	191	74	3	3	NUM
ejpam-4530	191	75	,	,	PUNCT
ejpam-4530	191	76	0][3	0][3	NUM
ejpam-4530	191	77	,	,	PUNCT
ejpam-4530	191	78	3	3	NUM
ejpam-4530	191	79	]	]	PUNCT
ejpam-4530	191	80	,	,	PUNCT
ejpam-4530	191	81	[	[	X
ejpam-4530	191	82	1	1	NUM
ejpam-4530	191	83	,	,	PUNCT
ejpam-4530	191	84	1][3	1][3	NUM
ejpam-4530	191	85	,	,	PUNCT
ejpam-4530	191	86	1	1	NUM
ejpam-4530	191	87	]	]	PUNCT
ejpam-4530	191	88	,	,	PUNCT
ejpam-4530	191	89	[	[	X
ejpam-4530	191	90	1	1	NUM
ejpam-4530	191	91	,	,	PUNCT
ejpam-4530	191	92	1][3	1][3	NUM
ejpam-4530	191	93	,	,	PUNCT
ejpam-4530	191	94	3	3	NUM
ejpam-4530	191	95	]	]	PUNCT
ejpam-4530	191	96	,	,	PUNCT
ejpam-4530	191	97	[	[	X
ejpam-4530	191	98	1	1	NUM
ejpam-4530	191	99	,	,	PUNCT
ejpam-4530	191	100	3][3	3][3	NUM
ejpam-4530	191	101	,	,	PUNCT
ejpam-4530	191	102	1	1	NUM
ejpam-4530	191	103	]	]	PUNCT
ejpam-4530	191	104	,	,	PUNCT
ejpam-4530	191	105	[	[	X
ejpam-4530	191	106	1	1	NUM
ejpam-4530	191	107	,	,	PUNCT
ejpam-4530	191	108	3][3	3][3	NUM
ejpam-4530	191	109	,	,	PUNCT
ejpam-4530	191	110	3	3	NUM
ejpam-4530	191	111	]	]	PUNCT
ejpam-4530	191	112	}	}	PUNCT
ejpam-4530	191	113	.	.	PUNCT
ejpam-4530	192	1	from	from	ADP
ejpam-4530	192	2	the	the	DET
ejpam-4530	192	3	above	above	ADJ
ejpam-4530	192	4	example	example	NOUN
ejpam-4530	192	5	,	,	PUNCT
ejpam-4530	192	6	we	we	PRON
ejpam-4530	192	7	see	see	VERB
ejpam-4530	192	8	that	that	SCONJ
ejpam-4530	192	9	there	there	PRON
ejpam-4530	192	10	is	be	VERB
ejpam-4530	192	11	a	a	DET
ejpam-4530	192	12	loop	loop	NOUN
ejpam-4530	192	13	at	at	ADP
ejpam-4530	192	14	vertices	vertex	NOUN
ejpam-4530	192	15	[	[	X
ejpam-4530	192	16	1	1	NUM
ejpam-4530	192	17	,	,	PUNCT
ejpam-4530	192	18	0	0	NUM
ejpam-4530	192	19	]	]	PUNCT
ejpam-4530	192	20	and	and	CCONJ
ejpam-4530	192	21	[	[	X
ejpam-4530	192	22	3	3	NUM
ejpam-4530	192	23	,	,	PUNCT
ejpam-4530	192	24	0	0	NUM
ejpam-4530	192	25	]	]	PUNCT
ejpam-4530	192	26	and	and	CCONJ
ejpam-4530	192	27	because	because	SCONJ
ejpam-4530	192	28	it	it	PRON
ejpam-4530	192	29	is	be	AUX
ejpam-4530	192	30	not	not	PART
ejpam-4530	192	31	important	important	ADJ
ejpam-4530	192	32	in	in	ADP
ejpam-4530	192	33	graph	graph	NOUN
ejpam-4530	192	34	theory	theory	NOUN
ejpam-4530	192	35	,	,	PUNCT
ejpam-4530	192	36	we	we	PRON
ejpam-4530	192	37	will	will	AUX
ejpam-4530	192	38	ignore	ignore	VERB
ejpam-4530	192	39	it	it	PRON
ejpam-4530	192	40	,	,	PUNCT
ejpam-4530	192	41	and	and	CCONJ
ejpam-4530	192	42	the	the	DET
ejpam-4530	192	43	girth	girth	NOUN
ejpam-4530	192	44	of	of	ADP
ejpam-4530	192	45	clt(z4	clt(z4	PROPN
ejpam-4530	192	46	)	)	PUNCT
ejpam-4530	192	47	is	be	AUX
ejpam-4530	192	48	three	three	NUM
ejpam-4530	192	49	.	.	PUNCT
ejpam-4530	193	1	there	there	PRON
ejpam-4530	193	2	are	be	VERB
ejpam-4530	193	3	many	many	ADJ
ejpam-4530	193	4	recent	recent	ADJ
ejpam-4530	193	5	studies	study	NOUN
ejpam-4530	193	6	that	that	PRON
ejpam-4530	193	7	connected	connect	VERB
ejpam-4530	193	8	the	the	DET
ejpam-4530	193	9	ring	ring	NOUN
ejpam-4530	193	10	theory	theory	NOUN
ejpam-4530	193	11	with	with	ADP
ejpam-4530	193	12	the	the	DET
ejpam-4530	193	13	graph	graph	NOUN
ejpam-4530	193	14	theory	theory	NOUN
ejpam-4530	193	15	to	to	PART
ejpam-4530	193	16	review	review	VERB
ejpam-4530	193	17	the	the	DET
ejpam-4530	193	18	paper	paper	NOUN
ejpam-4530	193	19	,	,	PUNCT
ejpam-4530	193	20	see	see	VERB
ejpam-4530	193	21	[	[	X
ejpam-4530	193	22	3	3	X
ejpam-4530	193	23	]	]	X
ejpam-4530	193	24	[	[	X
ejpam-4530	193	25	10	10	NUM
ejpam-4530	193	26	]	]	X
ejpam-4530	194	1	[	[	X
ejpam-4530	194	2	1	1	NUM
ejpam-4530	194	3	]	]	PUNCT
ejpam-4530	194	4	.	.	PUNCT
ejpam-4530	195	1	using	use	VERB
ejpam-4530	195	2	the	the	DET
ejpam-4530	195	3	python	python	NOUN
ejpam-4530	195	4	programming	programming	NOUN
ejpam-4530	195	5	language	language	NOUN
ejpam-4530	195	6	,	,	PUNCT
ejpam-4530	195	7	we	we	PRON
ejpam-4530	195	8	get	get	VERB
ejpam-4530	195	9	all	all	DET
ejpam-4530	195	10	connected	connected	ADJ
ejpam-4530	195	11	graphs	graph	NOUN
ejpam-4530	195	12	and	and	CCONJ
ejpam-4530	195	13	the	the	DET
ejpam-4530	195	14	result	result	NOUN
ejpam-4530	195	15	from	from	ADP
ejpam-4530	195	16	definition	definition	NOUN
ejpam-4530	195	17	3.1	3.1	NUM
ejpam-4530	195	18	,	,	PUNCT
ejpam-4530	195	19	and	and	CCONJ
ejpam-4530	195	20	then	then	ADV
ejpam-4530	195	21	we	we	PRON
ejpam-4530	195	22	get	get	VERB
ejpam-4530	195	23	some	some	DET
ejpam-4530	195	24	invariant	invariant	ADJ
ejpam-4530	195	25	properties	property	NOUN
ejpam-4530	195	26	in	in	ADP
ejpam-4530	195	27	graph	graph	NOUN
ejpam-4530	195	28	theory	theory	NOUN
ejpam-4530	195	29	,	,	PUNCT
ejpam-4530	195	30	such	such	ADJ
ejpam-4530	195	31	as	as	ADP
ejpam-4530	195	32	:	:	PUNCT
ejpam-4530	195	33	hosoya	hosoya	NOUN
ejpam-4530	195	34	polynomial	polynomial	ADJ
ejpam-4530	195	35	,	,	PUNCT
ejpam-4530	195	36	wiener	wiener	NOUN
ejpam-4530	195	37	index	index	NOUN
ejpam-4530	195	38	,	,	PUNCT
ejpam-4530	195	39	average	average	ADJ
ejpam-4530	195	40	distance	distance	NOUN
ejpam-4530	195	41	and	and	CCONJ
ejpam-4530	195	42	average	average	ADJ
ejpam-4530	195	43	degree	degree	NOUN
ejpam-4530	195	44	.	.	PUNCT
ejpam-4530	196	1	in	in	ADP
ejpam-4530	196	2	the	the	DET
ejpam-4530	196	3	next	next	ADJ
ejpam-4530	196	4	table	table	NOUN
ejpam-4530	196	5	,	,	PUNCT
ejpam-4530	196	6	the	the	DET
ejpam-4530	196	7	graphs	graph	NOUN
ejpam-4530	196	8	structures	structure	VERB
ejpam-4530	196	9	corresponding	correspond	VERB
ejpam-4530	196	10	invo	invo	PROPN
ejpam-4530	196	11	-	-	PUNCT
ejpam-4530	196	12	t	t	NOUN
ejpam-4530	196	13	-	-	PUNCT
ejpam-4530	196	14	clean	clean	ADJ
ejpam-4530	196	15	ring	ring	PROPN
ejpam-4530	196	16	zn	zn	PROPN
ejpam-4530	196	17	,	,	PUNCT
ejpam-4530	196	18	n	n	NOUN
ejpam-4530	196	19	=	=	SYM
ejpam-4530	196	20	2	2	NUM
