id	sid	tid	token	lemma	pos
ejpam-3123	1	1	european	european	PROPN
ejpam-3123	1	2	journal	journal	PROPN
ejpam-3123	1	3	of	of	ADP
ejpam-3123	1	4	pure	pure	ADJ
ejpam-3123	1	5	and	and	CCONJ
ejpam-3123	1	6	applied	apply	VERB
ejpam-3123	1	7	mathematics	mathematic	NOUN
ejpam-3123	1	8	vol	vol	NOUN
ejpam-3123	1	9	.	.	PROPN
ejpam-3123	2	1	10	10	NUM
ejpam-3123	2	2	,	,	PUNCT
ejpam-3123	2	3	no	no	INTJ
ejpam-3123	2	4	.	.	NOUN
ejpam-3123	2	5	5	5	NUM
ejpam-3123	2	6	,	,	PUNCT
ejpam-3123	2	7	2017	2017	NUM
ejpam-3123	2	8	,	,	PUNCT
ejpam-3123	2	9	967	967	NUM
ejpam-3123	2	10	-	-	SYM
ejpam-3123	2	11	980	980	NUM
ejpam-3123	2	12	issn	issn	PROPN
ejpam-3123	2	13	1307	1307	NUM
ejpam-3123	2	14	-	-	SYM
ejpam-3123	2	15	5543	5543	NUM
ejpam-3123	2	16	–	–	PUNCT
ejpam-3123	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3123	2	18	published	publish	VERB
ejpam-3123	2	19	by	by	ADP
ejpam-3123	2	20	new	new	PROPN
ejpam-3123	2	21	york	york	PROPN
ejpam-3123	2	22	business	business	PROPN
ejpam-3123	2	23	global	global	ADJ
ejpam-3123	2	24	on	on	ADP
ejpam-3123	2	25	weak	weak	ADJ
ejpam-3123	2	26	graded	grade	VERB
ejpam-3123	2	27	rings	ring	NOUN
ejpam-3123	2	28	najla	najla	PROPN
ejpam-3123	2	29	al	al	PROPN
ejpam-3123	2	30	-	-	PUNCT
ejpam-3123	2	31	subaie1	subaie1	PROPN
ejpam-3123	2	32	,	,	PUNCT
ejpam-3123	2	33	m.	m.	NOUN
ejpam-3123	2	34	m.	m.	NOUN
ejpam-3123	2	35	al	al	PROPN
ejpam-3123	2	36	-	-	PUNCT
ejpam-3123	2	37	shomrani	shomrani	ADJ
ejpam-3123	2	38	2,∗	2,∗	NUM
ejpam-3123	2	39	1	1	NUM
ejpam-3123	2	40	department	department	NOUN
ejpam-3123	2	41	of	of	ADP
ejpam-3123	2	42	mathematics	mathematics	PROPN
ejpam-3123	2	43	,	,	PUNCT
ejpam-3123	2	44	taif	taif	PROPN
ejpam-3123	2	45	university	university	PROPN
ejpam-3123	2	46	,	,	PUNCT
ejpam-3123	2	47	taif	taif	PROPN
ejpam-3123	2	48	,	,	PUNCT
ejpam-3123	2	49	saudi	saudi	PROPN
ejpam-3123	2	50	arabia	arabia	PROPN
ejpam-3123	2	51	2	2	NUM
ejpam-3123	2	52	department	department	NOUN
ejpam-3123	2	53	of	of	ADP
ejpam-3123	2	54	mathematics	mathematic	NOUN
ejpam-3123	2	55	,	,	PUNCT
ejpam-3123	2	56	king	king	PROPN
ejpam-3123	2	57	abdulaziz	abdulaziz	PROPN
ejpam-3123	2	58	university	university	PROPN
ejpam-3123	2	59	,	,	PUNCT
ejpam-3123	2	60	jeddah	jeddah	PROPN
ejpam-3123	2	61	,	,	PUNCT
ejpam-3123	2	62	saudi	saudi	PROPN
ejpam-3123	2	63	arabia	arabia	PROPN
ejpam-3123	2	64	abstract	abstract	NOUN
ejpam-3123	2	65	.	.	PUNCT
ejpam-3123	3	1	in	in	ADP
ejpam-3123	3	2	this	this	DET
ejpam-3123	3	3	paper	paper	NOUN
ejpam-3123	3	4	,	,	PUNCT
ejpam-3123	3	5	we	we	PRON
ejpam-3123	3	6	investigate	investigate	VERB
ejpam-3123	3	7	some	some	DET
ejpam-3123	3	8	properties	property	NOUN
ejpam-3123	3	9	of	of	ADP
ejpam-3123	3	10	weak	weak	ADJ
ejpam-3123	3	11	graded	grade	VERB
ejpam-3123	3	12	rings	ring	NOUN
ejpam-3123	3	13	that	that	PRON
ejpam-3123	3	14	are	be	AUX
ejpam-3123	3	15	rings	ring	NOUN
ejpam-3123	3	16	graded	grade	VERB
ejpam-3123	3	17	by	by	ADP
ejpam-3123	3	18	a	a	DET
ejpam-3123	3	19	set	set	NOUN
ejpam-3123	3	20	g	g	NOUN
ejpam-3123	3	21	of	of	ADP
ejpam-3123	3	22	coset	coset	NOUN
ejpam-3123	3	23	representatives	representative	NOUN
ejpam-3123	3	24	for	for	ADP
ejpam-3123	3	25	the	the	DET
ejpam-3123	3	26	left	left	ADJ
ejpam-3123	3	27	action	action	NOUN
ejpam-3123	3	28	of	of	ADP
ejpam-3123	3	29	a	a	DET
ejpam-3123	3	30	subgroup	subgroup	NOUN
ejpam-3123	3	31	h	h	NOUN
ejpam-3123	3	32	on	on	ADP
ejpam-3123	3	33	a	a	DET
ejpam-3123	3	34	group	group	NOUN
ejpam-3123	3	35	x.	x.	NOUN
ejpam-3123	3	36	moreover	moreover	ADV
ejpam-3123	3	37	,	,	PUNCT
ejpam-3123	3	38	a	a	DET
ejpam-3123	3	39	graded	grade	VERB
ejpam-3123	3	40	rings	ring	NOUN
ejpam-3123	3	41	by	by	ADP
ejpam-3123	3	42	using	use	VERB
ejpam-3123	3	43	the	the	DET
ejpam-3123	3	44	product	product	NOUN
ejpam-3123	3	45	h	h	NOUN
ejpam-3123	3	46	×g	×g	NOUN
ejpam-3123	3	47	are	be	AUX
ejpam-3123	3	48	also	also	ADV
ejpam-3123	3	49	discussed	discuss	VERB
ejpam-3123	3	50	.	.	PUNCT
ejpam-3123	4	1	a	a	DET
ejpam-3123	4	2	detailed	detailed	ADJ
ejpam-3123	4	3	example	example	NOUN
ejpam-3123	4	4	is	be	AUX
ejpam-3123	4	5	given	give	VERB
ejpam-3123	4	6	.	.	PUNCT
ejpam-3123	5	1	2010	2010	NUM
ejpam-3123	5	2	mathematics	mathematic	NOUN
ejpam-3123	5	3	subject	subject	NOUN
ejpam-3123	5	4	classifications	classification	NOUN
ejpam-3123	5	5	:	:	PUNCT
ejpam-3123	5	6	16w50	16w50	NUM
ejpam-3123	5	7	,	,	PUNCT
ejpam-3123	5	8	13a02	13a02	NUM
ejpam-3123	5	9	,	,	PUNCT
ejpam-3123	5	10	16d25	16d25	NUM
ejpam-3123	5	11	.	.	PUNCT
ejpam-3123	6	1	key	key	ADJ
ejpam-3123	6	2	words	word	NOUN
ejpam-3123	6	3	and	and	CCONJ
ejpam-3123	6	4	phrases	phrase	NOUN
ejpam-3123	6	5	:	:	PUNCT
ejpam-3123	6	6	weak	weak	ADJ
ejpam-3123	6	7	graded	grade	VERB
ejpam-3123	6	8	rings	ring	NOUN
ejpam-3123	6	9	,	,	PUNCT
ejpam-3123	6	10	fully	fully	ADV
ejpam-3123	6	11	graded	grade	VERB
ejpam-3123	6	12	rings	ring	NOUN
ejpam-3123	6	13	,	,	PUNCT
ejpam-3123	6	14	left	leave	VERB
ejpam-3123	6	15	coset	coset	NOUN
ejpam-3123	6	16	representatives	representative	NOUN
ejpam-3123	6	17	.	.	PUNCT
ejpam-3123	7	1	1	1	X
ejpam-3123	7	2	.	.	X
ejpam-3123	7	3	introduction	introduction	NOUN
ejpam-3123	7	4	let	let	VERB
ejpam-3123	7	5	r	r	PRON
ejpam-3123	7	6	be	be	AUX
ejpam-3123	7	7	an	an	DET
ejpam-3123	7	8	associative	associative	ADJ
ejpam-3123	7	9	ring	ring	NOUN
ejpam-3123	7	10	and	and	CCONJ
ejpam-3123	7	11	g	g	NOUN
ejpam-3123	7	12	be	be	AUX
ejpam-3123	7	13	a	a	DET
ejpam-3123	7	14	semigroup	semigroup	NOUN
ejpam-3123	7	15	.	.	PUNCT
ejpam-3123	8	1	recall	recall	NOUN
ejpam-3123	8	2	that	that	SCONJ
ejpam-3123	8	3	r	r	NOUN
ejpam-3123	8	4	is	be	AUX
ejpam-3123	8	5	called	call	VERB
ejpam-3123	8	6	g	g	NOUN
ejpam-3123	8	7	-	-	PUNCT
ejpam-3123	8	8	graded	grade	VERB
ejpam-3123	8	9	if	if	SCONJ
ejpam-3123	8	10	there	there	PRON
ejpam-3123	8	11	is	be	VERB
ejpam-3123	8	12	an	an	DET
ejpam-3123	8	13	additive	additive	ADJ
ejpam-3123	8	14	subgroup	subgroup	NOUN
ejpam-3123	8	15	rg	rg	PROPN
ejpam-3123	8	16	of	of	ADP
ejpam-3123	8	17	r	r	PROPN
ejpam-3123	8	18	,	,	PUNCT
ejpam-3123	8	19	for	for	ADP
ejpam-3123	8	20	each	each	DET
ejpam-3123	8	21	g	g	PROPN
ejpam-3123	8	22	∈	∈	PROPN
ejpam-3123	8	23	g	g	NOUN
ejpam-3123	8	24	,	,	PUNCT
ejpam-3123	8	25	such	such	ADJ
ejpam-3123	8	26	that	that	SCONJ
ejpam-3123	8	27	r	r	NOUN
ejpam-3123	8	28	=	=	SYM
ejpam-3123	8	29	⊕	⊕	PROPN
ejpam-3123	8	30	g∈grg	g∈grg	PROPN
ejpam-3123	8	31	and	and	CCONJ
ejpam-3123	8	32	the	the	DET
ejpam-3123	8	33	inclusion	inclusion	NOUN
ejpam-3123	8	34	property	property	NOUN
ejpam-3123	8	35	rgrh	rgrh	NOUN
ejpam-3123	8	36	⊆	⊆	PROPN
ejpam-3123	8	37	rgh	rgh	PROPN
ejpam-3123	8	38	is	be	AUX
ejpam-3123	8	39	satisfied	satisfied	ADJ
ejpam-3123	8	40	for	for	ADP
ejpam-3123	8	41	all	all	DET
ejpam-3123	8	42	g	g	NOUN
ejpam-3123	8	43	,	,	PUNCT
ejpam-3123	8	44	h	h	PROPN
ejpam-3123	8	45	∈	∈	PROPN
ejpam-3123	8	46	g.	g.	PROPN
ejpam-3123	8	47	semigroup	semigroup	PROPN
ejpam-3123	8	48	graded	grade	VERB
ejpam-3123	8	49	rings	ring	NOUN
ejpam-3123	8	50	and	and	CCONJ
ejpam-3123	8	51	modules	module	NOUN
ejpam-3123	8	52	as	as	ADV
ejpam-3123	8	53	well	well	ADV
ejpam-3123	8	54	as	as	ADP
ejpam-3123	8	55	a	a	DET
ejpam-3123	8	56	lot	lot	NOUN
ejpam-3123	8	57	of	of	ADP
ejpam-3123	8	58	their	their	PRON
ejpam-3123	8	59	properties	property	NOUN
ejpam-3123	8	60	were	be	AUX
ejpam-3123	8	61	investigated	investigate	VERB
ejpam-3123	8	62	by	by	ADP
ejpam-3123	8	63	many	many	ADJ
ejpam-3123	8	64	mathematicians	mathematician	NOUN
ejpam-3123	8	65	,	,	PUNCT
ejpam-3123	8	66	see	see	VERB
ejpam-3123	8	67	for	for	ADP
ejpam-3123	8	68	example	example	NOUN
ejpam-3123	8	69	[	[	X
ejpam-3123	8	70	1	1	NUM
ejpam-3123	8	71	]	]	PUNCT
ejpam-3123	8	72	,	,	PUNCT
ejpam-3123	8	73	[	[	X
ejpam-3123	8	74	7	7	NUM
ejpam-3123	8	75	]	]	PUNCT
ejpam-3123	8	76	,	,	PUNCT
ejpam-3123	8	77	[	[	X
ejpam-3123	8	78	10	10	NUM
ejpam-3123	8	79	]	]	PUNCT
ejpam-3123	8	80	,	,	PUNCT
ejpam-3123	8	81	[	[	X
ejpam-3123	8	82	11	11	NUM
ejpam-3123	8	83	]	]	PUNCT
ejpam-3123	8	84	,	,	PUNCT
ejpam-3123	8	85	[	[	X
ejpam-3123	8	86	12	12	NUM
ejpam-3123	8	87	]	]	PUNCT
ejpam-3123	8	88	,	,	PUNCT
ejpam-3123	8	89	[	[	X
ejpam-3123	8	90	13	13	NUM
ejpam-3123	8	91	]	]	PUNCT
ejpam-3123	8	92	and	and	CCONJ
ejpam-3123	8	93	[	[	X
ejpam-3123	8	94	15	15	NUM
ejpam-3123	8	95	]	]	PUNCT
ejpam-3123	8	96	.	.	PUNCT
ejpam-3123	9	1	the	the	DET
ejpam-3123	9	2	construction	construction	NOUN
ejpam-3123	9	3	of	of	ADP
ejpam-3123	9	4	group	group	NOUN
ejpam-3123	9	5	graded	grade	VERB
ejpam-3123	9	6	rings	ring	NOUN
ejpam-3123	9	7	and	and	CCONJ
ejpam-3123	9	8	their	their	PRON
ejpam-3123	9	9	modules	module	NOUN
ejpam-3123	9	10	were	be	AUX
ejpam-3123	9	11	deeply	deeply	ADV
ejpam-3123	9	12	studied	study	VERB
ejpam-3123	9	13	by	by	ADP
ejpam-3123	9	14	dade	dade	NOUN
ejpam-3123	9	15	in	in	ADP
ejpam-3123	9	16	[	[	X
ejpam-3123	9	17	6	6	NUM
ejpam-3123	9	18	]	]	PUNCT
ejpam-3123	9	19	that	that	PRON
ejpam-3123	9	20	enriched	enrich	VERB