ejpam-4530	196	21	,	,	PUNCT
ejpam-4530	196	22	3,4	3,4	NUM
ejpam-4530	196	23	,	,	PUNCT
ejpam-4530	196	24	5	5	NUM
ejpam-4530	196	25	,	,	PUNCT
ejpam-4530	196	26	6,8	6,8	NUM
ejpam-4530	196	27	,	,	PUNCT
ejpam-4530	196	28	10	10	NUM
ejpam-4530	196	29	,	,	PUNCT
ejpam-4530	196	30	12	12	NUM
ejpam-4530	196	31	,	,	PUNCT
ejpam-4530	196	32	15	15	NUM
ejpam-4530	196	33	,	,	PUNCT
ejpam-4530	196	34	20	20	NUM
ejpam-4530	196	35	,	,	PUNCT
ejpam-4530	196	36	24	24	NUM
ejpam-4530	196	37	,	,	PUNCT
ejpam-4530	196	38	30	30	NUM
ejpam-4530	196	39	,	,	PUNCT
ejpam-4530	196	40	40	40	NUM
ejpam-4530	196	41	,	,	PUNCT
ejpam-4530	196	42	60	60	NUM
ejpam-4530	196	43	,	,	PUNCT
ejpam-4530	196	44	120	120	NUM
ejpam-4530	196	45	.	.	PUNCT
ejpam-4530	196	46	table	table	NOUN
ejpam-4530	196	47	1	1	NUM
ejpam-4530	196	48	:	:	PUNCT
ejpam-4530	196	49	the	the	DET
ejpam-4530	196	50	graphs	graph	NOUN
ejpam-4530	196	51	clt(zn	clt(zn	NOUN
ejpam-4530	196	52	)	)	PUNCT
ejpam-4530	196	53	.	.	PUNCT
ejpam-4530	197	1	ring	ring	NOUN
ejpam-4530	197	2	graph	graph	NOUN
ejpam-4530	197	3	z2	z2	PROPN
ejpam-4530	197	4	h(clt(z2);x	h(clt(z2);x	NOUN
ejpam-4530	197	5	)	)	PUNCT
ejpam-4530	198	1	=	=	SYM
ejpam-4530	198	2	2	2	NUM
ejpam-4530	198	3	+	+	CCONJ
ejpam-4530	198	4	x	x	NOUN
ejpam-4530	198	5	,	,	PUNCT
ejpam-4530	198	6	w	w	PROPN
ejpam-4530	198	7	(	(	PUNCT
ejpam-4530	198	8	clt(z2	clt(z2	PROPN
ejpam-4530	198	9	)	)	PUNCT
ejpam-4530	198	10	)	)	PUNCT
ejpam-4530	199	1	=	=	SYM
ejpam-4530	199	2	1	1	NUM
ejpam-4530	199	3	,	,	PUNCT
ejpam-4530	199	4	ad(clt(z2	ad(clt(z2	NOUN
ejpam-4530	199	5	)	)	PUNCT
ejpam-4530	199	6	)	)	PUNCT
ejpam-4530	200	1	=	=	SYM
ejpam-4530	200	2	1d(clt(z2	1d(clt(z2	NUM
ejpam-4530	200	3	)	)	PUNCT
ejpam-4530	200	4	)	)	PUNCT
ejpam-4530	201	1	=	=	SYM
ejpam-4530	201	2	1	1	NUM
ejpam-4530	201	3	mohammed	mohammed	PROPN
ejpam-4530	201	4	al	al	PROPN
ejpam-4530	201	5	-	-	PUNCT
ejpam-4530	201	6	neima	neima	PROPN
ejpam-4530	201	7	et	et	PROPN
ejpam-4530	201	8	al	al	PROPN
ejpam-4530	201	9	.	.	PUNCT
ejpam-4530	201	10	/	/	SYM
ejpam-4530	201	11	eur	eur	PROPN
ejpam-4530	201	12	.	.	PUNCT
ejpam-4530	202	1	j.	j.	PROPN
ejpam-4530	202	2	pure	pure	PROPN
ejpam-4530	202	3	appl	appl	PROPN
ejpam-4530	202	4	.	.	PROPN
ejpam-4530	202	5	math	math	PROPN
ejpam-4530	202	6	,	,	PUNCT
ejpam-4530	202	7	15	15	NUM
ejpam-4530	202	8	(	(	PUNCT
ejpam-4530	202	9	4	4	NUM
ejpam-4530	202	10	)	)	PUNCT
ejpam-4530	202	11	(	(	PUNCT
ejpam-4530	202	12	2022	2022	NUM
ejpam-4530	202	13	)	)	PUNCT
ejpam-4530	202	14	,	,	PUNCT
ejpam-4530	202	15	1637	1637	NUM
ejpam-4530	202	16	-	-	SYM
ejpam-4530	202	17	1648	1648	NUM
ejpam-4530	202	18	1643	1643	NUM
ejpam-4530	202	19	ring	ring	NOUN
ejpam-4530	202	20	graph	graph	NOUN
ejpam-4530	202	21	z3	z3	PROPN
ejpam-4530	202	22	h(clt(z3);x	h(clt(z3);x	PROPN
ejpam-4530	202	23	)	)	PUNCT
ejpam-4530	202	24	=	=	NOUN
ejpam-4530	202	25	6	6	NUM
ejpam-4530	202	26	+	+	NUM
ejpam-4530	202	27	13x	13x	NUM
ejpam-4530	202	28	+	+	CCONJ
ejpam-4530	202	29	2x2	2x2	NUM
ejpam-4530	202	30	,	,	PUNCT
ejpam-4530	202	31	w	w	PROPN
ejpam-4530	202	32	(	(	PUNCT
ejpam-4530	202	33	clt(z3	clt(z3	ADJ
ejpam-4530	202	34	)	)	PUNCT
ejpam-4530	202	35	)	)	PUNCT
ejpam-4530	203	1	=	=	SYM
ejpam-4530	203	2	17	17	NUM
ejpam-4530	203	3	,	,	PUNCT
ejpam-4530	203	4	ad(clt(z3	ad(clt(z3	ADJ
ejpam-4530	203	5	)	)	PUNCT
ejpam-4530	203	6	)	)	PUNCT
ejpam-4530	204	1	=	=	SYM
ejpam-4530	204	2	4.333	4.333	NUM
ejpam-4530	204	3	,	,	PUNCT
ejpam-4530	204	4	d(clt(z3	d(clt(z3	NOUN
ejpam-4530	204	5	)	)	PUNCT
ejpam-4530	204	6	)	)	PUNCT
ejpam-4530	205	1	=	=	PUNCT
ejpam-4530	205	2	1.1333	1.1333	NUM
ejpam-4530	205	3	z4	z4	NOUN
ejpam-4530	205	4	h(clt(z4);x	h(clt(z4);x	NOUN
ejpam-4530	205	5	)	)	PUNCT
ejpam-4530	205	6	=	=	SYM
ejpam-4530	205	7	6	6	NUM
ejpam-4530	205	8	+	+	NUM
ejpam-4530	205	9	13x	13x	NUM
ejpam-4530	205	10	+	+	CCONJ
ejpam-4530	205	11	2x2	2x2	NUM
ejpam-4530	205	12	,	,	PUNCT
ejpam-4530	205	13	w	w	PROPN
ejpam-4530	205	14	(	(	PUNCT
ejpam-4530	205	15	clt(z4	clt(z4	PROPN
ejpam-4530	205	16	)	)	PUNCT
ejpam-4530	205	17	)	)	PUNCT
ejpam-4530	206	1	=	=	SYM
ejpam-4530	206	2	17	17	NUM
ejpam-4530	206	3	,	,	PUNCT
ejpam-4530	206	4	ad(clt(z4	ad(clt(z4	PROPN
ejpam-4530	206	5	)	)	PUNCT
ejpam-4530	206	6	)	)	PUNCT
ejpam-4530	207	1	=	=	SYM
ejpam-4530	207	2	4.333	4.333	NUM
ejpam-4530	207	3	,	,	PUNCT
ejpam-4530	207	4	d(clt(z4	d(clt(z4	NOUN
ejpam-4530	207	5	)	)	PUNCT
ejpam-4530	207	6	)	)	PUNCT
ejpam-4530	208	1	=	=	PUNCT
ejpam-4530	208	2	1.1333	1.1333	NUM
ejpam-4530	208	3	z5	z5	NOUN
ejpam-4530	208	4	h(clt(z5);x	h(clt(z5);x	NOUN
ejpam-4530	208	5	)	)	PUNCT
ejpam-4530	208	6	=	=	SYM
ejpam-4530	208	7	6	6	NUM
ejpam-4530	208	8	+	+	NUM
ejpam-4530	208	9	13x	13x	NUM
ejpam-4530	208	10	+	+	CCONJ
ejpam-4530	208	11	2x2	2x2	NUM
ejpam-4530	208	12	,	,	PUNCT
ejpam-4530	208	13	w	w	X
ejpam-4530	208	14	(	(	PUNCT
ejpam-4530	208	15	clt(z5	clt(z5	NOUN
ejpam-4530	208	16	)	)	PUNCT
ejpam-4530	208	17	)	)	PUNCT
ejpam-4530	209	1	=	=	SYM
ejpam-4530	209	2	17	17	NUM
ejpam-4530	209	3	,	,	PUNCT
ejpam-4530	209	4	ad(clt(z5	ad(clt(z5	PROPN
ejpam-4530	209	5	)	)	PUNCT
ejpam-4530	209	6	)	)	PUNCT
ejpam-4530	210	1	=	=	PUNCT
ejpam-4530	210	2	4.333	4.333	NUM
ejpam-4530	210	3	,	,	PUNCT
ejpam-4530	210	4	d(clt(z5	d(clt(z5	ADV
ejpam-4530	210	5	)	)	PUNCT
ejpam-4530	210	6	)	)	PUNCT
ejpam-4530	211	1	=	=	PUNCT
ejpam-4530	212	1	1.1333	1.1333	NUM
ejpam-4530	212	2	mohammed	mohammed	PROPN
ejpam-4530	212	3	al	al	PROPN
ejpam-4530	212	4	-	-	PUNCT
ejpam-4530	212	5	neima	neima	PROPN
ejpam-4530	212	6	et	et	PROPN
ejpam-4530	212	7	al	al	PROPN
ejpam-4530	212	8	.	.	PUNCT
ejpam-4530	212	9	/	/	SYM
ejpam-4530	212	10	eur	eur	PROPN
ejpam-4530	212	11	.	.	PUNCT
ejpam-4530	213	1	j.	j.	PROPN
ejpam-4530	213	2	pure	pure	PROPN
ejpam-4530	213	3	appl	appl	PROPN
ejpam-4530	213	4	.	.	PROPN
ejpam-4530	213	5	math	math	PROPN
ejpam-4530	213	6	,	,	PUNCT
ejpam-4530	213	7	15	15	NUM
ejpam-4530	213	8	(	(	PUNCT
ejpam-4530	213	9	4	4	NUM
ejpam-4530	213	10	)	)	PUNCT
ejpam-4530	213	11	(	(	PUNCT
ejpam-4530	213	12	2022	2022	NUM
ejpam-4530	213	13	)	)	PUNCT
ejpam-4530	213	14	,	,	PUNCT
ejpam-4530	213	15	1637	1637	NUM
ejpam-4530	213	16	-	-	SYM
ejpam-4530	213	17	1648	1648	NUM
ejpam-4530	213	18	1644	1644	NUM
ejpam-4530	213	19	ring	ring	NOUN
ejpam-4530	213	20	graph	graph	NOUN
ejpam-4530	213	21	z6	z6	PROPN
ejpam-4530	213	22	h(clt(z6);x	h(clt(z6);x	NOUN
ejpam-4530	213	23	)	)	PUNCT
ejpam-4530	214	1	=	=	NOUN
ejpam-4530	215	1	12	12	NUM
ejpam-4530	215	2	+	+	NUM
ejpam-4530	215	3	30x	30x	NOUN
ejpam-4530	215	4	+	+	CCONJ
ejpam-4530	215	5	16x2	16x2	NUM
ejpam-4530	215	6	,	,	PUNCT
ejpam-4530	215	7	w	w	PROPN
ejpam-4530	215	8	(	(	PUNCT
ejpam-4530	215	9	clt(z6	clt(z6	PROPN
ejpam-4530	215	10	)	)	PUNCT
ejpam-4530	215	11	)	)	PUNCT
ejpam-4530	216	1	=	=	SYM
ejpam-4530	216	2	82	82	NUM
ejpam-4530	216	3	,	,	PUNCT
ejpam-4530	216	4	ad(clt(z6	ad(clt(z6	PROPN
ejpam-4530	216	5	)	)	PUNCT
ejpam-4530	216	6	)	)	PUNCT
ejpam-4530	217	1	=	=	SYM
ejpam-4530	217	2	5	5	NUM
ejpam-4530	217	3	,	,	PUNCT
ejpam-4530	217	4	d(clt(z6	d(clt(z6	NOUN
ejpam-4530	217	5	)	)	PUNCT
ejpam-4530	217	6	)	)	PUNCT
ejpam-4530	218	1	=	=	PUNCT
ejpam-4530	218	2	1.242	1.242	NUM
ejpam-4530	218	3	z8	z8	PROPN
ejpam-4530	218	4	h(clt(z8);x	h(clt(z8);x	NOUN
ejpam-4530	218	5	)	)	PUNCT
ejpam-4530	218	6	=	=	SYM
ejpam-4530	218	7	20	20	NUM
ejpam-4530	218	8	+	+	NOUN
ejpam-4530	218	9	102x+88x2	102x+88x2	NUM
ejpam-4530	218	10	,	,	PUNCT
ejpam-4530	218	11	w	w	NOUN
ejpam-4530	218	12	(	(	PUNCT
ejpam-4530	218	13	clt(z8	clt(z8	NOUN
ejpam-4530	218	14	)	)	PUNCT
ejpam-4530	218	15	)	)	PUNCT
ejpam-4530	219	1	=	=	SYM
ejpam-4530	219	2	278	278	NUM
ejpam-4530	219	3	,	,	PUNCT
ejpam-4530	219	4	ad(clt(z8	ad(clt(z8	NOUN
ejpam-4530	219	5	)	)	PUNCT
ejpam-4530	219	6	)	)	PUNCT
ejpam-4530	220	1	=	=	PUNCT
ejpam-4530	220	2	10.2	10.2	NUM
ejpam-4530	220	3	,	,	PUNCT
ejpam-4530	220	4	d(clt(z8	d(clt(z8	NOUN
ejpam-4530	220	5	)	)	PUNCT
ejpam-4530	220	6	)	)	PUNCT
ejpam-4530	221	1	=	=	PUNCT
ejpam-4530	221	2	1.46	1.46	NUM
ejpam-4530	221	3	z10	z10	NOUN
ejpam-4530	221	4	(	(	PUNCT
ejpam-4530	221	5	clt(z10);x	clt(z10);x	PROPN
ejpam-4530	221	6	)	)	PUNCT
ejpam-4530	221	7	=	=	NOUN
ejpam-4530	222	1	12	12	NUM
ejpam-4530	222	2	+	+	NUM
ejpam-4530	222	3	50x+	50x+	NUM
ejpam-4530	222	4	16x2	16x2	NUM
ejpam-4530	222	5	,	,	PUNCT
ejpam-4530	222	6	w	w	PROPN
ejpam-4530	222	7	(	(	PUNCT
ejpam-4530	222	8	clt(z10	clt(z10	NOUN
ejpam-4530	222	9	)	)	PUNCT
ejpam-4530	222	10	)	)	PUNCT
ejpam-4530	223	1	=	=	SYM
ejpam-4530	223	2	82	82	NUM
ejpam-4530	223	3	,	,	PUNCT
ejpam-4530	223	4	ad(clt(z10	ad(clt(z10	NUM
ejpam-4530	223	5	)	)	PUNCT
ejpam-4530	223	6	)	)	PUNCT
ejpam-4530	224	1	=	=	SYM
ejpam-4530	224	2	5	5	NUM
ejpam-4530	224	3	,	,	PUNCT
ejpam-4530	224	4	d(clt(z10	d(clt(z10	NOUN
ejpam-4530	224	5	)	)	PUNCT
ejpam-4530	224	6	)	)	PUNCT
ejpam-4530	225	1	=	=	SYM
ejpam-4530	225	2	1.242	1.242	NUM
ejpam-4530	225	3	mohammed	mohammed	PROPN
ejpam-4530	225	4	al	al	PROPN
ejpam-4530	225	5	-	-	PUNCT
ejpam-4530	225	6	neima	neima	PROPN
ejpam-4530	225	7	et	et	PROPN
ejpam-4530	225	8	al	al	PROPN
ejpam-4530	225	9	.	.	PUNCT
ejpam-4530	225	10	/	/	SYM
ejpam-4530	225	11	eur	eur	PROPN
ejpam-4530	225	12	.	.	PUNCT
ejpam-4530	226	1	j.	j.	PROPN
ejpam-4530	226	2	pure	pure	PROPN
ejpam-4530	226	3	appl	appl	PROPN
ejpam-4530	226	4	.	.	PROPN
ejpam-4530	226	5	math	math	PROPN
ejpam-4530	226	6	,	,	PUNCT
ejpam-4530	226	7	15	15	NUM
ejpam-4530	226	8	(	(	PUNCT
ejpam-4530	226	9	4	4	NUM
ejpam-4530	226	10	)	)	PUNCT
ejpam-4530	226	11	(	(	PUNCT
ejpam-4530	226	12	2022	2022	NUM
ejpam-4530	226	13	)	)	PUNCT
ejpam-4530	226	14	,	,	PUNCT
ejpam-4530	226	15	1637	1637	NUM
ejpam-4530	226	16	-	-	SYM
ejpam-4530	226	17	1648	1648	NUM
ejpam-4530	226	18	1645	1645	NUM
ejpam-4530	226	19	ring	ring	NOUN
ejpam-4530	226	20	graph	graph	NOUN
ejpam-4530	226	21	z12	z12	PROPN
ejpam-4530	226	22	h(clt(z12);x	h(clt(z12);x	PROPN
ejpam-4530	226	23	)	)	PUNCT
ejpam-4530	226	24	=	=	SYM
ejpam-4530	227	1	36	36	NUM
ejpam-4530	227	2	+	+	NUM
ejpam-4530	227	3	310x	310x	ADJ
ejpam-4530	227	4	+	+	CCONJ
ejpam-4530	227	5	320x2	320x2	NUM
ejpam-4530	227	6	,	,	PUNCT
ejpam-4530	227	7	w	w	NOUN
ejpam-4530	227	8	(	(	PUNCT
ejpam-4530	227	9	clt(z12	clt(z12	NOUN
ejpam-4530	227	10	)	)	PUNCT
ejpam-4530	227	11	)	)	PUNCT
ejpam-4530	228	1	=	=	SYM
ejpam-4530	228	2	950	950	NUM
ejpam-4530	228	3	,	,	PUNCT
ejpam-4530	228	4	ad(clt(z12	ad(clt(z12	NOUN
ejpam-4530	228	5	)	)	PUNCT
ejpam-4530	228	6	)	)	PUNCT
ejpam-4530	228	7	=	=	SYM
ejpam-4530	228	8	17.222	17.222	NUM
ejpam-4530	228	9	,	,	PUNCT
ejpam-4530	228	10	d(clt(z12	d(clt(z12	NOUN
ejpam-4530	228	11	)	)	PUNCT
ejpam-4530	228	12	)	)	PUNCT
ejpam-4530	229	1	=	=	SYM
ejpam-4530	229	2	1.50	1.50	NUM
ejpam-4530	229	3	z15	z15	PROPN
ejpam-4530	229	4	h(clt(z15);x	h(clt(z15);x	PROPN
ejpam-4530	229	5	)	)	PUNCT
ejpam-4530	229	6	=	=	PUNCT
ejpam-4530	230	1	36	36	NUM
ejpam-4530	230	2	+	+	NUM
ejpam-4530	230	3	310x	310x	VERB
ejpam-4530	230	4	+	+	CCONJ
ejpam-4530	230	5	320x2	320x2	NUM
ejpam-4530	230	6	w	w	NOUN
ejpam-4530	230	7	(	(	PUNCT
ejpam-4530	230	8	clt(z15	clt(z15	NOUN
ejpam-4530	230	9	)	)	PUNCT
ejpam-4530	230	10	)	)	PUNCT
ejpam-4530	231	1	=	=	SYM
ejpam-4530	231	2	950	950	NUM
ejpam-4530	231	3	,	,	PUNCT
ejpam-4530	231	4	ad(clt(z15	ad(clt(z15	ADJ
ejpam-4530	231	5	)	)	PUNCT
ejpam-4530	231	6	)	)	PUNCT
ejpam-4530	232	1	=	=	SYM
ejpam-4530	232	2	17.222	17.222	NUM
ejpam-4530	232	3	,	,	PUNCT
ejpam-4530	232	4	d(clt(z15	d(clt(z15	NOUN
ejpam-4530	232	5	)	)	PUNCT
ejpam-4530	232	6	)	)	PUNCT
ejpam-4530	233	1	=	=	PUNCT
ejpam-4530	233	2	1.50	1.50	NUM