ejpam-3123	9	21	and	and	CCONJ
ejpam-3123	9	22	extended	extend	VERB
ejpam-3123	9	23	the	the	DET
ejpam-3123	9	24	concept	concept	NOUN
ejpam-3123	9	25	of	of	ADP
ejpam-3123	9	26	the	the	DET
ejpam-3123	9	27	classical	classical	ADJ
ejpam-3123	9	28	stable	stable	ADJ
ejpam-3123	9	29	clifford	clifford	PROPN
ejpam-3123	9	30	theory	theory	NOUN
ejpam-3123	9	31	.	.	PUNCT
ejpam-3123	10	1	the	the	DET
ejpam-3123	10	2	work	work	NOUN
ejpam-3123	10	3	of	of	ADP
ejpam-3123	10	4	dade	dade	PROPN
ejpam-3123	10	5	was	be	AUX
ejpam-3123	10	6	an	an	DET
ejpam-3123	10	7	initial	initial	ADJ
ejpam-3123	10	8	source	source	NOUN
ejpam-3123	10	9	for	for	ADP
ejpam-3123	10	10	many	many	ADJ
ejpam-3123	10	11	researchers	researcher	NOUN
ejpam-3123	10	12	who	who	PRON
ejpam-3123	10	13	were	be	AUX
ejpam-3123	10	14	interested	interested	ADJ
ejpam-3123	10	15	in	in	ADP
ejpam-3123	10	16	the	the	DET
ejpam-3123	10	17	field	field	NOUN
ejpam-3123	10	18	of	of	ADP
ejpam-3123	10	19	group	group	NOUN
ejpam-3123	10	20	graded	grade	VERB
ejpam-3123	10	21	rings	ring	NOUN
ejpam-3123	10	22	and	and	CCONJ
ejpam-3123	10	23	their	their	PRON
ejpam-3123	10	24	modules	module	NOUN
ejpam-3123	10	25	,	,	PUNCT
ejpam-3123	10	26	see	see	VERB
ejpam-3123	10	27	for	for	ADP
ejpam-3123	10	28	exampl	exampl	NOUN
ejpam-3123	10	29	[	[	X
ejpam-3123	10	30	5	5	NUM
ejpam-3123	10	31	]	]	PUNCT
ejpam-3123	10	32	,	,	PUNCT
ejpam-3123	10	33	[	[	X
ejpam-3123	10	34	8	8	NUM
ejpam-3123	10	35	]	]	PUNCT
ejpam-3123	10	36	and	and	CCONJ
ejpam-3123	10	37	[	[	X
ejpam-3123	10	38	9	9	NUM
ejpam-3123	10	39	]	]	PUNCT
ejpam-3123	10	40	.	.	PUNCT
ejpam-3123	11	1	in	in	ADP
ejpam-3123	11	2	[	[	X
ejpam-3123	11	3	4	4	NUM
ejpam-3123	11	4	]	]	PUNCT
ejpam-3123	11	5	,	,	PUNCT
ejpam-3123	11	6	beggs	beggs	PROPN
ejpam-3123	11	7	form	form	VERB
ejpam-3123	11	8	a	a	DET
ejpam-3123	11	9	set	set	NOUN
ejpam-3123	11	10	g	g	NOUN
ejpam-3123	11	11	of	of	ADP
ejpam-3123	11	12	left	left	ADJ
ejpam-3123	11	13	coset	coset	NOUN
ejpam-3123	11	14	representatives	representative	NOUN
ejpam-3123	11	15	for	for	ADP
ejpam-3123	11	16	the	the	DET
ejpam-3123	11	17	left	left	ADJ
ejpam-3123	11	18	action	action	NOUN
ejpam-3123	11	19	of	of	ADP
ejpam-3123	11	20	a	a	DET
ejpam-3123	11	21	subgroup	subgroup	NOUN
ejpam-3123	11	22	h	h	NOUN
ejpam-3123	11	23	on	on	ADP
ejpam-3123	11	24	a	a	DET
ejpam-3123	11	25	group	group	NOUN
ejpam-3123	11	26	x	x	PUNCT
ejpam-3123	11	27	and	and	CCONJ
ejpam-3123	11	28	defined	define	VERB
ejpam-3123	11	29	a	a	DET
ejpam-3123	11	30	binary	binary	ADJ
ejpam-3123	11	31	operation	operation	NOUN
ejpam-3123	11	32	on	on	ADP
ejpam-3123	11	33	g	g	PROPN
ejpam-3123	11	34	which	which	PRON
ejpam-3123	11	35	has	have	VERB
ejpam-3123	11	36	a	a	DET
ejpam-3123	11	37	left	left	ADJ
ejpam-3123	11	38	identity	identity	NOUN
ejpam-3123	11	39	and	and	CCONJ
ejpam-3123	11	40	the	the	DET
ejpam-3123	11	41	right	right	ADJ
ejpam-3123	11	42	division	division	NOUN
ejpam-3123	11	43	property	property	NOUN
ejpam-3123	11	44	.	.	PUNCT
ejpam-3123	12	1	this	this	DET
ejpam-3123	12	2	binary	binary	ADJ
ejpam-3123	12	3	operation	operation	NOUN
ejpam-3123	12	4	is	be	AUX
ejpam-3123	12	5	not	not	PART
ejpam-3123	12	6	associative	associative	ADJ
ejpam-3123	12	7	,	,	PUNCT
ejpam-3123	12	8	but	but	CCONJ
ejpam-3123	12	9	the	the	DET
ejpam-3123	12	10	associativity	associativity	NOUN
ejpam-3123	12	11	can	can	AUX
ejpam-3123	12	12	be	be	AUX
ejpam-3123	12	13	obtained	obtain	VERB
ejpam-3123	12	14	by	by	ADP
ejpam-3123	12	15	a	a	DET
ejpam-3123	12	16	”	"	PUNCT
ejpam-3123	12	17	cocycle	cocycle	NOUN
ejpam-3123	12	18	”	"	PUNCT
ejpam-3123	12	19	f	f	NOUN
ejpam-3123	12	20	:	:	PUNCT
ejpam-3123	12	21	g×g	g×g	VERB
ejpam-3123	12	22	−→	−→	NOUN
ejpam-3123	12	23	h.	h.	NOUN
ejpam-3123	12	24	in	in	ADP
ejpam-3123	12	25	[	[	X
ejpam-3123	12	26	2	2	NUM
ejpam-3123	12	27	]	]	PUNCT
ejpam-3123	12	28	,	,	PUNCT
ejpam-3123	12	29	a	a	DET
ejpam-3123	12	30	new	new	ADJ
ejpam-3123	12	31	concept	concept	NOUN
ejpam-3123	12	32	named	name	VERB
ejpam-3123	12	33	the	the	DET
ejpam-3123	12	34	weak	weak	ADJ
ejpam-3123	12	35	graded	grade	VERB
ejpam-3123	12	36	rings	ring	NOUN
ejpam-3123	12	37	and	and	CCONJ
ejpam-3123	12	38	modules	module	NOUN
ejpam-3123	12	39	were	be	AUX
ejpam-3123	12	40	introduced	introduce	VERB
ejpam-3123	12	41	.	.	PUNCT
ejpam-3123	13	1	in	in	ADP
ejpam-3123	13	2	more	more	ADJ
ejpam-3123	13	3	details	detail	NOUN
ejpam-3123	13	4	,	,	PUNCT
ejpam-3123	13	5	a	a	DET
ejpam-3123	13	6	graded	grade	VERB
ejpam-3123	13	7	ring	ring	NOUN
ejpam-3123	13	8	r	r	NOUN
ejpam-3123	13	9	were	be	AUX
ejpam-3123	13	10	constructed	construct	VERB
ejpam-3123	13	11	using	use	VERB
ejpam-3123	13	12	a	a	DET
ejpam-3123	13	13	set	set	NOUN
ejpam-3123	13	14	g	g	NOUN
ejpam-3123	13	15	of	of	ADP
ejpam-3123	13	16	left	left	ADJ
ejpam-3123	13	17	coset	coset	NOUN
ejpam-3123	13	18	representatives	representative	NOUN
ejpam-3123	13	19	and	and	CCONJ
ejpam-3123	13	20	some	some	DET
ejpam-3123	13	21	results	result	NOUN
ejpam-3123	13	22	were	be	AUX
ejpam-3123	13	23	proved	prove	VERB
ejpam-3123	13	24	in	in	ADP
ejpam-3123	13	25	the	the	DET
ejpam-3123	13	26	new	new	ADJ
ejpam-3123	13	27	setting	setting	NOUN
ejpam-3123	13	28	.	.	PUNCT
ejpam-3123	14	1	in	in	ADP
ejpam-3123	14	2	addition	addition	NOUN
ejpam-3123	14	3	,	,	PUNCT
ejpam-3123	14	4	some	some	DET
ejpam-3123	14	5	properties	property	NOUN
ejpam-3123	14	6	of	of	ADP
ejpam-3123	14	7	these	these	DET
ejpam-3123	14	8	graded	grade	VERB
ejpam-3123	14	9	rings	ring	NOUN
ejpam-3123	14	10	and	and	CCONJ
ejpam-3123	14	11	their	their	PRON
ejpam-3123	14	12	modules	module	NOUN
ejpam-3123	14	13	were	be	AUX
ejpam-3123	14	14	derived	derive	VERB
ejpam-3123	14	15	.	.	PUNCT
ejpam-3123	15	1	in	in	ADP
ejpam-3123	15	2	this	this	DET
ejpam-3123	15	3	paper	paper	NOUN
ejpam-3123	15	4	,	,	PUNCT
ejpam-3123	15	5	some	some	DET
ejpam-3123	15	6	properties	property	NOUN
ejpam-3123	15	7	of	of	ADP
ejpam-3123	15	8	weak	weak	ADJ
ejpam-3123	15	9	graded	grade	VERB
ejpam-3123	15	10	rings	ring	NOUN
ejpam-3123	15	11	,	,	PUNCT
ejpam-3123	15	12	that	that	PRON
ejpam-3123	15	13	are	be	AUX
ejpam-3123	15	14	rings	ring	NOUN
ejpam-3123	15	15	graded	grade	VERB
ejpam-3123	15	16	by	by	ADP
ejpam-3123	15	17	a	a	DET
ejpam-3123	15	18	set	set	NOUN
ejpam-3123	15	19	g	g	NOUN
ejpam-3123	15	20	of	of	ADP
ejpam-3123	15	21	coset	coset	NOUN
ejpam-3123	15	22	representatives	representative	NOUN
ejpam-3123	15	23	for	for	ADP
ejpam-3123	15	24	the	the	DET
ejpam-3123	15	25	left	left	ADJ
ejpam-3123	15	26	action	action	NOUN
ejpam-3123	15	27	of	of	ADP
ejpam-3123	15	28	a	a	DET
ejpam-3123	15	29	subgroup	subgroup	NOUN
ejpam-3123	15	30	h	h	NOUN
ejpam-3123	15	31	on	on	ADP
ejpam-3123	15	32	a	a	DET
ejpam-3123	15	33	group	group	NOUN
ejpam-3123	15	34	x	x	NOUN
ejpam-3123	15	35	,	,	PUNCT
ejpam-3123	15	36	are	be	AUX
ejpam-3123	15	37	investigated	investigate	VERB
ejpam-3123	15	38	.	.	PUNCT
ejpam-3123	16	1	∗corresponding	∗corresponde	VERB
ejpam-3123	16	2	author	author	NOUN
ejpam-3123	16	3	.	.	PUNCT
ejpam-3123	17	1	email	email	NOUN
ejpam-3123	17	2	addresses	address	NOUN
ejpam-3123	17	3	:	:	PUNCT
ejpam-3123	17	4	njlalsubaie@gmail.com	njlalsubaie@gmail.com	PROPN
ejpam-3123	17	5	(	(	PUNCT
ejpam-3123	17	6	n.	n.	PROPN
ejpam-3123	17	7	al	al	PROPN
ejpam-3123	17	8	-	-	PUNCT
ejpam-3123	17	9	subaie	subaie	NOUN
ejpam-3123	17	10	)	)	PUNCT
ejpam-3123	17	11	,	,	PUNCT
ejpam-3123	17	12	malshomrani@hotmail.com	malshomrani@hotmail.com	X
ejpam-3123	17	13	(	(	PUNCT
ejpam-3123	17	14	m.	m.	PROPN
ejpam-3123	17	15	al	al	PROPN
ejpam-3123	17	16	-	-	PUNCT
ejpam-3123	17	17	shomrani	shomrani	PROPN
ejpam-3123	17	18	)	)	PUNCT
ejpam-3123	17	19	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3123	18	1	967	967	NUM
ejpam-3123	18	2	c	c	X
ejpam-3123	18	3	©	©	PROPN
ejpam-3123	18	4	2017	2017	NUM
ejpam-3123	18	5	ejpam	ejpam	NOUN
ejpam-3123	18	6	all	all	DET
ejpam-3123	18	7	rights	right	NOUN
ejpam-3123	18	8	reserved	reserve	VERB
ejpam-3123	18	9	.	.	PUNCT
ejpam-3123	19	1	n.	n.	PROPN
ejpam-3123	19	2	al	al	PROPN
ejpam-3123	19	3	-	-	PUNCT
ejpam-3123	19	4	subaie	subaie	NOUN
ejpam-3123	19	5	,	,	PUNCT
ejpam-3123	19	6	m.	m.	NOUN
ejpam-3123	19	7	m.	m.	PROPN
ejpam-3123	19	8	al	al	PROPN
ejpam-3123	19	9	-	-	PUNCT
ejpam-3123	19	10	shomrani	shomrani	PROPN
ejpam-3123	19	11	/	/	SYM
ejpam-3123	19	12	eur	eur	NOUN
ejpam-3123	19	13	.	.	PUNCT
ejpam-3123	20	1	j.	j.	PROPN
ejpam-3123	20	2	pure	pure	PROPN
ejpam-3123	20	3	appl	appl	PROPN
ejpam-3123	20	4	.	.	PROPN
ejpam-3123	20	5	math	math	PROPN
ejpam-3123	20	6	,	,	PUNCT
ejpam-3123	20	7	10	10	NUM
ejpam-3123	20	8	(	(	PUNCT
ejpam-3123	20	9	5	5	NUM
ejpam-3123	20	10	)	)	PUNCT
ejpam-3123	20	11	(	(	PUNCT
ejpam-3123	20	12	2017	2017	NUM
ejpam-3123	20	13	)	)	PUNCT
ejpam-3123	20	14	,	,	PUNCT
ejpam-3123	20	15	967	967	NUM
ejpam-3123	20	16	-	-	SYM
ejpam-3123	20	17	980	980	NUM
ejpam-3123	20	18	968	968	NUM
ejpam-3123	20	19	moreover	moreover	ADV
ejpam-3123	20	20	a	a	DET
ejpam-3123	20	21	graded	grade	VERB
ejpam-3123	20	22	rings	ring	NOUN
ejpam-3123	20	23	by	by	ADP
ejpam-3123	20	24	using	use	VERB
ejpam-3123	20	25	the	the	DET
ejpam-3123	20	26	product	product	NOUN
ejpam-3123	20	27	h	h	NOUN
ejpam-3123	20	28	×g	×g	NOUN
ejpam-3123	20	29	are	be	AUX
ejpam-3123	20	30	also	also	ADV
ejpam-3123	20	31	discussed	discuss	VERB
ejpam-3123	20	32	.	.	PUNCT
ejpam-3123	21	1	a	a	DET
ejpam-3123	21	2	detailed	detailed	ADJ
ejpam-3123	21	3	example	example	NOUN
ejpam-3123	21	4	is	be	AUX
ejpam-3123	21	5	given	give	VERB
ejpam-3123	21	6	.	.	PUNCT
ejpam-3123	22	1	throughout	throughout	ADP
ejpam-3123	22	2	this	this	DET
ejpam-3123	22	3	paper	paper	NOUN
ejpam-3123	22	4	,	,	PUNCT
ejpam-3123	22	5	for	for	ADP
ejpam-3123	22	6	the	the	DET
ejpam-3123	22	7	sake	sake	NOUN
ejpam-3123	22	8	of	of	ADP
ejpam-3123	22	9	simplicity	simplicity	NOUN
ejpam-3123	22	10	,	,	PUNCT
ejpam-3123	22	11	it	it	PRON
ejpam-3123	22	12	is	be	AUX
ejpam-3123	22	13	assumed	assume	VERB
ejpam-3123	22	14	that	that	SCONJ
ejpam-3123	22	15	all	all	DET
ejpam-3123	22	16	rings	ring	NOUN
ejpam-3123	22	17	are	be	AUX
ejpam-3123	22	18	associative	associative	ADJ
ejpam-3123	22	19	,	,	PUNCT
ejpam-3123	22	20	commutative	commutative	ADJ
ejpam-3123	22	21	and	and	CCONJ
ejpam-3123	22	22	with	with	ADP
ejpam-3123	22	23	unities	unity	NOUN
ejpam-3123	22	24	,	,	PUNCT
ejpam-3123	22	25	although	although	SCONJ
ejpam-3123	22	26	for	for	ADP
ejpam-3123	22	27	many	many	ADJ
ejpam-3123	22	28	results	result	NOUN
ejpam-3123	22	29	associative	associative	ADJ
ejpam-3123	22	30	rings	ring	NOUN
ejpam-3123	22	31	are	be	AUX
ejpam-3123	22	32	only	only	ADV
ejpam-3123	22	33	required	require	VERB
ejpam-3123	22	34	.	.	PUNCT
ejpam-3123	23	1	2	2	X
ejpam-3123	23	2	.	.	X
ejpam-3123	23	3	preliminaries	preliminary	NOUN
ejpam-3123	23	4	in	in	ADP
ejpam-3123	23	5	this	this	DET
ejpam-3123	23	6	section	section	NOUN
ejpam-3123	23	7	some	some	DET
ejpam-3123	23	8	definitions	definition	NOUN
ejpam-3123	23	9	and	and	CCONJ
ejpam-3123	23	10	required	require	VERB
ejpam-3123	23	11	results	result	NOUN
ejpam-3123	23	12	from	from	ADP
ejpam-3123	23	13	[	[	X
ejpam-3123	23	14	4	4	NUM
ejpam-3123	23	15	]	]	PUNCT
ejpam-3123	23	16	are	be	AUX
ejpam-3123	23	17	presented	present	VERB
ejpam-3123	23	18	.	.	PUNCT
ejpam-3123	24	1	definition	definition	NOUN
ejpam-3123	24	2	1	1	NUM
ejpam-3123	24	3	.	.	PUNCT
ejpam-3123	25	1	for	for	ADP
ejpam-3123	25	2	a	a	DET
ejpam-3123	25	3	group	group	NOUN
ejpam-3123	25	4	x	x	X
ejpam-3123	25	5	and	and	CCONJ
ejpam-3123	25	6	a	a	DET
ejpam-3123	25	7	subgroup	subgroup	NOUN
ejpam-3123	25	8	h	h	NOUN
ejpam-3123	25	9	,	,	PUNCT
ejpam-3123	25	10	we	we	PRON
ejpam-3123	25	11	call	call	VERB
ejpam-3123	25	12	g	g	PROPN
ejpam-3123	25	13	⊂	⊂	PROPN
ejpam-3123	25	14	x	x	PUNCT
ejpam-3123	25	15	a	a	DET
ejpam-3123	25	16	set	set	NOUN
ejpam-3123	25	17	of	of	ADP
ejpam-3123	25	18	left	left	ADJ
ejpam-3123	25	19	coset	coset	NOUN
ejpam-3123	25	20	representatives	representative	NOUN
ejpam-3123	25	21	if	if	SCONJ
ejpam-3123	25	22	for	for	ADP
ejpam-3123	25	23	every	every	DET
ejpam-3123	25	24	x	x	SYM
ejpam-3123	25	25	∈	∈	PROPN
ejpam-3123	25	26	x	x	PUNCT
ejpam-3123	25	27	there	there	PRON
ejpam-3123	25	28	is	be	VERB
ejpam-3123	25	29	a	a	DET
ejpam-3123	25	30	unique	unique	ADJ
ejpam-3123	25	31	s	s	X
ejpam-3123	25	32	∈	∈	NOUN
ejpam-3123	25	33	g	g	NOUN
ejpam-3123	25	34	such	such	ADJ
ejpam-3123	25	35	that	that	SCONJ
ejpam-3123	25	36	x	x	SYM
ejpam-3123	25	37	∈	∈	PROPN
ejpam-3123	25	38	hs	hs	PROPN
ejpam-3123	25	39	.	.	PUNCT
ejpam-3123	26	1	the	the	DET
ejpam-3123	26	2	decomposition	decomposition	NOUN
ejpam-3123	26	3	x	x	PUNCT
ejpam-3123	27	1	=	=	PUNCT
ejpam-3123	27	2	us	we	PRON
ejpam-3123	27	3	for	for	ADP
ejpam-3123	27	4	u	u	PROPN
ejpam-3123	27	5	∈	∈	PROPN
ejpam-3123	27	6	h	h	NOUN
ejpam-3123	27	7	and	and	CCONJ
ejpam-3123	27	8	s	s	PROPN
ejpam-3123	27	9	∈	∈	PROPN
ejpam-3123	27	10	g	g	NOUN
ejpam-3123	27	11	is	be	AUX
ejpam-3123	27	12	called	call	VERB
ejpam-3123	27	13	the	the	DET
ejpam-3123	27	14	unique	unique	ADJ
ejpam-3123	27	15	factorization	factorization	NOUN
ejpam-3123	27	16	of	of	ADP
ejpam-3123	27	17	x.	x.	NOUN
ejpam-3123	27	18	in	in	ADP
ejpam-3123	27	19	what	what	PRON
ejpam-3123	27	20	follows	follow	VERB
ejpam-3123	27	21	,	,	PUNCT
ejpam-3123	27	22	it	it	PRON
ejpam-3123	27	23	will	will	AUX
ejpam-3123	27	24	be	be	AUX
ejpam-3123	27	25	assumed	assume	VERB
ejpam-3123	27	26	that	that	SCONJ
ejpam-3123	27	27	g	g	PROPN
ejpam-3123	27	28	⊂	⊂	PROPN
ejpam-3123	27	29	x	x	X
ejpam-3123	27	30	is	be	AUX
ejpam-3123	27	31	a	a	DET
ejpam-3123	27	32	fixed	fix	VERB
ejpam-3123	27	33	set	set	NOUN
ejpam-3123	27	34	of	of	ADP
ejpam-3123	27	35	left	left	ADJ
ejpam-3123	27	36	coset	coset	NOUN
ejpam-3123	27	37	representatives	representative	NOUN
ejpam-3123	27	38	for	for	ADP
ejpam-3123	27	39	the	the	DET
ejpam-3123	27	40	subgroup	subgroup	PROPN
ejpam-3123	27	41	h	h	PROPN
ejpam-3123	27	42	⊂	⊂	PROPN
ejpam-3123	27	43	x.	x.	PROPN
ejpam-3123	27	44	also	also	ADV
ejpam-3123	27	45	,	,	PUNCT
ejpam-3123	27	46	the	the	DET
ejpam-3123	27	47	identity	identity	NOUN
ejpam-3123	27	48	in	in	ADP
ejpam-3123	27	49	x	x	X
ejpam-3123	27	50	will	will	AUX
ejpam-3123	27	51	be	be	AUX
ejpam-3123	27	52	denoted	denote	VERB
ejpam-3123	27	53	by	by	ADP
ejpam-3123	27	54	e.	e.	PROPN
ejpam-3123	27	55	definition	definition	PROPN
ejpam-3123	27	56	2	2	NUM
ejpam-3123	27	57	.	.	PUNCT
ejpam-3123	27	58	for	for	ADP
ejpam-3123	27	59	elements	element	NOUN
ejpam-3123	27	60	s	s	PART
ejpam-3123	27	61	,	,	PUNCT
ejpam-3123	27	62	t	t	PROPN
ejpam-3123	27	63	∈	∈	PROPN
ejpam-3123	27	64	g	g	NOUN
ejpam-3123	27	65	we	we	PRON
ejpam-3123	27	66	define	define	VERB
ejpam-3123	27	67	f(s	f(	NOUN
ejpam-3123	27	68	,	,	PUNCT
ejpam-3123	27	69	t	t	PROPN
ejpam-3123	27	70	)	)	PUNCT
ejpam-3123	27	71	∈	∈	PROPN
ejpam-3123	27	72	h	h	NOUN
ejpam-3123	27	73	and	and	CCONJ
ejpam-3123	27	74	s	s	NOUN
ejpam-3123	27	75	∗	∗	NOUN
ejpam-3123	27	76	t	t	NOUN
ejpam-3123	27	77	∈	∈	PROPN
ejpam-3123	27	78	g	g	NOUN
ejpam-3123	27	79	by	by	ADP
ejpam-3123	27	80	the	the	DET
ejpam-3123	27	81	unique	unique	ADJ
ejpam-3123	27	82	factorization	factorization	NOUN
ejpam-3123	27	83	st	st	NOUN
ejpam-3123	27	84	=	=	SYM
ejpam-3123	27	85	f(s	f(s	PROPN
ejpam-3123	27	86	,	,	PUNCT
ejpam-3123	27	87	t)(s	t)(s	PROPN
ejpam-3123	27	88	∗	∗	NOUN
ejpam-3123	27	89	t	t	PROPN
ejpam-3123	27	90	)	)	PUNCT
ejpam-3123	27	91	in	in	ADP
ejpam-3123	27	92	x	x	NOUN
ejpam-3123	27	93	,	,	PUNCT
ejpam-3123	27	94	where	where	SCONJ
ejpam-3123	27	95	f	f	PROPN
ejpam-3123	27	96	is	be	AUX
ejpam-3123	27	97	the	the	DET
ejpam-3123	27	98	cocycle	cocycle	NOUN
ejpam-3123	27	99	map	map	NOUN
ejpam-3123	27	100	.	.	PUNCT
ejpam-3123	28	1	also	also	ADV
ejpam-3123	28	2	,	,	PUNCT
ejpam-3123	28	3	the	the	DET
ejpam-3123	28	4	functions	function	NOUN
ejpam-3123	28	5	.	.	PUNCT
ejpam-3123	29	1	:	:	PUNCT
ejpam-3123	29	2	g	g	PROPN
ejpam-3123	29	3	×	×	PROPN
ejpam-3123	29	4	h	h	NOUN
ejpam-3123	29	5	→	→	SYM
ejpam-3123	29	6	h	h	NOUN
ejpam-3123	29	7	and	and	CCONJ
ejpam-3123	29	8	/	/	SYM
ejpam-3123	29	9	:	:	PUNCT
ejpam-3123	29	10	g	g	ADP
ejpam-3123	29	11	×	×	PROPN
ejpam-3123	29	12	h	h	NOUN
ejpam-3123	29	13	→	→	SYM
ejpam-3123	29	14	g	g	NOUN
ejpam-3123	29	15	are	be	AUX
ejpam-3123	29	16	also	also	ADV
ejpam-3123	29	17	defined	define	VERB
ejpam-3123	29	18	by	by	ADP
ejpam-3123	29	19	the	the	DET
ejpam-3123	29	20	unique	unique	ADJ
ejpam-3123	29	21	factorization	factorization	NOUN
ejpam-3123	29	22	su	su	PROPN
ejpam-3123	30	1	=	=	PUNCT
ejpam-3123	30	2	(	(	PUNCT
ejpam-3123	30	3	s	s	NOUN
ejpam-3123	30	4	.	.	PUNCT
ejpam-3123	30	5	u)(s	u)(s	NOUN
ejpam-3123	30	6	/	/	SYM
ejpam-3123	30	7	u	u	NOUN
ejpam-3123	30	8	)	)	PUNCT
ejpam-3123	30	9	for	for	ADP
ejpam-3123	30	10	s	s	PROPN
ejpam-3123	30	11	,	,	PUNCT
ejpam-3123	30	12	s	s	PART
ejpam-3123	30	13	/	/	SYM
ejpam-3123	30	14	u	u	NOUN
ejpam-3123	30	15	∈	∈	PROPN
ejpam-3123	30	16	g	g	NOUN
ejpam-3123	30	17	and	and	CCONJ
ejpam-3123	30	18	u	u	NOUN
ejpam-3123	30	19	,	,	PUNCT
ejpam-3123	30	20	s	s	PART
ejpam-3123	30	21	.	.	PUNCT
ejpam-3123	31	1	u	u	PROPN
ejpam-3123	31	2	∈	∈	PROPN
ejpam-3123	31	3	h.	h.	NOUN
ejpam-3123	31	4	it	it	PRON
ejpam-3123	31	5	was	be	AUX
ejpam-3123	31	6	proved	prove	VERB
ejpam-3123	31	7	that	that	SCONJ
ejpam-3123	31	8	the	the	DET
ejpam-3123	31	9	binary	binary	PROPN
ejpam-3123	31	10	operation	operation	NOUN
ejpam-3123	31	11	∗	∗	NOUN
ejpam-3123	31	12	on	on	ADP
ejpam-3123	31	13	g	g	PROPN
ejpam-3123	31	14	has	have	VERB
ejpam-3123	31	15	a	a	DET
ejpam-3123	31	16	unique	unique	ADJ
ejpam-3123	31	17	left	leave	VERB
ejpam-3123	31	18	identity	identity	NOUN
ejpam-3123	31	19	eg	eg	NOUN
ejpam-3123	31	20	∈	∈	PROPN
ejpam-3123	31	21	g	g	PROPN
ejpam-3123	31	22	and	and	CCONJ
ejpam-3123	31	23	also	also	ADV
ejpam-3123	31	24	has	have	VERB
ejpam-3123	31	25	the	the	DET
ejpam-3123	31	26	right	right	ADJ