ejpam-4530	233	3	z20	z20	NOUN
ejpam-4530	233	4	h(clt(z20);x	h(clt(z20);x	PROPN
ejpam-4530	233	5	)	)	PUNCT
ejpam-4530	233	6	=	=	SYM
ejpam-4530	234	1	36	36	NUM
ejpam-4530	234	2	+	+	NUM
ejpam-4530	234	3	310x	310x	ADJ
ejpam-4530	234	4	+	+	CCONJ
ejpam-4530	234	5	320x2	320x2	NUM
ejpam-4530	234	6	,	,	PUNCT
ejpam-4530	234	7	w	w	X
ejpam-4530	234	8	(	(	PUNCT
ejpam-4530	234	9	clt(z20	clt(z20	NOUN
ejpam-4530	234	10	)	)	PUNCT
ejpam-4530	234	11	)	)	PUNCT
ejpam-4530	235	1	=	=	SYM
ejpam-4530	235	2	950	950	NUM
ejpam-4530	235	3	,	,	PUNCT
ejpam-4530	235	4	ad(clt(z20	ad(clt(z20	NOUN
ejpam-4530	235	5	)	)	PUNCT
ejpam-4530	235	6	)	)	PUNCT
ejpam-4530	236	1	=	=	SYM
ejpam-4530	236	2	17.222	17.222	NUM
ejpam-4530	236	3	,	,	PUNCT
ejpam-4530	236	4	d(clt(z20	d(clt(z20	NOUN
ejpam-4530	236	5	)	)	PUNCT
ejpam-4530	236	6	)	)	PUNCT
ejpam-4530	237	1	=	=	SYM
ejpam-4530	237	2	1.50	1.50	NUM
ejpam-4530	237	3	mohammed	mohammed	PROPN
ejpam-4530	237	4	al	al	PROPN
ejpam-4530	237	5	-	-	PUNCT
ejpam-4530	237	6	neima	neima	PROPN
ejpam-4530	237	7	et	et	PROPN
ejpam-4530	237	8	al	al	PROPN
ejpam-4530	237	9	.	.	PUNCT
ejpam-4530	237	10	/	/	SYM
ejpam-4530	237	11	eur	eur	PROPN
ejpam-4530	237	12	.	.	PUNCT
ejpam-4530	238	1	j.	j.	PROPN
ejpam-4530	238	2	pure	pure	PROPN
ejpam-4530	238	3	appl	appl	PROPN
ejpam-4530	238	4	.	.	PROPN
ejpam-4530	238	5	math	math	PROPN
ejpam-4530	238	6	,	,	PUNCT
ejpam-4530	238	7	15	15	NUM
ejpam-4530	238	8	(	(	PUNCT
ejpam-4530	238	9	4	4	NUM
ejpam-4530	238	10	)	)	PUNCT
ejpam-4530	238	11	(	(	PUNCT
ejpam-4530	238	12	2022	2022	NUM
ejpam-4530	238	13	)	)	PUNCT
ejpam-4530	238	14	,	,	PUNCT
ejpam-4530	238	15	1637	1637	NUM
ejpam-4530	238	16	-	-	SYM
ejpam-4530	238	17	1648	1648	NUM
ejpam-4530	238	18	1646	1646	NUM
ejpam-4530	238	19	ring	ring	NOUN
ejpam-4530	238	20	graph	graph	NOUN
ejpam-4530	238	21	z24	z24	PROPN
ejpam-4530	238	22	h(clt(z24);x	h(clt(z24);x	PROPN
ejpam-4530	238	23	)	)	PUNCT
ejpam-4530	238	24	=	=	SYM
ejpam-4530	239	1	120	120	NUM
ejpam-4530	239	2	+	+	NUM
ejpam-4530	239	3	2156x	2156x	NUM
ejpam-4530	239	4	+	+	CCONJ
ejpam-4530	239	5	4984x2	4984x2	NOUN
ejpam-4530	239	6	,	,	PUNCT
ejpam-4530	239	7	w	w	PROPN
ejpam-4530	239	8	(	(	PUNCT
ejpam-4530	239	9	clt(z24	clt(z24	NOUN
ejpam-4530	239	10	)	)	PUNCT
ejpam-4530	239	11	)	)	PUNCT
ejpam-4530	240	1	=	=	SYM
ejpam-4530	240	2	12124	12124	NUM
ejpam-4530	240	3	,	,	PUNCT
ejpam-4530	240	4	ad(clt(z24	ad(clt(z24	NOUN
ejpam-4530	240	5	)	)	PUNCT
ejpam-4530	240	6	)	)	PUNCT
ejpam-4530	241	1	=	=	SYM
ejpam-4530	241	2	35.9333	35.9333	NUM
ejpam-4530	241	3	,	,	PUNCT
ejpam-4530	241	4	d(clt(z24	d(clt(z24	NOUN
ejpam-4530	241	5	)	)	PUNCT
ejpam-4530	241	6	)	)	PUNCT
ejpam-4530	242	1	=	=	SYM
ejpam-4530	242	2	1.69	1.69	NUM
ejpam-4530	242	3	z30	z30	NOUN
ejpam-4530	242	4	h(clt(z30);x	h(clt(z30);x	PROPN
ejpam-4530	242	5	)	)	PUNCT
ejpam-4530	242	6	=	=	SYM
ejpam-4530	242	7	72	72	NUM
ejpam-4530	242	8	+	+	NUM
ejpam-4530	242	9	1096x	1096x	NUM
ejpam-4530	242	10	+	+	CCONJ
ejpam-4530	242	11	1460x2	1460x2	NUM
ejpam-4530	242	12	,	,	PUNCT
ejpam-4530	242	13	w	w	PROPN
ejpam-4530	242	14	(	(	PUNCT
ejpam-4530	242	15	clt(z30	clt(z30	NOUN
ejpam-4530	242	16	)	)	PUNCT
ejpam-4530	242	17	)	)	PUNCT
ejpam-4530	243	1	=	=	SYM
ejpam-4530	243	2	4016	4016	NUM
ejpam-4530	243	3	,	,	PUNCT
ejpam-4530	243	4	ad(clt(z30	ad(clt(z30	NOUN
ejpam-4530	243	5	)	)	PUNCT
ejpam-4530	243	6	)	)	PUNCT
ejpam-4530	244	1	=	=	SYM
ejpam-4530	244	2	30.444	30.444	NUM
ejpam-4530	244	3	,	,	PUNCT
ejpam-4530	244	4	d(clt(z30	d(clt(z30	NUM
ejpam-4530	244	5	)	)	PUNCT
ejpam-4530	244	6	)	)	PUNCT
ejpam-4530	245	1	=	=	SYM
ejpam-4530	245	2	1.57	1.57	NUM
ejpam-4530	245	3	z40	z40	ADJ
ejpam-4530	245	4	h(clt(z40);x	h(clt(z40);x	NOUN
ejpam-4530	245	5	)	)	PUNCT
ejpam-4530	245	6	=	=	SYM
ejpam-4530	246	1	120	120	NUM
ejpam-4530	246	2	+	+	NUM
ejpam-4530	246	3	2156x	2156x	NUM
ejpam-4530	246	4	+	+	CCONJ
ejpam-4530	246	5	4984x2	4984x2	NOUN
ejpam-4530	246	6	,	,	PUNCT
ejpam-4530	246	7	w	w	PROPN
ejpam-4530	246	8	(	(	PUNCT
ejpam-4530	246	9	clt(z40	clt(z40	NOUN
ejpam-4530	246	10	)	)	PUNCT
ejpam-4530	246	11	)	)	PUNCT
ejpam-4530	247	1	=	=	SYM
ejpam-4530	247	2	12124	12124	NUM
ejpam-4530	247	3	,	,	PUNCT
ejpam-4530	247	4	ad(clt(z40	ad(clt(z40	ADV
ejpam-4530	247	5	)	)	PUNCT
ejpam-4530	247	6	)	)	PUNCT
ejpam-4530	248	1	=	=	SYM
ejpam-4530	248	2	35.9333	35.9333	NUM
ejpam-4530	248	3	,	,	PUNCT
ejpam-4530	248	4	d(clt(z40	d(clt(z40	NOUN
ejpam-4530	248	5	)	)	PUNCT
ejpam-4530	248	6	)	)	PUNCT
ejpam-4530	249	1	=	=	SYM
ejpam-4530	249	2	1.69	1.69	NUM
ejpam-4530	249	3	mohammed	mohammed	PROPN
ejpam-4530	249	4	al	al	PROPN
ejpam-4530	249	5	-	-	PUNCT
ejpam-4530	249	6	neima	neima	PROPN
ejpam-4530	249	7	et	et	PROPN
ejpam-4530	249	8	al	al	PROPN
ejpam-4530	249	9	.	.	PUNCT
ejpam-4530	249	10	/	/	SYM
ejpam-4530	249	11	eur	eur	PROPN
ejpam-4530	249	12	.	.	PUNCT
ejpam-4530	250	1	j.	j.	PROPN
ejpam-4530	250	2	pure	pure	PROPN
ejpam-4530	250	3	appl	appl	PROPN
ejpam-4530	250	4	.	.	PROPN
ejpam-4530	250	5	math	math	PROPN
ejpam-4530	250	6	,	,	PUNCT
ejpam-4530	250	7	15	15	NUM
ejpam-4530	250	8	(	(	PUNCT
ejpam-4530	250	9	4	4	NUM
ejpam-4530	250	10	)	)	PUNCT
ejpam-4530	250	11	(	(	PUNCT
ejpam-4530	250	12	2022	2022	NUM
ejpam-4530	250	13	)	)	PUNCT
ejpam-4530	250	14	,	,	PUNCT
ejpam-4530	250	15	1637	1637	NUM
ejpam-4530	250	16	-	-	SYM
ejpam-4530	250	17	1648	1648	NUM
ejpam-4530	250	18	1647	1647	NUM
ejpam-4530	250	19	ring	ring	NOUN
ejpam-4530	250	20	graph	graph	NOUN
ejpam-4530	250	21	z60	z60	NOUN
ejpam-4530	250	22	h(clt(z60);x	h(clt(z60);x	NOUN
ejpam-4530	250	23	)	)	PUNCT
ejpam-4530	251	1	=	=	PUNCT
ejpam-4530	252	1	216	216	NUM
ejpam-4530	252	2	+	+	NUM
ejpam-4530	252	3	6412x	6412x	NOUN
ejpam-4530	252	4	+	+	CCONJ
ejpam-4530	252	5	16808x2	16808x2	NUM
ejpam-4530	252	6	w	w	NOUN