ejpam-3123	31	27	division	division	NOUN
ejpam-3123	31	28	property	property	NOUN
ejpam-3123	31	29	which	which	PRON
ejpam-3123	31	30	means	mean	VERB
ejpam-3123	31	31	that	that	SCONJ
ejpam-3123	31	32	,	,	PUNCT
ejpam-3123	31	33	there	there	PRON
ejpam-3123	31	34	is	be	VERB
ejpam-3123	31	35	a	a	DET
ejpam-3123	31	36	unique	unique	ADJ
ejpam-3123	31	37	solution	solution	NOUN
ejpam-3123	31	38	p	p	X
ejpam-3123	31	39	∈	∈	PROPN
ejpam-3123	31	40	g	g	NOUN
ejpam-3123	31	41	satisfies	satisfy	VERB
ejpam-3123	31	42	the	the	DET
ejpam-3123	31	43	equation	equation	NOUN
ejpam-3123	31	44	p	p	NOUN
ejpam-3123	31	45	∗	∗	NOUN
ejpam-3123	31	46	s	s	PART
ejpam-3123	31	47	=	=	X
ejpam-3123	31	48	t	t	PROPN
ejpam-3123	31	49	for	for	ADP
ejpam-3123	31	50	all	all	DET
ejpam-3123	31	51	s	s	PROPN
ejpam-3123	31	52	,	,	PUNCT
ejpam-3123	31	53	t	t	PROPN
ejpam-3123	31	54	∈	∈	PROPN
ejpam-3123	31	55	g.	g.	NOUN
ejpam-3123	31	56	it	it	PRON
ejpam-3123	31	57	is	be	AUX
ejpam-3123	31	58	noted	note	VERB
ejpam-3123	31	59	that	that	SCONJ
ejpam-3123	31	60	if	if	SCONJ
ejpam-3123	31	61	e	e	PROPN
ejpam-3123	31	62	∈	∈	PROPN
ejpam-3123	31	63	g	g	PROPN
ejpam-3123	31	64	then	then	ADV
ejpam-3123	31	65	eg	eg	PROPN
ejpam-3123	31	66	=	=	PUNCT
ejpam-3123	31	67	e	e	PROPN
ejpam-3123	31	68	is	be	AUX
ejpam-3123	31	69	also	also	ADV
ejpam-3123	31	70	a	a	DET
ejpam-3123	31	71	right	right	ADJ
ejpam-3123	31	72	identity	identity	NOUN
ejpam-3123	31	73	.	.	PUNCT
ejpam-3123	32	1	proposition	proposition	NOUN
ejpam-3123	32	2	1	1	NUM
ejpam-3123	32	3	.	.	PUNCT
ejpam-3123	33	1	for	for	ADP
ejpam-3123	33	2	s	s	PROPN
ejpam-3123	33	3	,	,	PUNCT
ejpam-3123	33	4	t	t	PROPN
ejpam-3123	33	5	,	,	PUNCT
ejpam-3123	33	6	p	p	PROPN
ejpam-3123	33	7	∈	∈	PROPN
ejpam-3123	33	8	g	g	NOUN
ejpam-3123	33	9	and	and	CCONJ
ejpam-3123	33	10	u	u	NOUN
ejpam-3123	33	11	,	,	PUNCT
ejpam-3123	33	12	v	v	PROPN
ejpam-3123	33	13	∈	∈	PROPN
ejpam-3123	33	14	h	h	NOUN
ejpam-3123	33	15	,	,	PUNCT
ejpam-3123	33	16	the	the	DET
ejpam-3123	33	17	following	follow	VERB
ejpam-3123	33	18	identities	identity	NOUN
ejpam-3123	33	19	between	between	ADP
ejpam-3123	33	20	(	(	PUNCT
ejpam-3123	33	21	g	g	NOUN
ejpam-3123	33	22	,	,	PUNCT
ejpam-3123	33	23	∗	∗	NOUN
ejpam-3123	33	24	)	)	PUNCT
ejpam-3123	33	25	and	and	CCONJ
ejpam-3123	33	26	f	f	PROPN
ejpam-3123	33	27	hold	hold	VERB
ejpam-3123	33	28	:	:	PUNCT
ejpam-3123	33	29	s	s	X
ejpam-3123	33	30	.	.	PUNCT
ejpam-3123	34	1	(	(	PUNCT
ejpam-3123	34	2	t	t	PROPN
ejpam-3123	34	3	.	.	PUNCT
ejpam-3123	35	1	u	u	NOUN
ejpam-3123	35	2	)	)	PUNCT
ejpam-3123	35	3	=	=	PUNCT
ejpam-3123	35	4	f(s	f(s	PROPN
ejpam-3123	35	5	,	,	PUNCT
ejpam-3123	35	6	t	t	PROPN
ejpam-3123	35	7	)	)	PUNCT
ejpam-3123	35	8	(	(	PUNCT
ejpam-3123	35	9	(	(	PUNCT
ejpam-3123	35	10	s	s	NOUN
ejpam-3123	35	11	∗	∗	X
ejpam-3123	35	12	t	t	NOUN
ejpam-3123	35	13	)	)	PUNCT
ejpam-3123	35	14	.	.	PUNCT
ejpam-3123	36	1	u)f	u)f	PROPN
ejpam-3123	36	2	(	(	PUNCT
ejpam-3123	36	3	s	s	NOUN
ejpam-3123	36	4	/	/	SYM
ejpam-3123	36	5	(	(	PUNCT
ejpam-3123	36	6	t	t	PROPN
ejpam-3123	36	7	.	.	PUNCT
ejpam-3123	37	1	u	u	NOUN
ejpam-3123	37	2	)	)	PUNCT
ejpam-3123	37	3	,	,	PUNCT
ejpam-3123	37	4	t	t	PROPN
ejpam-3123	37	5	/	/	SYM
ejpam-3123	37	6	u	u	PROPN
ejpam-3123	37	7	)	)	PUNCT
ejpam-3123	37	8	−1	−1	NOUN
ejpam-3123	37	9	(	(	PUNCT
ejpam-3123	37	10	s	s	NOUN
ejpam-3123	37	11	∗	∗	X
ejpam-3123	37	12	t	t	PROPN
ejpam-3123	37	13	)	)	PUNCT
ejpam-3123	37	14	/	/	SYM
ejpam-3123	37	15	u	u	NOUN
ejpam-3123	37	16	=	=	PUNCT
ejpam-3123	37	17	(	(	PUNCT
ejpam-3123	37	18	s	s	NOUN
ejpam-3123	37	19	/	/	SYM
ejpam-3123	37	20	(	(	PUNCT
ejpam-3123	37	21	t	t	PROPN
ejpam-3123	37	22	.	.	PUNCT
ejpam-3123	38	1	u	u	NOUN
ejpam-3123	38	2	)	)	PUNCT
ejpam-3123	38	3	)	)	PUNCT
ejpam-3123	39	1	∗	∗	NOUN
ejpam-3123	39	2	(	(	PUNCT
ejpam-3123	39	3	t	t	PROPN
ejpam-3123	39	4	/	/	SYM
ejpam-3123	39	5	u	u	NOUN
ejpam-3123	39	6	)	)	PUNCT
ejpam-3123	39	7	s	s	PART
ejpam-3123	39	8	.	.	PUNCT
ejpam-3123	40	1	uv	uv	NOUN
ejpam-3123	40	2	=	=	PUNCT
ejpam-3123	40	3	(	(	PUNCT
ejpam-3123	40	4	s	s	NOUN
ejpam-3123	40	5	.	.	PUNCT
ejpam-3123	40	6	u	u	NOUN
ejpam-3123	40	7	)	)	PUNCT
ejpam-3123	40	8	(	(	PUNCT
ejpam-3123	40	9	(	(	PUNCT
ejpam-3123	40	10	s	s	NOUN
ejpam-3123	40	11	/	/	SYM
ejpam-3123	40	12	u	u	NOUN
ejpam-3123	40	13	)	)	PUNCT
ejpam-3123	40	14	.	.	PUNCT
ejpam-3123	41	1	v	v	X
ejpam-3123	41	2	)	)	PUNCT
ejpam-3123	41	3	s	s	NOUN
ejpam-3123	41	4	/	/	SYM
ejpam-3123	41	5	uv	uv	NOUN
ejpam-3123	41	6	=	=	PUNCT
ejpam-3123	41	7	(	(	PUNCT
ejpam-3123	41	8	s	s	NOUN
ejpam-3123	41	9	/	/	SYM
ejpam-3123	41	10	u	u	NOUN
ejpam-3123	41	11	)	)	PUNCT
ejpam-3123	41	12	/	/	SYM
ejpam-3123	42	1	v	v	PROPN
ejpam-3123	42	2	f(p	f(p	PROPN
ejpam-3123	42	3	,	,	PUNCT
ejpam-3123	42	4	s)f(p	s)f(p	PROPN
ejpam-3123	42	5	∗	∗	PROPN
ejpam-3123	42	6	s	s	PROPN
ejpam-3123	42	7	,	,	PUNCT
ejpam-3123	42	8	t	t	PROPN
ejpam-3123	42	9	)	)	PUNCT
ejpam-3123	43	1	=	=	PUNCT
ejpam-3123	44	1	(	(	PUNCT
ejpam-3123	44	2	p	p	X
ejpam-3123	44	3	.	.	PUNCT
ejpam-3123	45	1	f(s	f(s	PROPN
ejpam-3123	45	2	,	,	PUNCT
ejpam-3123	45	3	t	t	PROPN
ejpam-3123	45	4	)	)	PUNCT
ejpam-3123	45	5	)	)	PUNCT
ejpam-3123	46	1	f	f	NOUN
ejpam-3123	46	2	(	(	PUNCT
ejpam-3123	46	3	p	p	X
ejpam-3123	46	4	/	/	SYM
ejpam-3123	46	5	f(s	f(s	PROPN
ejpam-3123	46	6	,	,	PUNCT
ejpam-3123	46	7	t	t	PROPN
ejpam-3123	46	8	)	)	PUNCT
ejpam-3123	46	9	,	,	PUNCT
ejpam-3123	46	10	s	s	NOUN
ejpam-3123	46	11	∗	∗	NOUN
ejpam-3123	46	12	t	t	NOUN
ejpam-3123	46	13	)	)	PUNCT
ejpam-3123	47	1	(	(	PUNCT
ejpam-3123	47	2	p	p	NOUN
ejpam-3123	47	3	/	/	SYM
ejpam-3123	47	4	f(s	f(s	PROPN
ejpam-3123	47	5	,	,	PUNCT
ejpam-3123	47	6	t	t	PROPN
ejpam-3123	47	7	)	)	PUNCT
ejpam-3123	47	8	)	)	PUNCT
ejpam-3123	48	1	∗	∗	NOUN
ejpam-3123	48	2	(	(	PUNCT
ejpam-3123	48	3	s	s	NOUN
ejpam-3123	48	4	∗	∗	X
ejpam-3123	48	5	t	t	NOUN
ejpam-3123	48	6	)	)	PUNCT
ejpam-3123	48	7	=	=	PUNCT
ejpam-3123	49	1	(	(	PUNCT
ejpam-3123	49	2	p	p	NOUN
ejpam-3123	49	3	∗	∗	PRON
ejpam-3123	49	4	s	s	PART
ejpam-3123	49	5	)	)	PUNCT
ejpam-3123	49	6	∗	∗	NOUN
ejpam-3123	49	7	t.	t.	NOUN
ejpam-3123	49	8	proposition	proposition	NOUN
ejpam-3123	49	9	2	2	NUM
ejpam-3123	49	10	.	.	X
ejpam-3123	50	1	for	for	ADP
ejpam-3123	50	2	t	t	PROPN
ejpam-3123	50	3	∈	∈	PROPN
ejpam-3123	50	4	g	g	PROPN
ejpam-3123	50	5	and	and	CCONJ
ejpam-3123	50	6	v	v	ADP
ejpam-3123	50	7	∈	∈	PROPN
ejpam-3123	50	8	h	h	NOUN
ejpam-3123	50	9	,	,	PUNCT
ejpam-3123	50	10	the	the	DET
ejpam-3123	50	11	following	follow	VERB
ejpam-3123	50	12	identities	identity	NOUN
ejpam-3123	50	13	between	between	ADP
ejpam-3123	50	14	(	(	PUNCT
ejpam-3123	50	15	g	g	NOUN
ejpam-3123	50	16	,	,	PUNCT
ejpam-3123	50	17	∗	∗	NOUN
ejpam-3123	50	18	)	)	PUNCT
ejpam-3123	50	19	and	and	CCONJ
ejpam-3123	50	20	f	f	PROPN
ejpam-3123	50	21	hold	hold	VERB
ejpam-3123	50	22	:	:	PUNCT
ejpam-3123	50	23	eg	eg	PROPN
ejpam-3123	50	24	/	/	SYM
ejpam-3123	50	25	v	v	PROPN
ejpam-3123	50	26	=	=	SYM
ejpam-3123	50	27	eg	eg	NOUN
ejpam-3123	50	28	,	,	PUNCT
ejpam-3123	50	29	eg	eg	NOUN
ejpam-3123	50	30	.	.	PUNCT
ejpam-3123	51	1	v	v	X
ejpam-3123	51	2	=	=	NOUN
ejpam-3123	51	3	egve	egve	NOUN
ejpam-3123	51	4	−1	−1	NOUN
ejpam-3123	51	5	g	g	PROPN
ejpam-3123	51	6	,	,	PUNCT
ejpam-3123	51	7	t	t	PROPN
ejpam-3123	51	8	.	.	PUNCT
ejpam-3123	52	1	e	e	X
ejpam-3123	52	2	=	=	SYM
ejpam-3123	52	3	e	e	PROPN
ejpam-3123	52	4	,	,	PUNCT
ejpam-3123	52	5	t	t	PROPN
ejpam-3123	52	6	/	/	SYM
ejpam-3123	52	7	e	e	PROPN
ejpam-3123	52	8	=	=	PROPN
ejpam-3123	52	9	t	t	PROPN
ejpam-3123	52	10	,	,	PUNCT
ejpam-3123	52	11	f(eg	f(eg	NUM
ejpam-3123	52	12	,	,	PUNCT
ejpam-3123	52	13	t	t	NOUN
ejpam-3123	52	14	)	)	PUNCT
ejpam-3123	52	15	=	=	SYM
ejpam-3123	52	16	eg	eg	NOUN
ejpam-3123	52	17	,	,	PUNCT
ejpam-3123	52	18	t	t	PROPN
ejpam-3123	52	19	.	.	PUNCT
ejpam-3123	53	1	e−1	e−1	NOUN
ejpam-3123	53	2	g	g	PROPN
ejpam-3123	53	3	=	=	SYM
ejpam-3123	53	4	f	f	PROPN
ejpam-3123	53	5	(	(	PUNCT
ejpam-3123	53	6	t	t	PROPN
ejpam-3123	53	7	/	/	SYM
ejpam-3123	53	8	e−1	e−1	PROPN
ejpam-3123	53	9	g	g	PROPN
ejpam-3123	53	10	,	,	PUNCT
ejpam-3123	53	11	eg	eg	NOUN
ejpam-3123	53	12	)	)	PUNCT
ejpam-3123	53	13	−1	−1	NOUN
ejpam-3123	53	14	,	,	PUNCT
ejpam-3123	53	15	(	(	PUNCT
ejpam-3123	53	16	t	t	PROPN
ejpam-3123	53	17	/	/	SYM
ejpam-3123	53	18	e−1	e−1	PROPN
ejpam-3123	53	19	g	g	NOUN
ejpam-3123	53	20	)	)	PUNCT
ejpam-3123	53	21	∗	∗	NOUN
ejpam-3123	53	22	eg	eg	NOUN
ejpam-3123	53	23	=	=	PUNCT
ejpam-3123	53	24	t.	t.	PROPN
ejpam-3123	53	25	n.	n.	PROPN
ejpam-3123	53	26	al	al	PROPN
ejpam-3123	53	27	-	-	PUNCT
ejpam-3123	53	28	subaie	subaie	NOUN
ejpam-3123	53	29	,	,	PUNCT
ejpam-3123	53	30	m.	m.	NOUN
ejpam-3123	53	31	m.	m.	PROPN
ejpam-3123	53	32	al	al	PROPN
ejpam-3123	53	33	-	-	PUNCT
ejpam-3123	53	34	shomrani	shomrani	PROPN
ejpam-3123	53	35	/	/	SYM
ejpam-3123	53	36	eur	eur	NOUN
ejpam-3123	53	37	.	.	PUNCT
ejpam-3123	54	1	j.	j.	PROPN
ejpam-3123	54	2	pure	pure	PROPN
ejpam-3123	54	3	appl	appl	PROPN
ejpam-3123	54	4	.	.	PROPN
ejpam-3123	54	5	math	math	PROPN
ejpam-3123	54	6	,	,	PUNCT
ejpam-3123	54	7	10	10	NUM
ejpam-3123	54	8	(	(	PUNCT
ejpam-3123	54	9	5	5	NUM
ejpam-3123	54	10	)	)	PUNCT
ejpam-3123	54	11	(	(	PUNCT
ejpam-3123	54	12	2017	2017	NUM
ejpam-3123	54	13	)	)	PUNCT
ejpam-3123	54	14	,	,	PUNCT
ejpam-3123	54	15	967	967	NUM
ejpam-3123	54	16	-	-	SYM
ejpam-3123	54	17	980	980	NUM
ejpam-3123	54	18	969	969	NUM
ejpam-3123	54	19	3	3	NUM
ejpam-3123	54	20	.	.	PUNCT
ejpam-3123	55	1	g	g	NOUN
ejpam-3123	55	2	-	-	PUNCT
ejpam-3123	55	3	weak	weak	ADJ
ejpam-3123	55	4	graded	grade	VERB
ejpam-3123	55	5	rings	ring	NOUN
ejpam-3123	55	6	definition	definition	NOUN
ejpam-3123	55	7	3	3	NUM
ejpam-3123	55	8	.	.	PUNCT
ejpam-3123	56	1	[	[	X
ejpam-3123	56	2	2	2	X
ejpam-3123	56	3	]	]	AUX
ejpam-3123	56	4	let	let	VERB
ejpam-3123	56	5	x	x	PRON
ejpam-3123	56	6	be	be	AUX
ejpam-3123	56	7	a	a	DET
ejpam-3123	56	8	group	group	NOUN
ejpam-3123	56	9	,	,	PUNCT
ejpam-3123	56	10	h	h	PROPN
ejpam-3123	56	11	be	be	VERB
ejpam-3123	56	12	a	a	DET
ejpam-3123	56	13	subgroup	subgroup	NOUN
ejpam-3123	56	14	of	of	ADP
ejpam-3123	56	15	x	x	PUNCT
ejpam-3123	56	16	and	and	CCONJ
ejpam-3123	56	17	(	(	PUNCT
ejpam-3123	56	18	g	g	NOUN
ejpam-3123	56	19	,	,	PUNCT
ejpam-3123	56	20	∗	∗	NOUN
ejpam-3123	56	21	)	)	PUNCT
ejpam-3123	56	22	be	be	VERB
ejpam-3123	56	23	a	a	DET
ejpam-3123	56	24	fixed	fix	VERB
ejpam-3123	56	25	set	set	NOUN
ejpam-3123	56	26	of	of	ADP
ejpam-3123	56	27	left	left	ADJ
ejpam-3123	56	28	coset	coset	NOUN
ejpam-3123	56	29	representatives	representative	NOUN
ejpam-3123	56	30	for	for	ADP
ejpam-3123	56	31	the	the	DET
ejpam-3123	56	32	subgroup	subgroup	PROPN
ejpam-3123	56	33	h	h	NOUN
ejpam-3123	56	34	with	with	ADP
ejpam-3123	56	35	the	the	DET
ejpam-3123	56	36	binary	binary	PROPN
ejpam-3123	56	37	operation	operation	NOUN
ejpam-3123	56	38	∗	∗	NOUN
ejpam-3123	56	39	which	which	PRON
ejpam-3123	56	40	is	be	AUX
ejpam-3123	56	41	defined	define	VERB
ejpam-3123	56	42	as	as	ADP
ejpam-3123	56	43	in	in	ADP
ejpam-3123	56	44	2	2	NUM
ejpam-3123	56	45	.	.	PUNCT
ejpam-3123	57	1	a	a	DET
ejpam-3123	57	2	ring	ring	NOUN
ejpam-3123	57	3	r	r	NOUN
ejpam-3123	57	4	is	be	AUX
ejpam-3123	57	5	called	call	VERB
ejpam-3123	57	6	a	a	DET
ejpam-3123	57	7	g	g	NOUN
ejpam-3123	57	8	-	-	PUNCT
ejpam-3123	57	9	weak	weak	ADJ
ejpam-3123	57	10	graded	grade	VERB
ejpam-3123	57	11	ring	ring	NOUN
ejpam-3123	57	12	if	if	SCONJ
ejpam-3123	57	13	r	r	NOUN
ejpam-3123	57	14	=	=	SYM
ejpam-3123	57	15	⊕	⊕	PROPN
ejpam-3123	57	16	s∈g	s∈g	VERB
ejpam-3123	57	17	rs	rs	NOUN
ejpam-3123	57	18	(	(	PUNCT
ejpam-3123	57	19	1	1	NUM
ejpam-3123	57	20	)	)	PUNCT
ejpam-3123	57	21	and	and	CCONJ
ejpam-3123	57	22	rsrt	rsrt	VERB
ejpam-3123	57	23	⊆	⊆	NUM
ejpam-3123	57	24	rs∗t	rs∗t	NOUN
ejpam-3123	57	25	for	for	ADP
ejpam-3123	57	26	all	all	DET
ejpam-3123	57	27	s	s	PROPN
ejpam-3123	57	28	,	,	PUNCT
ejpam-3123	57	29	t	t	PROPN
ejpam-3123	57	30	∈	∈	PROPN
ejpam-3123	57	31	g	g	PROPN
ejpam-3123	57	32	,	,	PUNCT
ejpam-3123	57	33	(	(	PUNCT
ejpam-3123	57	34	2	2	X
ejpam-3123	57	35	)	)	PUNCT
ejpam-3123	57	36	where	where	SCONJ
ejpam-3123	57	37	rs	rs	NOUN
ejpam-3123	57	38	is	be	AUX
ejpam-3123	57	39	an	an	DET
ejpam-3123	57	40	additive	additive	ADJ
ejpam-3123	57	41	subgroup	subgroup	NOUN
ejpam-3123	57	42	for	for	ADP
ejpam-3123	57	43	each	each	DET
ejpam-3123	57	44	s	s	PROPN
ejpam-3123	57	45	∈	∈	PROPN
ejpam-3123	57	46	g.	g.	NOUN
ejpam-3123	58	1	if	if	SCONJ
ejpam-3123	58	2	(	(	PUNCT
ejpam-3123	58	3	2	2	X
ejpam-3123	58	4	)	)	PUNCT
ejpam-3123	58	5	is	be	AUX
ejpam-3123	58	6	replaced	replace	VERB
ejpam-3123	58	7	by	by	ADP
ejpam-3123	58	8	rsrt	rsrt	NOUN
ejpam-3123	58	9	=	=	SYM
ejpam-3123	58	10	rs∗t	rs∗t	NOUN
ejpam-3123	58	11	for	for	ADP
ejpam-3123	58	12	all	all	DET
ejpam-3123	58	13	s	s	PROPN
ejpam-3123	58	14	,	,	PUNCT
ejpam-3123	58	15	t	t	PROPN
ejpam-3123	58	16	∈	∈	PROPN
ejpam-3123	58	17	g	g	PROPN
ejpam-3123	58	18	,	,	PUNCT
ejpam-3123	58	19	(	(	PUNCT
ejpam-3123	58	20	3	3	X
ejpam-3123	58	21	)	)	PUNCT
ejpam-3123	58	22	then	then	ADV
ejpam-3123	58	23	r	r	NOUN
ejpam-3123	58	24	is	be	AUX
ejpam-3123	58	25	called	call	VERB
ejpam-3123	58	26	a	a	DET
ejpam-3123	58	27	fully	fully	ADV
ejpam-3123	58	28	(	(	PUNCT
ejpam-3123	58	29	or	or	CCONJ
ejpam-3123	58	30	strongly	strongly	ADV
ejpam-3123	58	31	)	)	PUNCT
ejpam-3123	58	32	g	g	NOUN
ejpam-3123	58	33	-	-	PUNCT
ejpam-3123	58	34	weak	weak	ADJ
ejpam-3123	58	35	graded	grade	VERB
ejpam-3123	58	36	ring	ring	NOUN
ejpam-3123	58	37	.	.	PUNCT
ejpam-3123	59	1	it	it	PRON
ejpam-3123	59	2	can	can	AUX
ejpam-3123	59	3	be	be	AUX
ejpam-3123	59	4	noted	note	VERB
ejpam-3123	59	5	that	that	SCONJ
ejpam-3123	59	6	any	any	DET
ejpam-3123	59	7	ring	ring	NOUN
ejpam-3123	59	8	r	r	NOUN
ejpam-3123	59	9	can	can	AUX
ejpam-3123	59	10	be	be	AUX
ejpam-3123	59	11	put	put	VERB
ejpam-3123	59	12	into	into	ADP
ejpam-3123	59	13	a	a	DET
ejpam-3123	59	14	g	g	NOUN
ejpam-3123	59	15	-	-	PUNCT
ejpam-3123	59	16	weak	weak	ADJ
ejpam-3123	59	17	graded	grade	VERB
ejpam-3123	59	18	ring	ring	NOUN
ejpam-3123	59	19	by	by	ADP
ejpam-3123	59	20	placing	place	VERB
ejpam-3123	59	21	r	r	NOUN
ejpam-3123	59	22	=	=	SYM
ejpam-3123	59	23	reg	reg	NOUN
ejpam-3123	59	24	and	and	CCONJ
ejpam-3123	59	25	rs	rs	NOUN
ejpam-3123	60	1	=	=	SYM
ejpam-3123	60	2	0	0	NUM
ejpam-3123	60	3	for	for	ADP
ejpam-3123	60	4	all	all	DET
ejpam-3123	60	5	eg	eg	NOUN
ejpam-3123	60	6	6=	6=	ADP
ejpam-3123	60	7	s	s	NOUN
ejpam-3123	60	8	∈	∈	PROPN
ejpam-3123	60	9	g	g	NOUN
ejpam-3123	60	10	which	which	PRON
ejpam-3123	60	11	is	be	AUX
ejpam-3123	60	12	called	call	VERB
ejpam-3123	60	13	the	the	DET
ejpam-3123	60	14	trivial	trivial	ADJ
ejpam-3123	60	15	g	g	NOUN
ejpam-3123	60	16	-	-	PUNCT
ejpam-3123	60	17	weak	weak	ADJ
ejpam-3123	60	18	graded	grade	VERB
ejpam-3123	60	19	ring	ring	NOUN
ejpam-3123	60	20	.	.	PUNCT
ejpam-3123	61	1	example	example	NOUN
ejpam-3123	62	1	1	1	NUM
ejpam-3123	62	2	.	.	X
ejpam-3123	62	3	consider	consider	VERB
ejpam-3123	62	4	the	the	DET
ejpam-3123	62	5	morita	morita	PROPN
ejpam-3123	62	6	ring	ring	PROPN
ejpam-3123	62	7	t	t	PROPN
ejpam-3123	62	8	=	=	PUNCT
ejpam-3123	62	9	{	{	PUNCT
ejpam-3123	62	10	(	(	PUNCT
ejpam-3123	62	11	r	r	NOUN
ejpam-3123	62	12	m	m	VERB
ejpam-3123	62	13	n	n	NUM
ejpam-3123	62	14	s	s	NOUN
ejpam-3123	62	15	)	)	PUNCT
ejpam-3123	62	16	:	:	PUNCT
ejpam-3123	62	17	r	r	NOUN
ejpam-3123	62	18	∈	∈	PROPN
ejpam-3123	62	19	r	r	NOUN
ejpam-3123	62	20	,	,	PUNCT
ejpam-3123	62	21	m	m	NOUN
ejpam-3123	62	22	∈m	∈m	NOUN
ejpam-3123	62	23	,	,	PUNCT
ejpam-3123	62	24	n	n	NOUN
ejpam-3123	62	25	∈	∈	NOUN
ejpam-3123	62	26	nand	nand	NOUN
ejpam-3123	62	27	s	s	PART
ejpam-3123	62	28	∈	∈	PROPN
ejpam-3123	62	29	s	s	X
ejpam-3123	62	30	}	}	PUNCT
ejpam-3123	62	31	,	,	PUNCT
ejpam-3123	62	32	with	with	ADP
ejpam-3123	62	33	a	a	DET
ejpam-3123	62	34	morita	morita	NOUN
ejpam-3123	62	35	contex	contex	NOUN
ejpam-3123	62	36	(	(	PUNCT
ejpam-3123	62	37	r	r	NOUN
ejpam-3123	62	38	,	,	PUNCT
ejpam-3123	62	39	s	s	PART
ejpam-3123	62	40	,	,	PUNCT
ejpam-3123	62	41	rms	rm	NOUN
ejpam-3123	62	42	,	,	PUNCT
ejpam-3123	62	43	snr	snr	PROPN
ejpam-3123	62	44	,	,	PUNCT
ejpam-3123	62	45	φ	φ	PROPN
ejpam-3123	62	46	,	,	PUNCT
ejpam-3123	62	47	ϕ	ϕ	NOUN
ejpam-3123	62	48	)	)	PUNCT
ejpam-3123	62	49	where	where	SCONJ
ejpam-3123	62	50	the	the	DET
ejpam-3123	62	51	bimodule	bimodule	NOUN
ejpam-3123	62	52	homomorphisms	homomorphisms	PROPN
ejpam-3123	62	53	φ	φ	NOUN
ejpam-3123	62	54	:	:	PUNCT
ejpam-3123	62	55	m	m	VERB
ejpam-3123	62	56	⊗s	⊗s	ADJ
ejpam-3123	62	57	n	n	CCONJ
ejpam-3123	62	58	−→	−→	NOUN
ejpam-3123	62	59	r	r	NOUN
ejpam-3123	62	60	ϕ	ϕ	NOUN
ejpam-3123	62	61	:	:	PUNCT
ejpam-3123	62	62	n	n	CCONJ
ejpam-3123	62	63	⊗r	⊗r	NOUN
ejpam-3123	63	1	m	m	NOUN
ejpam-3123	64	1	−→	−→	NOUN
ejpam-3123	64	2	s	s	X
ejpam-3123	64	3	satisfy	satisfy	NOUN
ejpam-3123	64	4	(	(	PUNCT
ejpam-3123	64	5	mn)m′	mn)m′	PROPN
ejpam-3123	64	6	=	=	SYM
ejpam-3123	64	7	m(nm′	m(nm′	PROPN
ejpam-3123	64	8	)	)	PUNCT
ejpam-3123	64	9	as	as	ADP
ejpam-3123	64	10	φ(m	φ(m	NOUN
ejpam-3123	64	11	,	,	PUNCT
ejpam-3123	64	12	n	n	CCONJ
ejpam-3123	64	13	)	)	PUNCT
ejpam-3123	64	14	=	=	SYM
ejpam-3123	64	15	mn	mn	PROPN
ejpam-3123	64	16	and	and	CCONJ
ejpam-3123	64	17	ϕ(n	ϕ(n	PROPN
ejpam-3123	64	18	,	,	PUNCT
ejpam-3123	64	19	m	m	NOUN
ejpam-3123	64	20	)	)	PUNCT
ejpam-3123	64	21	=	=	SYM
ejpam-3123	64	22	nm	nm	ADJ
ejpam-3123	64	23	,	,	PUNCT
ejpam-3123	64	24	i.e.	i.e.	X
ejpam-3123	64	25	φ(m	φ(m	PROPN
ejpam-3123	64	26	⊗	⊗	PROPN
ejpam-3123	64	27	n)m′	n)m′	NOUN
ejpam-3123	64	28	=	=	SYM
ejpam-3123	64	29	mϕ(n	mϕ(n	PART
ejpam-3123	64	30	⊗	⊗	NUM
ejpam-3123	64	31	m′	m′	NUM
ejpam-3123	64	32	)	)	PUNCT
ejpam-3123	64	33	and	and	CCONJ
ejpam-3123	64	34	ϕ(n	ϕ(n	PROPN
ejpam-3123	64	35	⊗	⊗	NOUN
ejpam-3123	64	36	m)n′	m)n′	PROPN
ejpam-3123	64	37	=	=	SYM
ejpam-3123	64	38	nφ(m	nφ(m	PROPN
ejpam-3123	64	39	⊗	⊗	PROPN
ejpam-3123	64	40	n′	n′	PROPN
ejpam-3123	64	41	)	)	PUNCT
ejpam-3123	64	42	for	for	ADP
ejpam-3123	64	43	all	all	DET