ejpam-4530	252	7	(	(	PUNCT
ejpam-4530	252	8	clt(z60	clt(z60	NOUN
ejpam-4530	252	9	)	)	PUNCT
ejpam-4530	252	10	)	)	PUNCT
ejpam-4530	253	1	=	=	SYM
ejpam-4530	253	2	40028	40028	NUM
ejpam-4530	253	3	,	,	PUNCT
ejpam-4530	253	4	ad(clt(z60	ad(clt(z60	PROPN
ejpam-4530	253	5	)	)	PUNCT
ejpam-4530	253	6	)	)	PUNCT
ejpam-4530	254	1	=	=	PUNCT
ejpam-4530	255	1	59.370	59.370	NUM
ejpam-4530	255	2	,	,	PUNCT
ejpam-4530	255	3	d(clt(z60	d(clt(z60	NOUN
ejpam-4530	255	4	)	)	PUNCT
ejpam-4530	255	5	)	)	PUNCT
ejpam-4530	256	1	=	=	PUNCT
ejpam-4530	256	2	1.72	1.72	NUM
ejpam-4530	256	3	z120	z120	NUM
ejpam-4530	256	4	h(clt(z120);x	h(clt(z120);x	NOUN
ejpam-4530	256	5	)	)	PUNCT
ejpam-4530	256	6	=	=	PUNCT
ejpam-4530	257	1	720	720	NUM
ejpam-4530	257	2	+	+	NOUN
ejpam-4530	257	3	43192x+215648x2	43192x+215648x2	NUM
ejpam-4530	257	4	,	,	PUNCT
ejpam-4530	257	5	w	w	PROPN
ejpam-4530	257	6	(	(	PUNCT
ejpam-4530	257	7	clt(z120	clt(z120	NUM
ejpam-4530	257	8	)	)	PUNCT
ejpam-4530	257	9	)	)	PUNCT
ejpam-4530	258	1	=	=	SYM
ejpam-4530	258	2	474488	474488	NUM
ejpam-4530	258	3	,	,	PUNCT
ejpam-4530	258	4	ad(clt(z120	ad(clt(z120	NOUN
ejpam-4530	258	5	)	)	PUNCT
ejpam-4530	258	6	)	)	PUNCT
ejpam-4530	259	1	=	=	PUNCT
ejpam-4530	259	2	119.97	119.97	NUM
ejpam-4530	259	3	,	,	PUNCT
ejpam-4530	259	4	d(clt(z60	d(clt(z60	NOUN
ejpam-4530	259	5	)	)	PUNCT
ejpam-4530	259	6	)	)	PUNCT
ejpam-4530	260	1	=	=	SYM
ejpam-4530	260	2	1.83	1.83	NUM
ejpam-4530	260	3	theorem	theorem	NOUN
ejpam-4530	260	4	3.2	3.2	NUM
ejpam-4530	260	5	.	.	PUNCT
ejpam-4530	261	1	the	the	DET
ejpam-4530	261	2	graph	graph	NOUN
ejpam-4530	261	3	clt(r	clt(r	PROPN
ejpam-4530	261	4	)	)	PUNCT
ejpam-4530	261	5	is	be	AUX
ejpam-4530	261	6	connected	connect	VERB
ejpam-4530	261	7	for	for	ADP
ejpam-4530	261	8	any	any	DET
ejpam-4530	261	9	invo	invo	PROPN
ejpam-4530	261	10	-	-	PUNCT
ejpam-4530	261	11	t	t	NOUN
ejpam-4530	261	12	-	-	PUNCT
ejpam-4530	261	13	clean	clean	ADJ
ejpam-4530	261	14	ring	ring	NOUN
ejpam-4530	261	15	and	and	CCONJ
ejpam-4530	261	16	has	have	VERB
ejpam-4530	261	17	a	a	DET
ejpam-4530	261	18	diameter	diameter	NOUN
ejpam-4530	261	19	less	less	ADJ
ejpam-4530	261	20	than	than	ADP
ejpam-4530	261	21	and	and	CCONJ
ejpam-4530	261	22	equal	equal	ADJ
ejpam-4530	261	23	2	2	NUM
ejpam-4530	261	24	.	.	PUNCT
ejpam-4530	262	1	proof	proof	NOUN
ejpam-4530	262	2	.	.	PUNCT
ejpam-4530	263	1	since	since	SCONJ
ejpam-4530	263	2	(	(	PUNCT
ejpam-4530	263	3	u	u	NOUN
ejpam-4530	263	4	,	,	PUNCT
ejpam-4530	263	5	0	0	NUM
ejpam-4530	263	6	)	)	PUNCT
ejpam-4530	263	7	belong	belong	VERB
ejpam-4530	263	8	to	to	ADP
ejpam-4530	263	9	v	v	NOUN
ejpam-4530	263	10	(	(	PUNCT
ejpam-4530	263	11	clt(r	clt(r	PROPN
ejpam-4530	263	12	)	)	PUNCT
ejpam-4530	263	13	)	)	PUNCT
ejpam-4530	263	14	,	,	PUNCT
ejpam-4530	263	15	then	then	ADV
ejpam-4530	263	16	(	(	PUNCT
ejpam-4530	263	17	u	u	NOUN
ejpam-4530	263	18	,	,	PUNCT
ejpam-4530	263	19	0	0	NUM
ejpam-4530	263	20	)	)	PUNCT
ejpam-4530	263	21	is	be	AUX
ejpam-4530	263	22	adjacent	adjacent	ADJ
ejpam-4530	263	23	to	to	ADP
ejpam-4530	263	24	all	all	DET
ejpam-4530	263	25	vertices	vertex	NOUN
ejpam-4530	263	26	in	in	ADP
ejpam-4530	263	27	a	a	DET
ejpam-4530	263	28	graph	graph	NOUN
ejpam-4530	263	29	clt(r	clt(r	PROPN
ejpam-4530	263	30	)	)	PUNCT
ejpam-4530	263	31	.	.	PUNCT
ejpam-4530	264	1	hence	hence	ADV
ejpam-4530	264	2	then	then	ADV
ejpam-4530	264	3	clt(r	clt(r	PROPN
ejpam-4530	264	4	)	)	PUNCT
ejpam-4530	264	5	is	be	AUX
ejpam-4530	264	6	connected	connect	VERB
ejpam-4530	264	7	.	.	PUNCT
ejpam-4530	265	1	now	now	ADV
ejpam-4530	265	2	to	to	PART
ejpam-4530	265	3	prove	prove	VERB
ejpam-4530	265	4	that	that	SCONJ
ejpam-4530	265	5	clt(r	clt(r	PROPN
ejpam-4530	265	6	)	)	PUNCT
ejpam-4530	265	7	has	have	VERB
ejpam-4530	265	8	diameter	diameter	NOUN
ejpam-4530	265	9	less	less	ADV
ejpam-4530	265	10	and	and	CCONJ
ejpam-4530	265	11	equal	equal	ADJ
ejpam-4530	265	12	2	2	NUM
ejpam-4530	265	13	.	.	PUNCT
ejpam-4530	266	1	let	let	VERB
ejpam-4530	266	2	(	(	PUNCT
ejpam-4530	266	3	u1	u1	VERB
ejpam-4530	266	4	,	,	PUNCT
ejpam-4530	266	5	t1),(u2	t1),(u2	NOUN
ejpam-4530	266	6	,	,	PUNCT
ejpam-4530	266	7	t2	t2	NOUN
ejpam-4530	266	8	)	)	PUNCT
ejpam-4530	266	9	∈	∈	PROPN
ejpam-4530	266	10	v	v	NOUN
ejpam-4530	266	11	(	(	PUNCT
ejpam-4530	266	12	clt(r	clt(r	PROPN
ejpam-4530	266	13	)	)	PUNCT
ejpam-4530	266	14	)	)	PUNCT
ejpam-4530	266	15	,	,	PUNCT
ejpam-4530	266	16	then	then	ADV
ejpam-4530	266	17	we	we	PRON
ejpam-4530	266	18	have	have	VERB
ejpam-4530	266	19	the	the	DET
ejpam-4530	266	20	following	follow	VERB
ejpam-4530	266	21	two	two	NUM
ejpam-4530	266	22	cases	case	NOUN
ejpam-4530	266	23	:	:	PUNCT
ejpam-4530	266	24	case1	case1	NOUN
ejpam-4530	266	25	:	:	PUNCT
ejpam-4530	266	26	if	if	SCONJ
ejpam-4530	266	27	t1	t1	NOUN
ejpam-4530	266	28	=	=	SYM
ejpam-4530	266	29	0	0	NUM
ejpam-4530	266	30	,	,	PUNCT
ejpam-4530	266	31	then	then	ADV
ejpam-4530	266	32	d((u1	d((u1	NOUN
ejpam-4530	266	33	,	,	PUNCT
ejpam-4530	266	34	t1	t1	NOUN
ejpam-4530	266	35	)	)	PUNCT
ejpam-4530	266	36	,	,	PUNCT
ejpam-4530	266	37	(	(	PUNCT
ejpam-4530	266	38	u2	u2	NOUN
ejpam-4530	266	39	,	,	PUNCT
ejpam-4530	266	40	t2	t2	NOUN
ejpam-4530	266	41	)	)	PUNCT
ejpam-4530	266	42	)	)	PUNCT
ejpam-4530	267	1	=	=	SYM
ejpam-4530	267	2	1	1	X
ejpam-4530	267	3	.	.	PUNCT
ejpam-4530	267	4	case2	case2	PROPN
ejpam-4530	267	5	:	:	PUNCT
ejpam-4530	267	6	if	if	SCONJ
ejpam-4530	267	7	u1	u1	PROPN
ejpam-4530	267	8	+	+	CCONJ
ejpam-4530	267	9	u2	u2	PROPN
ejpam-4530	267	10	̸=	̸=	PROPN
ejpam-4530	267	11	0	0	NUM
ejpam-4530	267	12	and	and	CCONJ
ejpam-4530	267	13	t1	t1	NOUN
ejpam-4530	267	14	·	·	PUNCT
ejpam-4530	267	15	t2	t2	PROPN
ejpam-4530	267	16	̸=	̸=	PROPN
ejpam-4530	267	17	0	0	NUM
ejpam-4530	267	18	,	,	PUNCT