ejpam-3123	64	44	m	m	PROPN
ejpam-3123	64	45	,	,	PUNCT
ejpam-3123	64	46	m′	m′	NOUN
ejpam-3123	64	47	∈	∈	NOUN
ejpam-3123	64	48	m	m	NOUN
ejpam-3123	64	49	and	and	CCONJ
ejpam-3123	64	50	n	n	CCONJ
ejpam-3123	64	51	,	,	PUNCT
ejpam-3123	64	52	n′	n′	PROPN
ejpam-3123	64	53	∈	∈	PROPN
ejpam-3123	64	54	n	n	ADV
ejpam-3123	64	55	.	.	PUNCT
ejpam-3123	65	1	it	it	PRON
ejpam-3123	65	2	is	be	AUX
ejpam-3123	65	3	well	well	ADV
ejpam-3123	65	4	known	know	VERB
ejpam-3123	65	5	that	that	SCONJ
ejpam-3123	65	6	t	t	NOUN
ejpam-3123	65	7	with	with	ADP
ejpam-3123	65	8	the	the	DET
ejpam-3123	65	9	usual	usual	ADJ
ejpam-3123	65	10	matrix	matrix	NOUN
ejpam-3123	65	11	addition	addition	NOUN
ejpam-3123	65	12	and	and	CCONJ
ejpam-3123	65	13	multiplication	multiplication	NOUN
ejpam-3123	65	14	forms	form	VERB
ejpam-3123	65	15	a	a	DET
ejpam-3123	65	16	ring	ring	NOUN
ejpam-3123	65	17	.	.	PUNCT
ejpam-3123	66	1	now	now	ADV
ejpam-3123	66	2	to	to	PART
ejpam-3123	66	3	put	put	VERB
ejpam-3123	66	4	the	the	DET
ejpam-3123	66	5	morita	morita	PROPN
ejpam-3123	66	6	ring	ring	PROPN
ejpam-3123	66	7	t	t	PROPN
ejpam-3123	67	1	=	=	PUNCT
ejpam-3123	67	2	(	(	PUNCT
ejpam-3123	67	3	r	r	NOUN
ejpam-3123	67	4	m	m	VERB
ejpam-3123	67	5	n	n	NUM
ejpam-3123	67	6	s	s	NOUN
ejpam-3123	67	7	)	)	PUNCT
ejpam-3123	67	8	into	into	ADP
ejpam-3123	67	9	a	a	DET
ejpam-3123	67	10	weak	weak	ADJ
ejpam-3123	67	11	graded	grade	VERB
ejpam-3123	67	12	ring	ring	NOUN
ejpam-3123	67	13	we	we	PRON
ejpam-3123	67	14	consider	consider	VERB
ejpam-3123	67	15	the	the	DET
ejpam-3123	67	16	group	group	NOUN
ejpam-3123	67	17	x	x	PUNCT
ejpam-3123	67	18	=	=	SYM
ejpam-3123	67	19	z2	z2	NUM
ejpam-3123	67	20	×	×	PROPN
ejpam-3123	67	21	z3	z3	NOUN
ejpam-3123	67	22	under	under	ADP
ejpam-3123	67	23	addition	addition	NOUN
ejpam-3123	67	24	with	with	ADP
ejpam-3123	67	25	the	the	DET
ejpam-3123	67	26	additive	additive	ADJ
ejpam-3123	67	27	subgroup	subgroup	NOUN
ejpam-3123	67	28	h	h	NOUN
ejpam-3123	67	29	=	=	PRON
ejpam-3123	67	30	{	{	PUNCT
ejpam-3123	67	31	(	(	PUNCT
ejpam-3123	67	32	0	0	NUM
ejpam-3123	67	33	,	,	PUNCT
ejpam-3123	67	34	0	0	NUM
ejpam-3123	67	35	)	)	PUNCT
ejpam-3123	67	36	,	,	PUNCT
ejpam-3123	67	37	(	(	PUNCT
ejpam-3123	67	38	1	1	NUM
ejpam-3123	67	39	,	,	PUNCT
ejpam-3123	67	40	0	0	NUM
ejpam-3123	67	41	)	)	PUNCT
ejpam-3123	67	42	}	}	PUNCT
ejpam-3123	67	43	of	of	ADP
ejpam-3123	67	44	x.	x.	NOUN
ejpam-3123	67	45	take	take	VERB
ejpam-3123	67	46	the	the	DET
ejpam-3123	67	47	set	set	NOUN
ejpam-3123	67	48	of	of	ADP
ejpam-3123	67	49	left	left	ADJ
ejpam-3123	67	50	coset	coset	NOUN
ejpam-3123	67	51	representatives	representative	NOUN
ejpam-3123	67	52	to	to	PART
ejpam-3123	67	53	be	be	AUX
ejpam-3123	67	54	g	g	NOUN
ejpam-3123	67	55	=	=	PRON
ejpam-3123	67	56	{	{	PUNCT
ejpam-3123	67	57	(	(	PUNCT
ejpam-3123	67	58	1	1	NUM
ejpam-3123	67	59	,	,	PUNCT
ejpam-3123	67	60	0	0	NUM
ejpam-3123	67	61	)	)	PUNCT
ejpam-3123	67	62	,	,	PUNCT
ejpam-3123	67	63	(	(	PUNCT
ejpam-3123	67	64	0	0	NUM
ejpam-3123	67	65	,	,	PUNCT
ejpam-3123	67	66	1	1	NUM
ejpam-3123	67	67	)	)	PUNCT
ejpam-3123	67	68	,	,	PUNCT
ejpam-3123	67	69	(	(	PUNCT
ejpam-3123	67	70	1	1	NUM
ejpam-3123	67	71	,	,	PUNCT
ejpam-3123	67	72	2	2	NUM
ejpam-3123	67	73	)	)	PUNCT
ejpam-3123	67	74	}	}	PUNCT
ejpam-3123	67	75	.	.	PUNCT
ejpam-3123	68	1	then	then	ADV
ejpam-3123	68	2	the	the	DET
ejpam-3123	68	3	∗	∗	NOUN
ejpam-3123	68	4	and	and	CCONJ
ejpam-3123	68	5	f	f	PROPN
ejpam-3123	68	6	operations	operation	NOUN
ejpam-3123	68	7	as	as	ADV
ejpam-3123	68	8	well	well	ADV
ejpam-3123	68	9	as	as	ADP
ejpam-3123	68	10	the	the	DET
ejpam-3123	68	11	actions	action	NOUN
ejpam-3123	68	12	/	/	PUNCT
ejpam-3123	68	13	,	,	PUNCT
ejpam-3123	68	14	.	.	PUNCT
ejpam-3123	69	1	are	be	AUX
ejpam-3123	69	2	given	give	VERB
ejpam-3123	69	3	by	by	ADP
ejpam-3123	69	4	the	the	DET
ejpam-3123	69	5	following	following	ADJ
ejpam-3123	69	6	tables	table	NOUN
ejpam-3123	69	7	:	:	PUNCT
ejpam-3123	69	8	table	table	NOUN
ejpam-3123	69	9	1	1	NUM
ejpam-3123	69	10	:	:	PUNCT
ejpam-3123	69	11	∗	∗	NOUN
ejpam-3123	69	12	and	and	CCONJ
ejpam-3123	69	13	f	f	PROPN
ejpam-3123	69	14	operations	operation	NOUN
ejpam-3123	69	15	.	.	PUNCT
ejpam-3123	70	1	∗	∗	NOUN
ejpam-3123	70	2	(	(	PUNCT
ejpam-3123	70	3	1	1	NUM
ejpam-3123	70	4	,	,	PUNCT
ejpam-3123	70	5	0	0	NUM
ejpam-3123	70	6	)	)	PUNCT
ejpam-3123	70	7	(	(	PUNCT
ejpam-3123	70	8	0	0	NUM
ejpam-3123	70	9	,	,	PUNCT
ejpam-3123	70	10	1	1	NUM
ejpam-3123	70	11	)	)	PUNCT
ejpam-3123	70	12	(	(	PUNCT
ejpam-3123	70	13	1	1	NUM
ejpam-3123	70	14	,	,	PUNCT
ejpam-3123	70	15	2	2	NUM
ejpam-3123	70	16	)	)	PUNCT
ejpam-3123	70	17	(	(	PUNCT
ejpam-3123	70	18	1	1	NUM
ejpam-3123	70	19	,	,	PUNCT
ejpam-3123	70	20	0	0	NUM
ejpam-3123	70	21	)	)	PUNCT
ejpam-3123	70	22	(	(	PUNCT
ejpam-3123	70	23	1	1	NUM
ejpam-3123	70	24	,	,	PUNCT
ejpam-3123	70	25	0	0	NUM
ejpam-3123	70	26	)	)	PUNCT
ejpam-3123	70	27	(	(	PUNCT
ejpam-3123	70	28	0	0	NUM
ejpam-3123	70	29	,	,	PUNCT
ejpam-3123	70	30	1	1	NUM
ejpam-3123	70	31	)	)	PUNCT
ejpam-3123	70	32	(	(	PUNCT
ejpam-3123	70	33	1	1	NUM
ejpam-3123	70	34	,	,	PUNCT
ejpam-3123	70	35	2	2	NUM
ejpam-3123	70	36	)	)	PUNCT
ejpam-3123	70	37	(	(	PUNCT
ejpam-3123	70	38	0	0	NUM
ejpam-3123	70	39	,	,	PUNCT
ejpam-3123	70	40	1	1	NUM
ejpam-3123	70	41	)	)	PUNCT
ejpam-3123	70	42	(	(	PUNCT
ejpam-3123	70	43	0	0	NUM
ejpam-3123	70	44	,	,	PUNCT
ejpam-3123	70	45	1	1	NUM
ejpam-3123	70	46	)	)	PUNCT
ejpam-3123	70	47	(	(	PUNCT
ejpam-3123	70	48	1	1	NUM
ejpam-3123	70	49	,	,	PUNCT
ejpam-3123	70	50	2	2	NUM
ejpam-3123	70	51	)	)	PUNCT
ejpam-3123	70	52	(	(	PUNCT
ejpam-3123	70	53	1	1	NUM
ejpam-3123	70	54	,	,	PUNCT
ejpam-3123	70	55	0	0	NUM
ejpam-3123	70	56	)	)	PUNCT
ejpam-3123	70	57	(	(	PUNCT
ejpam-3123	70	58	1	1	NUM
ejpam-3123	70	59	,	,	PUNCT
ejpam-3123	70	60	2	2	NUM
ejpam-3123	70	61	)	)	PUNCT
ejpam-3123	70	62	(	(	PUNCT
ejpam-3123	70	63	1	1	NUM
ejpam-3123	70	64	,	,	PUNCT
ejpam-3123	70	65	2	2	NUM
ejpam-3123	70	66	)	)	PUNCT
ejpam-3123	70	67	(	(	PUNCT
ejpam-3123	70	68	1	1	NUM
ejpam-3123	70	69	,	,	PUNCT
ejpam-3123	70	70	0	0	NUM
ejpam-3123	70	71	)	)	PUNCT
ejpam-3123	70	72	(	(	PUNCT
ejpam-3123	70	73	0	0	NUM
ejpam-3123	70	74	,	,	PUNCT
ejpam-3123	70	75	1	1	X
ejpam-3123	70	76	)	)	PUNCT
ejpam-3123	70	77	f	f	NOUN
ejpam-3123	70	78	(	(	PUNCT
ejpam-3123	70	79	1	1	NUM
ejpam-3123	70	80	,	,	PUNCT
ejpam-3123	70	81	0	0	NUM
ejpam-3123	70	82	)	)	PUNCT
ejpam-3123	70	83	(	(	PUNCT
ejpam-3123	70	84	0	0	NUM
ejpam-3123	70	85	,	,	PUNCT
ejpam-3123	70	86	1	1	NUM
ejpam-3123	70	87	)	)	PUNCT
ejpam-3123	70	88	(	(	PUNCT
ejpam-3123	70	89	1	1	NUM
ejpam-3123	70	90	,	,	PUNCT
ejpam-3123	70	91	2	2	NUM
ejpam-3123	70	92	)	)	PUNCT
ejpam-3123	70	93	(	(	PUNCT
ejpam-3123	70	94	1	1	NUM
ejpam-3123	70	95	,	,	PUNCT
ejpam-3123	70	96	0	0	NUM
ejpam-3123	70	97	)	)	PUNCT
ejpam-3123	70	98	(	(	PUNCT
ejpam-3123	70	99	1	1	NUM
ejpam-3123	70	100	,	,	PUNCT
ejpam-3123	70	101	0	0	NUM
ejpam-3123	70	102	)	)	PUNCT
ejpam-3123	70	103	(	(	PUNCT
ejpam-3123	70	104	1	1	NUM
ejpam-3123	70	105	,	,	PUNCT
ejpam-3123	70	106	0	0	NUM
ejpam-3123	70	107	)	)	PUNCT
ejpam-3123	70	108	(	(	PUNCT
ejpam-3123	70	109	1	1	NUM
ejpam-3123	70	110	,	,	PUNCT
ejpam-3123	70	111	0	0	NUM
ejpam-3123	70	112	)	)	PUNCT
ejpam-3123	70	113	(	(	PUNCT
ejpam-3123	70	114	0	0	NUM
ejpam-3123	70	115	,	,	PUNCT
ejpam-3123	70	116	1	1	NUM
ejpam-3123	70	117	)	)	PUNCT
ejpam-3123	70	118	(	(	PUNCT
ejpam-3123	70	119	1	1	NUM
ejpam-3123	70	120	,	,	PUNCT
ejpam-3123	70	121	0	0	NUM
ejpam-3123	70	122	)	)	PUNCT
ejpam-3123	70	123	(	(	PUNCT
ejpam-3123	70	124	1	1	NUM
ejpam-3123	70	125	,	,	PUNCT
ejpam-3123	70	126	0	0	NUM
ejpam-3123	70	127	)	)	PUNCT
ejpam-3123	70	128	(	(	PUNCT
ejpam-3123	70	129	0	0	NUM
ejpam-3123	70	130	,	,	PUNCT
ejpam-3123	70	131	0	0	NUM
ejpam-3123	70	132	)	)	PUNCT
ejpam-3123	70	133	(	(	PUNCT
ejpam-3123	70	134	1	1	NUM
ejpam-3123	70	135	,	,	PUNCT
ejpam-3123	70	136	2	2	NUM
ejpam-3123	70	137	)	)	PUNCT
ejpam-3123	70	138	(	(	PUNCT
ejpam-3123	70	139	1	1	NUM
ejpam-3123	70	140	,	,	PUNCT
ejpam-3123	70	141	0	0	NUM
ejpam-3123	70	142	)	)	PUNCT
ejpam-3123	70	143	(	(	PUNCT
ejpam-3123	70	144	0	0	NUM
ejpam-3123	70	145	,	,	PUNCT
ejpam-3123	70	146	0	0	NUM
ejpam-3123	70	147	)	)	PUNCT
ejpam-3123	70	148	(	(	PUNCT
ejpam-3123	70	149	0	0	NUM
ejpam-3123	70	150	,	,	PUNCT
ejpam-3123	70	151	0	0	NUM
ejpam-3123	70	152	)	)	PUNCT
ejpam-3123	70	153	n.	n.	PROPN
ejpam-3123	70	154	al	al	PROPN
ejpam-3123	70	155	-	-	PUNCT
ejpam-3123	70	156	subaie	subaie	NOUN
ejpam-3123	70	157	,	,	PUNCT
ejpam-3123	70	158	m.	m.	NOUN
ejpam-3123	70	159	m.	m.	PROPN
ejpam-3123	70	160	al	al	PROPN
ejpam-3123	70	161	-	-	PUNCT
ejpam-3123	70	162	shomrani	shomrani	PROPN
ejpam-3123	70	163	/	/	SYM
ejpam-3123	70	164	eur	eur	NOUN
ejpam-3123	70	165	.	.	PUNCT
ejpam-3123	71	1	j.	j.	PROPN
ejpam-3123	71	2	pure	pure	PROPN
ejpam-3123	71	3	appl	appl	PROPN
ejpam-3123	71	4	.	.	PROPN
ejpam-3123	71	5	math	math	PROPN
ejpam-3123	71	6	,	,	PUNCT
ejpam-3123	71	7	10	10	NUM
ejpam-3123	71	8	(	(	PUNCT
ejpam-3123	71	9	5	5	NUM
ejpam-3123	71	10	)	)	PUNCT
ejpam-3123	71	11	(	(	PUNCT
ejpam-3123	71	12	2017	2017	NUM
ejpam-3123	71	13	)	)	PUNCT
ejpam-3123	71	14	,	,	PUNCT
ejpam-3123	71	15	967	967	NUM
ejpam-3123	71	16	-	-	SYM
ejpam-3123	71	17	980	980	NUM
ejpam-3123	71	18	970	970	NUM
ejpam-3123	71	19	table	table	NOUN
ejpam-3123	71	20	2	2	NUM
ejpam-3123	71	21	:	:	PUNCT
ejpam-3123	71	22	/	/	SYM
ejpam-3123	71	23	and	and	CCONJ
ejpam-3123	71	24	.	.	PUNCT
ejpam-3123	71	25	actions	action	NOUN
ejpam-3123	71	26	.	.	PUNCT
ejpam-3123	72	1	s	s	PART
ejpam-3123	72	2	.	.	PUNCT
ejpam-3123	73	1	u	u	NOUN
ejpam-3123	73	2	(	(	PUNCT
ejpam-3123	73	3	0	0	NUM
ejpam-3123	73	4	,	,	PUNCT
ejpam-3123	73	5	0	0	NUM
ejpam-3123	73	6	)	)	PUNCT
ejpam-3123	73	7	(	(	PUNCT
ejpam-3123	73	8	1	1	NUM
ejpam-3123	73	9	,	,	PUNCT
ejpam-3123	73	10	0	0	NUM
ejpam-3123	73	11	)	)	PUNCT
ejpam-3123	73	12	(	(	PUNCT
ejpam-3123	73	13	1	1	NUM
ejpam-3123	73	14	,	,	PUNCT
ejpam-3123	73	15	0	0	NUM
ejpam-3123	73	16	)	)	PUNCT
ejpam-3123	73	17	(	(	PUNCT
ejpam-3123	73	18	0	0	NUM
ejpam-3123	73	19	,	,	PUNCT
ejpam-3123	73	20	0	0	NUM
ejpam-3123	73	21	)	)	PUNCT
ejpam-3123	73	22	(	(	PUNCT
ejpam-3123	73	23	1	1	NUM
ejpam-3123	73	24	,	,	PUNCT
ejpam-3123	73	25	0	0	NUM
ejpam-3123	73	26	)	)	PUNCT
ejpam-3123	73	27	(	(	PUNCT
ejpam-3123	73	28	0	0	NUM
ejpam-3123	73	29	,	,	PUNCT
ejpam-3123	73	30	1	1	NUM
ejpam-3123	73	31	)	)	PUNCT
ejpam-3123	73	32	(	(	PUNCT
ejpam-3123	73	33	0	0	NUM
ejpam-3123	73	34	,	,	PUNCT
ejpam-3123	73	35	0	0	NUM
ejpam-3123	73	36	)	)	PUNCT
ejpam-3123	73	37	(	(	PUNCT
ejpam-3123	73	38	1	1	NUM
ejpam-3123	73	39	,	,	PUNCT
ejpam-3123	73	40	0	0	NUM
ejpam-3123	73	41	)	)	PUNCT
ejpam-3123	73	42	(	(	PUNCT
ejpam-3123	73	43	1	1	NUM
ejpam-3123	73	44	,	,	PUNCT
ejpam-3123	73	45	2	2	NUM
ejpam-3123	73	46	)	)	PUNCT
ejpam-3123	73	47	(	(	PUNCT
ejpam-3123	73	48	0	0	NUM
ejpam-3123	73	49	,	,	PUNCT
ejpam-3123	73	50	0	0	NUM
ejpam-3123	73	51	)	)	PUNCT
ejpam-3123	73	52	(	(	PUNCT
ejpam-3123	73	53	1	1	NUM
ejpam-3123	73	54	,	,	PUNCT
ejpam-3123	73	55	0	0	NUM
ejpam-3123	73	56	)	)	PUNCT
ejpam-3123	73	57	s	s	PART
ejpam-3123	73	58	/	/	SYM
ejpam-3123	73	59	u	u	NOUN
ejpam-3123	73	60	(	(	PUNCT
ejpam-3123	73	61	0	0	NUM
ejpam-3123	73	62	,	,	PUNCT
ejpam-3123	73	63	0	0	NUM
ejpam-3123	73	64	)	)	PUNCT
ejpam-3123	73	65	(	(	PUNCT
ejpam-3123	73	66	1	1	NUM
ejpam-3123	73	67	,	,	PUNCT
ejpam-3123	73	68	0	0	NUM
ejpam-3123	73	69	)	)	PUNCT
ejpam-3123	73	70	(	(	PUNCT
ejpam-3123	73	71	1	1	NUM
ejpam-3123	73	72	,	,	PUNCT
ejpam-3123	73	73	0	0	NUM
ejpam-3123	73	74	)	)	PUNCT
ejpam-3123	73	75	(	(	PUNCT
ejpam-3123	73	76	1	1	NUM
ejpam-3123	73	77	,	,	PUNCT
ejpam-3123	73	78	0	0	NUM
ejpam-3123	73	79	)	)	PUNCT
ejpam-3123	73	80	(	(	PUNCT
ejpam-3123	73	81	1	1	NUM
ejpam-3123	73	82	,	,	PUNCT
ejpam-3123	73	83	0	0	NUM
ejpam-3123	73	84	)	)	PUNCT
ejpam-3123	73	85	(	(	PUNCT
ejpam-3123	73	86	0	0	NUM
ejpam-3123	73	87	,	,	PUNCT
ejpam-3123	73	88	1	1	NUM
ejpam-3123	73	89	)	)	PUNCT
ejpam-3123	73	90	(	(	PUNCT
ejpam-3123	73	91	0	0	NUM
ejpam-3123	73	92	,	,	PUNCT
ejpam-3123	73	93	1	1	NUM
ejpam-3123	73	94	)	)	PUNCT
ejpam-3123	73	95	(	(	PUNCT
ejpam-3123	73	96	0	0	NUM
ejpam-3123	73	97	,	,	PUNCT
ejpam-3123	73	98	1	1	NUM
ejpam-3123	73	99	)	)	PUNCT
ejpam-3123	73	100	(	(	PUNCT
ejpam-3123	73	101	1	1	NUM
ejpam-3123	73	102	,	,	PUNCT
ejpam-3123	73	103	2	2	NUM
ejpam-3123	73	104	)	)	PUNCT
ejpam-3123	73	105	(	(	PUNCT
ejpam-3123	73	106	1	1	NUM
ejpam-3123	73	107	,	,	PUNCT
ejpam-3123	73	108	2	2	NUM
ejpam-3123	73	109	)	)	PUNCT
ejpam-3123	73	110	(	(	PUNCT
ejpam-3123	73	111	1	1	NUM
ejpam-3123	73	112	,	,	PUNCT
ejpam-3123	73	113	2	2	NUM
ejpam-3123	73	114	)	)	PUNCT
ejpam-3123	73	115	hence	hence	ADV
ejpam-3123	73	116	the	the	DET
ejpam-3123	73	117	ring	ring	NOUN
ejpam-3123	73	118	t	t	PROPN
ejpam-3123	73	119	can	can	AUX
ejpam-3123	73	120	be	be	AUX
ejpam-3123	73	121	written	write	VERB
ejpam-3123	73	122	as	as	ADP
ejpam-3123	73	123	t	t	PROPN
ejpam-3123	73	124	=	=	SYM
ejpam-3123	73	125	t(1,0	t(1,0	X
ejpam-3123	73	126	)	)	PUNCT
ejpam-3123	73	127	⊕	⊕	PROPN
ejpam-3123	73	128	t(0,1	t(0,1	ADP
ejpam-3123	73	129	)	)	PUNCT
ejpam-3123	73	130	⊕	⊕	PROPN
ejpam-3123	73	131	t(1,2	t(1,2	PROPN
ejpam-3123	73	132	)	)	PUNCT
ejpam-3123	73	133	where	where	SCONJ
ejpam-3123	73	134	,	,	PUNCT
ejpam-3123	73	135	t(1,0	t(1,0	NUM
ejpam-3123	73	136	)	)	PUNCT
ejpam-3123	73	137	=	=	SYM
ejpam-3123	74	1	(	(	PUNCT
ejpam-3123	74	2	r	r	NOUN
ejpam-3123	74	3	0	0	NUM
ejpam-3123	74	4	0	0	NUM
ejpam-3123	74	5	s	s	PART
ejpam-3123	74	6	)	)	PUNCT
ejpam-3123	74	7	=	=	SYM
ejpam-3123	74	8	{	{	PUNCT
ejpam-3123	74	9	(	(	PUNCT
ejpam-3123	74	10	r	r	NOUN
ejpam-3123	74	11	0	0	NUM
ejpam-3123	74	12	0	0	NUM
ejpam-3123	74	13	s	s	NOUN
ejpam-3123	74	14	)	)	PUNCT
ejpam-3123	74	15	:	:	PUNCT
ejpam-3123	75	1	r	r	NOUN
ejpam-3123	75	2	∈	∈	PROPN
ejpam-3123	75	3	r	r	NOUN
ejpam-3123	75	4	,	,	PUNCT
ejpam-3123	75	5	ands	and	NOUN
ejpam-3123	75	6	∈	∈	PROPN
ejpam-3123	75	7	s	s	PART
ejpam-3123	75	8	}	}	PUNCT
ejpam-3123	75	9	t(0,1	t(0,1	NOUN
ejpam-3123	75	10	)	)	PUNCT
ejpam-3123	75	11	=	=	SYM
ejpam-3123	75	12	(	(	PUNCT
ejpam-3123	75	13	0	0	NUM
ejpam-3123	75	14	m	m	NOUN
ejpam-3123	75	15	0	0	NUM
ejpam-3123	75	16	0	0	NUM
ejpam-3123	75	17	)	)	PUNCT
ejpam-3123	76	1	=	=	PRON
ejpam-3123	76	2	{	{	PUNCT
ejpam-3123	76	3	(	(	PUNCT
ejpam-3123	76	4	0	0	NUM
ejpam-3123	76	5	m	m	NOUN
ejpam-3123	76	6	0	0	NUM
ejpam-3123	76	7	0	0	NUM
ejpam-3123	76	8	)	)	PUNCT
ejpam-3123	76	9	:	:	PUNCT
ejpam-3123	76	10	m	m	VERB
ejpam-3123	76	11	∈m	∈m	ADJ
ejpam-3123	76	12	}	}	PUNCT
ejpam-3123	76	13	t(1,2	t(1,2	PROPN
ejpam-3123	76	14	)	)	PUNCT
ejpam-3123	76	15	=	=	SYM
ejpam-3123	76	16	(	(	PUNCT
ejpam-3123	76	17	0	0	NUM
ejpam-3123	76	18	0	0	NUM
ejpam-3123	76	19	n	n	NOUN
ejpam-3123	76	20	0	0	NUM
ejpam-3123	76	21	)	)	PUNCT
ejpam-3123	77	1	=	=	PRON
ejpam-3123	77	2	{	{	PUNCT
ejpam-3123	77	3	(	(	PUNCT
ejpam-3123	77	4	0	0	NUM
ejpam-3123	77	5	0	0	NUM
ejpam-3123	77	6	n	n	NOUN
ejpam-3123	77	7	0	0	NUM
ejpam-3123	77	8	)	)	PUNCT
ejpam-3123	77	9	:	:	PUNCT
ejpam-3123	77	10	n	n	X
ejpam-3123	77	11	∈	∈	PROPN
ejpam-3123	77	12	n	n	CCONJ
ejpam-3123	77	13	}	}	PUNCT
ejpam-3123	77	14	next	next	ADV
ejpam-3123	77	15	,	,	PUNCT
ejpam-3123	77	16	to	to	PART
ejpam-3123	77	17	ensure	ensure	VERB
ejpam-3123	77	18	that	that	SCONJ
ejpam-3123	77	19	the	the	DET
ejpam-3123	77	20	inclusion	inclusion	NOUN
ejpam-3123	77	21	property	property	NOUN
ejpam-3123	77	22	is	be	AUX
ejpam-3123	77	23	satisfied	satisfied	ADJ
ejpam-3123	77	24	,	,	PUNCT
ejpam-3123	77	25	the	the	DET
ejpam-3123	77	26	following	follow	VERB
ejpam-3123	77	27	calculations	calculation	NOUN
ejpam-3123	77	28	are	be	AUX
ejpam-3123	77	29	needed	need	VERB
ejpam-3123	77	30	:	:	PUNCT
ejpam-3123	77	31	(	(	PUNCT
ejpam-3123	77	32	1	1	X
ejpam-3123	77	33	)	)	PUNCT
ejpam-3123	77	34	t(1,0)t(1,0	t(1,0)t(1,0	PROPN
ejpam-3123	77	35	)	)	PUNCT
ejpam-3123	78	1	⊆	⊆	NUM
ejpam-3123	78	2	t(1,0)∗(1,0	t(1,0)∗(1,0	NOUN
ejpam-3123	78	3	)	)	PUNCT
ejpam-3123	78	4	as	as	ADP
ejpam-3123	78	5	for	for	ADP
ejpam-3123	78	6	all	all	PRON
ejpam-3123	78	7	(	(	PUNCT
ejpam-3123	78	8	r1	r1	PROPN
ejpam-3123	78	9	0	0	NUM
ejpam-3123	78	10	0	0	NUM
ejpam-3123	78	11	s1	s1	PROPN
ejpam-3123	78	12	)	)	PUNCT
ejpam-3123	78	13	,	,	PUNCT
ejpam-3123	78	14	(	(	PUNCT
ejpam-3123	78	15	r2	r2	PROPN
ejpam-3123	78	16	0	0	NUM
ejpam-3123	78	17	0	0	NUM
ejpam-3123	78	18	s2	s2	PROPN
ejpam-3123	78	19	)	)	PUNCT
ejpam-3123	78	20	∈	∈	PROPN
ejpam-3123	79	1	t(1,0	t(1,0	PRON
ejpam-3123	79	2	)	)	PUNCT
ejpam-3123	79	3	we	we	PRON
ejpam-3123	79	4	have	have	VERB
ejpam-3123	79	5	:(	:(	PUNCT
ejpam-3123	79	6	r1	r1	NOUN
ejpam-3123	79	7	0	0	NUM
ejpam-3123	79	8	0	0	NUM
ejpam-3123	79	9	s1	s1	NOUN
ejpam-3123	79	10	)	)	PUNCT
ejpam-3123	80	1	(	(	PUNCT
ejpam-3123	80	2	r2	r2	PROPN
ejpam-3123	80	3	0	0	NUM
ejpam-3123	80	4	0	0	NUM
ejpam-3123	80	5	s2	s2	NOUN
ejpam-3123	80	6	)	)	PUNCT
ejpam-3123	80	7	=	=	PUNCT
ejpam-3123	81	1	(	(	PUNCT
ejpam-3123	81	2	r1r2	r1r2	X
ejpam-3123	81	3	0	0	NUM
ejpam-3123	81	4	0	0	NUM
ejpam-3123	81	5	s1s2	s1s2	PROPN
ejpam-3123	81	6	)	)	PUNCT
ejpam-3123	81	7	∈	∈	PROPN
ejpam-3123	81	8	t(1,0	t(1,0	PRON
ejpam-3123	81	9	)	)	PUNCT
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ejpam-3123	82	2	2	2	X
ejpam-3123	82	3	)	)	PUNCT
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ejpam-3123	82	20	)	)	PUNCT
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ejpam-3123	83	4	)	)	PUNCT
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ejpam-3123	83	7	:(	:(	PUNCT
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ejpam-3123	84	13	)	)	PUNCT
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ejpam-3123	85	5	that	that	SCONJ
ejpam-3123	85	6	rm	rm	PROPN
ejpam-3123	85	7	∈m	∈m	NOUN
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ejpam-3123	85	9	m	m	PROPN
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ejpam-3123	85	11	a	a	DET
ejpam-3123	85	12	left	left	ADJ