ejpam-4530	267	19	ui	ui	PROPN
ejpam-4530	267	20	∈	∈	PROPN
ejpam-4530	267	21	u2(r	u2(r	PROPN
ejpam-4530	267	22	)	)	PUNCT
ejpam-4530	267	23	,	,	PUNCT
ejpam-4530	267	24	ti	ti	NOUN
ejpam-4530	267	25	∈	∈	PROPN
ejpam-4530	267	26	tri(r	tri(r	PROPN
ejpam-4530	267	27	)	)	PUNCT
ejpam-4530	267	28	,	,	PUNCT
ejpam-4530	267	29	i	i	PRON
ejpam-4530	267	30	=	=	NOUN
ejpam-4530	267	31	1	1	NUM
ejpam-4530	267	32	,	,	PUNCT
ejpam-4530	267	33	2,then	2,then	NUM
ejpam-4530	267	34	d((u1	d((u1	NOUN
ejpam-4530	267	35	,	,	PUNCT
ejpam-4530	267	36	t1	t1	NOUN
ejpam-4530	267	37	)	)	PUNCT
ejpam-4530	267	38	,	,	PUNCT
ejpam-4530	267	39	(	(	PUNCT
ejpam-4530	267	40	u2	u2	NOUN
ejpam-4530	267	41	,	,	PUNCT
ejpam-4530	267	42	t2	t2	NOUN
ejpam-4530	267	43	)	)	PUNCT
ejpam-4530	267	44	)	)	PUNCT
ejpam-4530	268	1	=	=	SYM
ejpam-4530	268	2	2	2	X
ejpam-4530	268	3	.	.	X
ejpam-4530	268	4	■	■	PUNCT
ejpam-4530	268	5	theorem	theorem	VERB
ejpam-4530	268	6	3.3	3.3	NUM
ejpam-4530	268	7	.	.	PUNCT
ejpam-4530	269	1	the	the	DET
ejpam-4530	269	2	graph	graph	NOUN
ejpam-4530	269	3	clt(r	clt(r	PROPN
ejpam-4530	269	4	)	)	PUNCT
ejpam-4530	269	5	has	have	VERB
ejpam-4530	269	6	girth	girth	ADV
ejpam-4530	269	7	g(clt(r	g(clt(r	ADJ
ejpam-4530	269	8	)	)	PUNCT
ejpam-4530	269	9	)	)	PUNCT
ejpam-4530	270	1	equal	equal	ADJ
ejpam-4530	270	2	three	three	NUM
ejpam-4530	270	3	for	for	ADP
ejpam-4530	270	4	all	all	DET
ejpam-4530	270	5	|clt(r)|	|clt(r)|	ADJ
ejpam-4530	270	6	≥	≥	NOUN
ejpam-4530	270	7	3	3	NUM
ejpam-4530	270	8	.	.	PUNCT
ejpam-4530	270	9	proof	proof	NOUN
ejpam-4530	270	10	.	.	PUNCT
ejpam-4530	271	1	since	since	SCONJ
ejpam-4530	271	2	r	r	NOUN
ejpam-4530	271	3	is	be	AUX
ejpam-4530	271	4	a	a	DET
ejpam-4530	271	5	ring	ring	NOUN
ejpam-4530	271	6	with	with	ADP
ejpam-4530	271	7	identity	identity	NOUN
ejpam-4530	271	8	,	,	PUNCT
ejpam-4530	271	9	there	there	PRON
ejpam-4530	271	10	are	be	VERB
ejpam-4530	271	11	two	two	NUM
ejpam-4530	271	12	vertices	vertex	NOUN
ejpam-4530	271	13	(	(	PUNCT
ejpam-4530	271	14	1	1	NUM
ejpam-4530	271	15	,	,	PUNCT
ejpam-4530	271	16	0	0	NUM
ejpam-4530	271	17	)	)	PUNCT
ejpam-4530	271	18	and	and	CCONJ
ejpam-4530	271	19	(	(	PUNCT
ejpam-4530	271	20	−1	−1	NOUN
ejpam-4530	271	21	,	,	PUNCT
ejpam-4530	271	22	0	0	NUM
ejpam-4530	271	23	)	)	PUNCT
ejpam-4530	271	24	belong	belong	VERB
ejpam-4530	271	25	to	to	ADP
ejpam-4530	271	26	v	v	NOUN
ejpam-4530	271	27	(	(	PUNCT
ejpam-4530	271	28	clt(r	clt(r	PROPN
ejpam-4530	271	29	)	)	PUNCT
ejpam-4530	271	30	)	)	PUNCT
ejpam-4530	271	31	.	.	PUNCT
ejpam-4530	272	1	since	since	SCONJ
ejpam-4530	272	2	|clt(r)|	|clt(r)|	ADJ
ejpam-4530	272	3	≥	≥	NOUN
ejpam-4530	272	4	3	3	NUM
ejpam-4530	272	5	,	,	PUNCT
ejpam-4530	272	6	there	there	PRON
ejpam-4530	272	7	is	be	VERB
ejpam-4530	272	8	another	another	DET
ejpam-4530	272	9	vertex	vertex	NOUN
ejpam-4530	272	10	(	(	PUNCT
ejpam-4530	272	11	u	u	NOUN
ejpam-4530	272	12	,	,	PUNCT
ejpam-4530	272	13	t	t	PROPN
ejpam-4530	272	14	)	)	PUNCT
ejpam-4530	272	15	,	,	PUNCT
ejpam-4530	272	16	(	(	PUNCT
ejpam-4530	272	17	u	u	NOUN
ejpam-4530	272	18	,	,	PUNCT
ejpam-4530	272	19	t	t	PROPN
ejpam-4530	272	20	)	)	PUNCT
ejpam-4530	272	21	̸=	̸=	PROPN
ejpam-4530	272	22	(	(	PUNCT
ejpam-4530	272	23	1	1	NUM
ejpam-4530	272	24	,	,	PUNCT
ejpam-4530	272	25	0	0	NUM
ejpam-4530	272	26	)	)	PUNCT
ejpam-4530	272	27	,	,	PUNCT
ejpam-4530	272	28	(	(	PUNCT
ejpam-4530	272	29	−1	−1	NOUN
ejpam-4530	272	30	,	,	PUNCT
ejpam-4530	272	31	0	0	NUM
ejpam-4530	272	32	)	)	PUNCT
ejpam-4530	272	33	such	such	ADJ
ejpam-4530	272	34	that	that	SCONJ
ejpam-4530	272	35	(	(	PUNCT
ejpam-4530	272	36	1	1	NUM
ejpam-4530	272	37	,	,	PUNCT
ejpam-4530	272	38	0	0	NUM
ejpam-4530	272	39	)	)	PUNCT
ejpam-4530	272	40	and	and	CCONJ
ejpam-4530	272	41	(	(	PUNCT
ejpam-4530	272	42	−1	−1	NOUN
ejpam-4530	272	43	,	,	PUNCT
ejpam-4530	272	44	0	0	NUM
ejpam-4530	272	45	)	)	PUNCT
ejpam-4530	272	46	are	be	AUX
ejpam-4530	272	47	adjacent	adjacent	ADJ
ejpam-4530	272	48	to	to	ADP
ejpam-4530	272	49	(	(	PUNCT
ejpam-4530	272	50	u	u	NOUN
ejpam-4530	272	51	,	,	PUNCT
ejpam-4530	272	52	t	t	PROPN
ejpam-4530	272	53	)	)	PUNCT
ejpam-4530	272	54	by	by	ADP
ejpam-4530	272	55	theorem	theorem	NOUN
ejpam-4530	272	56	3.2	3.2	NUM
ejpam-4530	272	57	,	,	PUNCT
ejpam-4530	272	58	also	also	ADV
ejpam-4530	272	59	since	since	SCONJ
ejpam-4530	272	60	(	(	PUNCT
ejpam-4530	272	61	1	1	NUM
ejpam-4530	272	62	,	,	PUNCT
ejpam-4530	272	63	0	0	NUM
ejpam-4530	272	64	)	)	PUNCT
ejpam-4530	272	65	and	and	CCONJ
ejpam-4530	272	66	(	(	PUNCT
ejpam-4530	272	67	−1	−1	NOUN
ejpam-4530	272	68	,	,	PUNCT
ejpam-4530	272	69	0	0	NUM
ejpam-4530	272	70	)	)	PUNCT
ejpam-4530	272	71	are	be	AUX
ejpam-4530	272	72	adjacent	adjacent	ADJ
ejpam-4530	272	73	.	.	PUNCT
ejpam-4530	273	1	hence	hence	ADV
ejpam-4530	273	2	then	then	ADV
ejpam-4530	273	3	g(clt(r	g(clt(r	PROPN
ejpam-4530	273	4	)	)	PUNCT
ejpam-4530	273	5	)	)	PUNCT
ejpam-4530	274	1	=	=	PUNCT
ejpam-4530	274	2	3	3	X
ejpam-4530	274	3	.	.	X
ejpam-4530	274	4	■	■	PUNCT
ejpam-4530	274	5	references	reference	NOUN
ejpam-4530	274	6	1648	1648	NUM
ejpam-4530	274	7	4	4	NUM
ejpam-4530	274	8	.	.	PUNCT
ejpam-4530	274	9	conclusion	conclusion	NOUN
ejpam-4530	274	10	through	through	ADP
ejpam-4530	274	11	this	this	DET
ejpam-4530	274	12	generalization	generalization	NOUN
ejpam-4530	274	13	,	,	PUNCT
ejpam-4530	274	14	14	14	NUM
ejpam-4530	274	15	rings	ring	NOUN
ejpam-4530	274	16	were	be	AUX
ejpam-4530	274	17	obtained	obtain	VERB
ejpam-4530	274	18	in	in	ADP
ejpam-4530	274	19	zn	zn	PROPN
ejpam-4530	274	20	for	for	ADP
ejpam-4530	274	21	invo	invo	PROPN
ejpam-4530	274	22	-	-	PUNCT
ejpam-4530	274	23	t	t	NOUN
ejpam-4530	274	24	-	-	PUNCT
ejpam-4530	274	25	clean	clean	ADJ
ejpam-4530	274	26	rings	ring	NOUN
ejpam-4530	274	27	,	,	PUNCT
ejpam-4530	274	28	but	but	CCONJ
ejpam-4530	274	29	it	it	PRON
ejpam-4530	274	30	was	be	AUX
ejpam-4530	274	31	7	7	NUM
ejpam-4530	274	32	rings	ring	NOUN
ejpam-4530	274	33	when	when	SCONJ
ejpam-4530	274	34	it	it	PRON
ejpam-4530	274	35	be	be	VERB
ejpam-4530	274	36	invo	invo	VERB
ejpam-4530	274	37	-	-	ADJ
ejpam-4530	274	38	clean	clean	ADJ
ejpam-4530	274	39	.	.	PUNCT
ejpam-4530	275	1	also	also	ADV
ejpam-4530	275	2	through	through	ADP
ejpam-4530	275	3	this	this	DET
ejpam-4530	275	4	generalization	generalization	NOUN
ejpam-4530	275	5	we	we	PRON
ejpam-4530	275	6	obtained	obtain	VERB
ejpam-4530	275	7	a	a	DET
ejpam-4530	275	8	representation	representation	NOUN
ejpam-4530	275	9	of	of	ADP
ejpam-4530	275	10	it	it	PRON
ejpam-4530	275	11	in	in	ADP
ejpam-4530	275	12	graph	graph	NOUN
ejpam-4530	275	13	theory	theory	NOUN
ejpam-4530	275	14	with	with	ADP
ejpam-4530	275	15	a	a	DET
ejpam-4530	275	16	study	study	NOUN
ejpam-4530	275	17	of	of	ADP
ejpam-4530	275	18	some	some	DET
ejpam-4530	275	19	properties	property	NOUN
ejpam-4530	275	20	.	.	PUNCT
ejpam-4530	276	1	references	reference	NOUN
ejpam-4530	276	2	[	[	X
ejpam-4530	276	3	1	1	NUM
ejpam-4530	276	4	]	]	X
ejpam-4530	276	5	f.h	f.h	PROPN
ejpam-4530	276	6	.	.	PROPN
ejpam-4530	276	7	abdulqadr	abdulqadr	PROPN
ejpam-4530	276	8	.	.	PUNCT
ejpam-4530	277	1	maximal	maximal	ADJ
ejpam-4530	277	2	ideal	ideal	ADJ
ejpam-4530	277	3	graph	graph	NOUN
ejpam-4530	277	4	of	of	ADP
ejpam-4530	277	5	commutative	commutative	ADJ
ejpam-4530	277	6	rings	ring	NOUN
ejpam-4530	277	7	.	.	PUNCT
ejpam-4530	278	1	iraqi	iraqi	ADJ
ejpam-4530	278	2	journal	journal	PROPN
ejpam-4530	278	3	of	of	ADP
ejpam-4530	278	4	science	science	NOUN
ejpam-4530	278	5	,	,	PUNCT
ejpam-4530	278	6	pages	page	NOUN
ejpam-4530	278	7	2070–2076	2070–2076	NUM
ejpam-4530	278	8	,	,	PUNCT
ejpam-4530	278	9	2020	2020	NUM
ejpam-4530	278	10	.	.	PUNCT
ejpam-4530	279	1	[	[	X
ejpam-4530	279	2	2	2	NUM
ejpam-4530	279	3	]	]	PUNCT
ejpam-4530	279	4	nahid	nahid	PROPN
ejpam-4530	279	5	ashrafi	ashrafi	PROPN
ejpam-4530	279	6	and	and	CCONJ
ejpam-4530	279	7	ebrahim	ebrahim	PROPN
ejpam-4530	279	8	nasibi	nasibi	NOUN
ejpam-4530	279	9	.	.	PUNCT
ejpam-4530	280	1	r	r	X
ejpam-4530	280	2	-	-	PUNCT
ejpam-4530	280	3	clean	clean	ADJ
ejpam-4530	280	4	rings	ring	NOUN
ejpam-4530	280	5	.	.	PUNCT
ejpam-4530	281	1	arxiv	arxiv	PROPN
ejpam-4530	281	2	preprint	preprint	VERB
ejpam-4530	281	3	arxiv:1104.2167	arxiv:1104.2167	ADJ
ejpam-4530	281	4	,	,	PUNCT
ejpam-4530	281	5	pages	page	NOUN
ejpam-4530	281	6	1–7	1–7	NUM
ejpam-4530	281	7	,	,	PUNCT
ejpam-4530	281	8	2011	2011	NUM
ejpam-4530	281	9	.	.	PUNCT
ejpam-4530	282	1	[	[	X
ejpam-4530	282	2	3	3	NUM
ejpam-4530	282	3	]	]	X
ejpam-4530	282	4	mohammed	mohammed	PROPN
ejpam-4530	282	5	authman	authman	PROPN
ejpam-4530	282	6	,	,	PUNCT
ejpam-4530	282	7	husam	husam	NOUN
ejpam-4530	282	8	qmohammad	qmohammad	NOUN
ejpam-4530	282	9	,	,	PUNCT
ejpam-4530	282	10	and	and	CCONJ
ejpam-4530	282	11	nazar	nazar	PROPN
ejpam-4530	282	12	h	h	PROPN
ejpam-4530	282	13	shuker	shuker	PROPN
ejpam-4530	282	14	.	.	PUNCT
ejpam-4530	283	1	vertex	vertex	NOUN
ejpam-4530	283	2	and	and	CCONJ
ejpam-4530	283	3	region	region	NOUN
ejpam-4530	283	4	colorings	coloring	NOUN
ejpam-4530	283	5	of	of	ADP
ejpam-4530	283	6	planar	planar	ADJ
ejpam-4530	283	7	idempotent	idempotent	ADJ
ejpam-4530	283	8	divisor	divisor	NOUN
ejpam-4530	283	9	graphs	graph	NOUN
ejpam-4530	283	10	of	of	ADP
ejpam-4530	283	11	commutative	commutative	ADJ
ejpam-4530	283	12	rings	ring	NOUN
ejpam-4530	283	13	.	.	PUNCT
ejpam-4530	284	1	iraqi	iraqi	ADJ
ejpam-4530	284	2	journal	journal	PROPN
ejpam-4530	284	3	for	for	ADP
ejpam-4530	284	4	computer	computer	NOUN
ejpam-4530	284	5	science	science	NOUN
ejpam-4530	284	6	and	and	CCONJ
ejpam-4530	284	7	mathematics	mathematic	NOUN
ejpam-4530	284	8	,	,	PUNCT
ejpam-4530	284	9	3(1):71–82	3(1):71–82	NUM
ejpam-4530	284	10	,	,	PUNCT
ejpam-4530	284	11	2022	2022	NUM
ejpam-4530	284	12	.	.	PUNCT
ejpam-4530	285	1	[	[	X
ejpam-4530	285	2	4	4	NUM
ejpam-4530	285	3	]	]	PUNCT
ejpam-4530	285	4	istvan	istvan	PROPN
ejpam-4530	285	5	beck	beck	PROPN
ejpam-4530	285	6	.	.	PUNCT
ejpam-4530	286	1	coloring	coloring	NOUN
ejpam-4530	286	2	of	of	ADP
ejpam-4530	286	3	commutative	commutative	ADJ
ejpam-4530	286	4	rings	ring	NOUN
ejpam-4530	286	5	.	.	PUNCT
ejpam-4530	287	1	journal	journal	PROPN
ejpam-4530	287	2	of	of	ADP
ejpam-4530	287	3	algebra	algebra	PROPN
ejpam-4530	287	4	,	,	PUNCT
ejpam-4530	287	5	116(1):208–226	116(1):208–226	NUM
ejpam-4530	287	6	,	,	PUNCT
ejpam-4530	287	7	1988	1988	NUM
ejpam-4530	287	8	.	.	PUNCT
ejpam-4530	288	1	[	[	X
ejpam-4530	288	2	5	5	X
ejpam-4530	288	3	]	]	X
ejpam-4530	288	4	gary	gary	PROPN
ejpam-4530	288	5	chartrand	chartrand	PROPN
ejpam-4530	288	6	,	,	PUNCT
ejpam-4530	288	7	linda	linda	PROPN
ejpam-4530	288	8	lesniak	lesniak	PROPN
ejpam-4530	288	9	,	,	PUNCT
ejpam-4530	288	10	and	and	CCONJ
ejpam-4530	288	11	ping	ping	PROPN
ejpam-4530	288	12	zhang	zhang	PROPN
ejpam-4530	288	13	.	.	PUNCT
ejpam-4530	288	14	graphs	graph	NOUN
ejpam-4530	288	15	&	&	CCONJ
ejpam-4530	288	16	digraphs	digraph	NOUN
ejpam-4530	288	17	.	.	PUNCT
ejpam-4530	289	1	crc	crc	PROPN
ejpam-4530	289	2	press	press	PROPN
ejpam-4530	289	3	,	,	PUNCT
ejpam-4530	289	4	taylor	taylor	PROPN
ejpam-4530	289	5	&	&	CCONJ
ejpam-4530	289	6	francis	francis	PROPN
ejpam-4530	289	7	group	group	PROPN
ejpam-4530	289	8	,	,	PUNCT
ejpam-4530	289	9	2016	2016	NUM
ejpam-4530	289	10	.	.	PUNCT
ejpam-4530	290	1	[	[	X
ejpam-4530	290	2	6	6	NUM
ejpam-4530	290	3	]	]	X
ejpam-4530	290	4	peter	peter	PROPN
ejpam-4530	290	5	v	v	PROPN
ejpam-4530	290	6	danchev	danchev	PROPN
ejpam-4530	290	7	.	.	PUNCT
ejpam-4530	291	1	invo	invo	ADJ
ejpam-4530	291	2	-	-	ADJ
ejpam-4530	291	3	clean	clean	ADJ
ejpam-4530	291	4	unital	unital	ADJ
ejpam-4530	291	5	rings	ring	NOUN
ejpam-4530	291	6	.	.	PUNCT
ejpam-4530	292	1	communications	communication	NOUN
ejpam-4530	292	2	of	of	ADP
ejpam-4530	292	3	the	the	DET
ejpam-4530	292	4	korean	korean	ADJ
ejpam-4530	292	5	mathematical	mathematical	ADJ
ejpam-4530	292	6	society	society	NOUN
ejpam-4530	292	7	,	,	PUNCT
ejpam-4530	292	8	32(1):19–27	32(1):19–27	NUM
ejpam-4530	292	9	,	,	PUNCT
ejpam-4530	292	10	2017	2017	NUM
ejpam-4530	292	11	.	.	PUNCT
ejpam-4530	293	1	[	[	X
ejpam-4530	293	2	7	7	X
ejpam-4530	293	3	]	]	X
ejpam-4530	293	4	i	i	PROPN
ejpam-4530	293	5	gutman	gutman	NOUN
ejpam-4530	293	6	.	.	PUNCT
ejpam-4530	294	1	some	some	DET
ejpam-4530	294	2	properties	property	NOUN
ejpam-4530	294	3	of	of	ADP
ejpam-4530	294	4	the	the	DET
ejpam-4530	294	5	wiener	wiener	NOUN
ejpam-4530	294	6	polynomial	polynomial	NOUN
ejpam-4530	294	7	;	;	PUNCT
ejpam-4530	294	8	graph	graph	NOUN
ejpam-4530	294	9	theory	theory	NOUN
ejpam-4530	294	10	notes	note	NOUN
ejpam-4530	294	11	of	of	ADP
ejpam-4530	294	12	new	new	PROPN
ejpam-4530	294	13	york	york	PROPN
ejpam-4530	294	14	;	;	PUNCT
ejpam-4530	294	15	xxv	xxv	PROPN
ejpam-4530	294	16	,	,	PUNCT
ejpam-4530	294	17	1993	1993	NUM
ejpam-4530	294	18	.	.	PUNCT
ejpam-4530	295	1	[	[	X
ejpam-4530	295	2	8	8	NUM
ejpam-4530	295	3	]	]	X
ejpam-4530	295	4	mohammad	mohammad	PROPN
ejpam-4530	295	5	habibi	habibi	PROPN
ejpam-4530	295	6	,	,	PUNCT
ejpam-4530	295	7	ece	ece	PROPN
ejpam-4530	295	8	yetkın	yetkın	PROPN
ejpam-4530	295	9	çelıkel	çelıkel	PROPN
ejpam-4530	295	10	,	,	PUNCT
ejpam-4530	295	11	and	and	CCONJ
ejpam-4530	295	12	cihat	cihat	ADP
ejpam-4530	295	13	abdıoğlu	abdıoğlu	PROPN
ejpam-4530	295	14	.	.	PUNCT
ejpam-4530	296	1	clean	clean	ADJ
ejpam-4530	296	2	graph	graph	NOUN
ejpam-4530	296	3	of	of	ADP
ejpam-4530	296	4	a	a	DET
ejpam-4530	296	5	ring	ring	NOUN
ejpam-4530	296	6	.	.	PUNCT
ejpam-4530	297	1	journal	journal	PROPN
ejpam-4530	297	2	of	of	ADP
ejpam-4530	297	3	algebra	algebra	PROPN
ejpam-4530	297	4	and	and	CCONJ
ejpam-4530	297	5	its	its	PRON
ejpam-4530	297	6	applications	application	NOUN
ejpam-4530	297	7	,	,	PUNCT
ejpam-4530	297	8	20(09):2150156	20(09):2150156	NUM
ejpam-4530	297	9	,	,	PUNCT
ejpam-4530	297	10	2021	2021	NUM
ejpam-4530	297	11	.	.	PUNCT
ejpam-4530	298	1	[	[	X
ejpam-4530	298	2	9	9	NUM
ejpam-4530	298	3	]	]	SYM
ejpam-4530	298	4	w	w	PROPN
ejpam-4530	298	5	keith	keith	PROPN
ejpam-4530	298	6	nicholson	nicholson	PROPN
ejpam-4530	298	7	.	.	PUNCT
ejpam-4530	299	1	lifting	lift	VERB
ejpam-4530	299	2	idempotents	idempotent	NOUN
ejpam-4530	299	3	and	and	CCONJ
ejpam-4530	299	4	exchange	exchange	NOUN
ejpam-4530	299	5	rings	ring	NOUN
ejpam-4530	299	6	.	.	PUNCT
ejpam-4530	300	1	transactions	transaction	NOUN
ejpam-4530	300	2	of	of	ADP
ejpam-4530	300	3	the	the	DET
ejpam-4530	300	4	american	american	PROPN
ejpam-4530	300	5	mathematical	mathematical	PROPN
ejpam-4530	300	6	society	society	NOUN
ejpam-4530	300	7	,	,	PUNCT
ejpam-4530	300	8	229:269–278	229:269–278	NUM
ejpam-4530	300	9	,	,	PUNCT
ejpam-4530	300	10	1977	1977	NUM
ejpam-4530	300	11	.	.	PUNCT
ejpam-4530	301	1	[	[	X
ejpam-4530	301	2	10	10	NUM
ejpam-4530	301	3	]	]	X
ejpam-4530	301	4	avinash	avinash	PROPN
ejpam-4530	301	5	patil	patil	PROPN
ejpam-4530	301	6	,	,	PUNCT
ejpam-4530	301	7	anil	anil	PROPN
ejpam-4530	301	8	khairnar	khairnar	PROPN
ejpam-4530	301	9	,	,	PUNCT
ejpam-4530	301	10	and	and	CCONJ
ejpam-4530	301	11	ps	ps	NOUN
ejpam-4530	301	12	momale	momale	NOUN
ejpam-4530	301	13	.	.	PUNCT
ejpam-4530	302	1	zero	zero	NUM
ejpam-4530	302	2	-	-	PUNCT
ejpam-4530	302	3	divisor	divisor	NOUN
ejpam-4530	302	4	graph	graph	NOUN
ejpam-4530	302	5	of	of	ADP
ejpam-4530	302	6	a	a	DET
ejpam-4530	302	7	ring	ring	NOUN
ejpam-4530	302	8	with	with	ADP
ejpam-4530	302	9	respect	respect	NOUN
ejpam-4530	302	10	to	to	ADP
ejpam-4530	302	11	an	an	DET
ejpam-4530	302	12	automorphism	automorphism	NOUN
ejpam-4530	302	13	.	.	PUNCT
ejpam-4530	303	1	soft	soft	ADJ
ejpam-4530	303	2	computing	computing	NOUN
ejpam-4530	303	3	,	,	PUNCT
ejpam-4530	303	4	26(5):2107–2119	26(5):2107–2119	NUM
ejpam-4530	303	5	,	,	PUNCT
ejpam-4530	303	6	2022	2022	NUM
ejpam-4530	303	7	.	.	PUNCT
ejpam-4530	304	1	[	[	X
ejpam-4530	304	2	11	11	NUM
ejpam-4530	304	3	]	]	PUNCT
ejpam-4530	304	4	john	john	PROPN
ejpam-4530	304	5	von	von	PROPN
ejpam-4530	304	6	neumann	neumann	PROPN
ejpam-4530	304	7	.	.	PUNCT
ejpam-4530	305	1	on	on	ADP
ejpam-4530	305	2	regular	regular	ADJ
ejpam-4530	305	3	rings	ring	NOUN
ejpam-4530	305	4	.	.	PUNCT
ejpam-4530	306	1	proceedings	proceeding	NOUN
ejpam-4530	306	2	of	of	ADP
ejpam-4530	306	3	the	the	DET
ejpam-4530	306	4	national	national	PROPN
ejpam-4530	306	5	academy	academy	PROPN
ejpam-4530	306	6	of	of	ADP
ejpam-4530	306	7	sciences	sciences	PROPN
ejpam-4530	306	8	,	,	PUNCT
ejpam-4530	306	9	22(12):707–713	22(12):707–713	NUM
ejpam-4530	306	10	,	,	PUNCT
ejpam-4530	306	11	1936	1936	NUM
ejpam-4530	306	12	.	.	PUNCT
ejpam-4530	307	1	[	[	X
ejpam-4530	307	2	12	12	NUM
ejpam-4530	307	3	]	]	X
ejpam-4530	307	4	harry	harry	PROPN
ejpam-4530	307	5	wiener	wiener	PROPN
ejpam-4530	307	6	.	.	PUNCT
ejpam-4530	308	1	structural	structural	ADJ
ejpam-4530	308	2	determination	determination	NOUN
ejpam-4530	308	3	of	of	ADP
ejpam-4530	308	4	paraffin	paraffin	NOUN
ejpam-4530	308	5	boiling	boiling	NOUN
ejpam-4530	308	6	points	point	NOUN
ejpam-4530	308	7	.	.	PUNCT
ejpam-4530	309	1	journal	journal	NOUN
ejpam-4530	309	2	of	of	ADP
ejpam-4530	309	3	the	the	DET
ejpam-4530	309	4	american	american	PROPN
ejpam-4530	309	5	chemical	chemical	PROPN
ejpam-4530	309	6	society	society	PROPN
ejpam-4530	309	7	,	,	PUNCT
ejpam-4530	309	8	69(1):17–20	69(1):17–20	NUM
ejpam-4530	309	9	,	,	PUNCT
ejpam-4530	309	10	1947	1947	NUM
ejpam-4530	309	11	.	.	PUNCT