ejpam-3123	85	13	r	r	NOUN
ejpam-3123	85	14	-	-	PUNCT
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ejpam-3123	86	20	)	)	PUNCT
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ejpam-3123	86	27	)	)	PUNCT
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ejpam-3123	87	3	)	)	PUNCT
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ejpam-3123	87	5	have	have	VERB
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ejpam-3123	87	7	t(1,0)t(1,2	t(1,0)t(1,2	ADJ
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ejpam-3123	90	7	∈	∈	PROPN
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ejpam-3123	90	12	a	a	DET
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ejpam-3123	90	14	s	s	NOUN
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ejpam-3123	96	11	a	a	DET
ejpam-3123	96	12	right	right	ADJ
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ejpam-3123	98	3	appl	appl	PROPN
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ejpam-3123	98	5	math	math	PROPN
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ejpam-3123	98	17	980	980	NUM
ejpam-3123	98	18	971	971	NUM
ejpam-3123	98	19	(	(	PUNCT
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ejpam-3123	98	21	)	)	PUNCT
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ejpam-3123	98	23	)	)	PUNCT
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ejpam-3123	106	1	⊆	⊆	NUM
ejpam-3123	106	2	t(1,2)∗(1,0	t(1,2)∗(1,0	NOUN
ejpam-3123	106	3	)	)	PUNCT
ejpam-3123	106	4	as	as	ADP
ejpam-3123	106	5	for	for	ADP
ejpam-3123	106	6	all	all	DET
ejpam-3123	106	7	(	(	PUNCT
ejpam-3123	106	8	0	0	NUM
ejpam-3123	106	9	0	0	NUM
ejpam-3123	106	10	n	n	NOUN
ejpam-3123	106	11	0	0	NUM
ejpam-3123	106	12	)	)	PUNCT
ejpam-3123	106	13	∈	∈	PROPN
ejpam-3123	106	14	t(1,2	t(1,2	PROPN
ejpam-3123	106	15	)	)	PUNCT
ejpam-3123	106	16	,	,	PUNCT
ejpam-3123	106	17	(	(	PUNCT
ejpam-3123	106	18	r	r	NOUN
ejpam-3123	106	19	0	0	NUM
ejpam-3123	106	20	0	0	NUM
ejpam-3123	106	21	s	s	PART
ejpam-3123	106	22	)	)	PUNCT
ejpam-3123	106	23	∈	∈	PROPN
ejpam-3123	106	24	t(1,0	t(1,0	PRON
ejpam-3123	106	25	)	)	PUNCT
ejpam-3123	106	26	we	we	PRON
ejpam-3123	106	27	have	have	VERB
ejpam-3123	106	28	:	:	PUNCT
ejpam-3123	106	29	t(1,2)t(1,0	t(1,2)t(1,0	PROPN
ejpam-3123	106	30	)	)	PUNCT
ejpam-3123	106	31	=	=	PUNCT
ejpam-3123	106	32	(	(	PUNCT
ejpam-3123	106	33	0	0	NUM
ejpam-3123	106	34	0	0	NUM
ejpam-3123	106	35	n	n	NOUN
ejpam-3123	106	36	0	0	NUM
ejpam-3123	106	37	)	)	PUNCT
ejpam-3123	106	38	(	(	PUNCT
ejpam-3123	106	39	r	r	NOUN
ejpam-3123	106	40	0	0	NUM
ejpam-3123	106	41	0	0	NUM
ejpam-3123	106	42	s	s	PART
ejpam-3123	106	43	)	)	PUNCT
ejpam-3123	106	44	=	=	SYM
ejpam-3123	106	45	(	(	PUNCT
ejpam-3123	106	46	0	0	NUM
ejpam-3123	106	47	0	0	NUM
ejpam-3123	106	48	nr	nr	NOUN
ejpam-3123	106	49	0	0	NUM
ejpam-3123	106	50	)	)	PUNCT
ejpam-3123	106	51	∈	∈	PROPN
ejpam-3123	107	1	t(1,2	t(1,2	PROPN
ejpam-3123	107	2	)	)	PUNCT
ejpam-3123	107	3	=	=	SYM
ejpam-3123	107	4	t(1,2)∗(1,0	t(1,2)∗(1,0	NOUN
ejpam-3123	107	5	)	)	PUNCT
ejpam-3123	107	6	.	.	PUNCT
ejpam-3123	108	1	it	it	PRON
ejpam-3123	108	2	can	can	AUX
ejpam-3123	108	3	be	be	AUX
ejpam-3123	108	4	noted	note	VERB
ejpam-3123	108	5	that	that	SCONJ
ejpam-3123	108	6	nr	nr	PRON
ejpam-3123	108	7	∈	∈	PROPN
ejpam-3123	108	8	n	n	PRON
ejpam-3123	108	9	as	as	ADP
ejpam-3123	108	10	n	n	NUM
ejpam-3123	108	11	is	be	AUX
ejpam-3123	108	12	a	a	DET
ejpam-3123	108	13	left	left	ADJ
ejpam-3123	108	14	r	r	NOUN
ejpam-3123	108	15	-	-	PUNCT
ejpam-3123	108	16	module	module	NOUN
ejpam-3123	108	17	(	(	PUNCT
ejpam-3123	108	18	8)	8)	NUM
ejpam-3123	108	19	t(1,2)t(0,1	t(1,2)t(0,1	NOUN
ejpam-3123	108	20	)	)	PUNCT
ejpam-3123	108	21	⊆	⊆	NUM
ejpam-3123	108	22	t(1,2)∗(0,1	t(1,2)∗(0,1	NOUN
ejpam-3123	108	23	)	)	PUNCT
ejpam-3123	108	24	as	as	ADP
ejpam-3123	108	25	for	for	ADP
ejpam-3123	108	26	all	all	DET
ejpam-3123	108	27	(	(	PUNCT
ejpam-3123	108	28	0	0	NUM
ejpam-3123	108	29	0	0	NUM
ejpam-3123	108	30	n	n	NOUN
ejpam-3123	108	31	0	0	NUM
ejpam-3123	108	32	)	)	PUNCT
ejpam-3123	108	33	∈	∈	PROPN
ejpam-3123	108	34	t(1,2	t(1,2	PROPN
ejpam-3123	108	35	)	)	PUNCT
ejpam-3123	108	36	,	,	PUNCT
ejpam-3123	108	37	(	(	PUNCT
ejpam-3123	108	38	0	0	NUM
ejpam-3123	108	39	m	m	NOUN
ejpam-3123	108	40	0	0	NUM
ejpam-3123	108	41	0	0	NUM
ejpam-3123	109	1	)	)	PUNCT
ejpam-3123	109	2	∈	∈	PROPN
ejpam-3123	109	3	t(0,1	t(0,1	NOUN
ejpam-3123	109	4	)	)	PUNCT
ejpam-3123	109	5	we	we	PRON
ejpam-3123	109	6	have	have	VERB
ejpam-3123	109	7	:	:	PUNCT
ejpam-3123	109	8	t(1,2)t(0,1	t(1,2)t(0,1	NOUN
ejpam-3123	109	9	)	)	PUNCT
ejpam-3123	109	10	=	=	PUNCT
ejpam-3123	110	1	(	(	PUNCT
ejpam-3123	110	2	0	0	NUM
ejpam-3123	110	3	0	0	NUM
ejpam-3123	110	4	n	n	NOUN
ejpam-3123	110	5	0	0	NUM
ejpam-3123	110	6	)	)	PUNCT
ejpam-3123	110	7	(	(	PUNCT
ejpam-3123	110	8	0	0	NUM
ejpam-3123	110	9	m	m	NOUN
ejpam-3123	110	10	0	0	NUM
ejpam-3123	110	11	0	0	NUM
ejpam-3123	110	12	)	)	PUNCT
ejpam-3123	111	1	=	=	PRON
ejpam-3123	111	2	(	(	PUNCT
ejpam-3123	111	3	0	0	NUM
ejpam-3123	111	4	0	0	NUM
ejpam-3123	111	5	0	0	NUM
ejpam-3123	111	6	nm	nm	NOUN
ejpam-3123	111	7	)	)	PUNCT
ejpam-3123	111	8	∈	∈	PROPN
ejpam-3123	111	9	t(1,0	t(1,0	PRON
ejpam-3123	111	10	)	)	PUNCT
ejpam-3123	111	11	=	=	PUNCT
ejpam-3123	111	12	t(1,2)∗(0,1	t(1,2)∗(0,1	NOUN
ejpam-3123	111	13	)	)	PUNCT
ejpam-3123	111	14	.	.	PUNCT
ejpam-3123	112	1	(	(	PUNCT
ejpam-3123	112	2	9	9	X
ejpam-3123	112	3	)	)	SYM
ejpam-3123	112	4	t(1,2)t(1,2	t(1,2)t(1,2	NOUN
ejpam-3123	112	5	)	)	PUNCT
ejpam-3123	112	6	⊆	⊆	NUM
ejpam-3123	112	7	t(1,2)∗(1,2	t(1,2)∗(1,2	NOUN
ejpam-3123	112	8	)	)	PUNCT
ejpam-3123	112	9	as	as	ADP
ejpam-3123	112	10	for	for	ADP
ejpam-3123	112	11	all	all	DET
ejpam-3123	112	12	(	(	PUNCT
ejpam-3123	112	13	0	0	NUM
ejpam-3123	112	14	0	0	NUM
ejpam-3123	112	15	n1	n1	NOUN
ejpam-3123	112	16	0	0	NUM
ejpam-3123	112	17	)	)	PUNCT
ejpam-3123	112	18	,	,	PUNCT
ejpam-3123	112	19	(	(	PUNCT
ejpam-3123	112	20	0	0	NUM
ejpam-3123	112	21	0	0	NUM
ejpam-3123	112	22	n2	n2	NOUN
ejpam-3123	112	23	0	0	NUM
ejpam-3123	112	24	)	)	PUNCT
ejpam-3123	113	1	∈	∈	PROPN
ejpam-3123	113	2	t(1,2	t(1,2	X
ejpam-3123	113	3	)	)	PUNCT
ejpam-3123	113	4	we	we	PRON
ejpam-3123	113	5	have	have	VERB
ejpam-3123	113	6	:	:	PUNCT
ejpam-3123	113	7	t(1,2)t(1,2	t(1,2)t(1,2	ADJ
ejpam-3123	113	8	)	)	PUNCT
ejpam-3123	113	9	=	=	SYM
ejpam-3123	114	1	(	(	PUNCT
ejpam-3123	114	2	0	0	NUM
ejpam-3123	114	3	0	0	NUM
ejpam-3123	114	4	n1	n1	NOUN
ejpam-3123	114	5	0	0	NUM
ejpam-3123	114	6	)	)	PUNCT
ejpam-3123	114	7	(	(	PUNCT
ejpam-3123	114	8	0	0	NUM
ejpam-3123	114	9	0	0	NUM
ejpam-3123	114	10	n2	n2	NOUN
ejpam-3123	114	11	0	0	NUM
ejpam-3123	114	12	)	)	PUNCT
ejpam-3123	114	13	=	=	PUNCT
ejpam-3123	114	14	(	(	PUNCT
ejpam-3123	114	15	0	0	NUM
ejpam-3123	114	16	0	0	NUM
ejpam-3123	114	17	0	0	NUM
ejpam-3123	114	18	0	0	NUM
ejpam-3123	114	19	)	)	PUNCT
ejpam-3123	114	20	∈	∈	PROPN
ejpam-3123	115	1	t(0,1	t(0,1	NOUN
ejpam-3123	115	2	)	)	PUNCT
ejpam-3123	115	3	=	=	SYM
ejpam-3123	115	4	t(1,2)∗(1,2	t(1,2)∗(1,2	NOUN
ejpam-3123	115	5	)	)	PUNCT
ejpam-3123	115	6	.	.	PUNCT
ejpam-3123	116	1	thus	thus	ADV
ejpam-3123	116	2	,	,	PUNCT
ejpam-3123	116	3	t	t	PROPN
ejpam-3123	116	4	is	be	AUX
ejpam-3123	116	5	a	a	DET
ejpam-3123	116	6	g	g	NOUN
ejpam-3123	116	7	-	-	PUNCT
ejpam-3123	116	8	weak	weak	ADJ
ejpam-3123	116	9	graded	grade	VERB
ejpam-3123	116	10	ring	ring	NOUN
ejpam-3123	116	11	.	.	PUNCT
ejpam-3123	117	1	however	however	ADV
ejpam-3123	117	2	,	,	PUNCT
ejpam-3123	117	3	it	it	PRON
ejpam-3123	117	4	is	be	AUX
ejpam-3123	117	5	not	not	PART
ejpam-3123	117	6	a	a	DET
ejpam-3123	117	7	fully	fully	ADV
ejpam-3123	117	8	(	(	PUNCT
ejpam-3123	117	9	strongly	strongly	ADV
ejpam-3123	117	10	)	)	PUNCT
ejpam-3123	117	11	g	g	NOUN
ejpam-3123	117	12	-	-	PUNCT
ejpam-3123	117	13	weak	weak	ADJ
ejpam-3123	117	14	graded	grade	VERB
ejpam-3123	117	15	ring	ring	NOUN
ejpam-3123	117	16	.	.	PUNCT
ejpam-3123	118	1	for	for	ADP
ejpam-3123	118	2	instance	instance	NOUN
ejpam-3123	118	3	,	,	PUNCT
ejpam-3123	118	4	t(1,2)t(1,2	t(1,2)t(1,2	PROPN
ejpam-3123	118	5	)	)	PUNCT
ejpam-3123	118	6	6=	6=	NOUN
ejpam-3123	118	7	t(1,2)∗(1,2	t(1,2)∗(1,2	ADJ
ejpam-3123	118	8	)	)	PUNCT
ejpam-3123	118	9	as	as	ADP
ejpam-3123	118	10	t(0,1	t(0,1	ADP
ejpam-3123	118	11	)	)	PUNCT
ejpam-3123	118	12	=	=	SYM
ejpam-3123	118	13	t(1,2)∗(1,2	t(1,2)∗(1,2	ADJ
ejpam-3123	118	14	)	)	PUNCT
ejpam-3123	118	15	*	*	PUNCT
ejpam-3123	118	16	t(1,2)t(1,2	t(1,2)t(1,2	NOUN
ejpam-3123	118	17	)	)	PUNCT
ejpam-3123	118	18	.	.	PUNCT
ejpam-3123	119	1	4	4	X
ejpam-3123	119	2	.	.	X
ejpam-3123	120	1	some	some	DET
ejpam-3123	120	2	properties	property	NOUN
ejpam-3123	120	3	of	of	ADP
ejpam-3123	120	4	g	g	NOUN
ejpam-3123	120	5	-	-	PUNCT
ejpam-3123	120	6	weak	weak	ADJ
ejpam-3123	120	7	graded	grade	VERB
ejpam-3123	120	8	rings	ring	NOUN
ejpam-3123	120	9	in	in	ADP
ejpam-3123	120	10	this	this	DET
ejpam-3123	120	11	section	section	NOUN
ejpam-3123	120	12	,	,	PUNCT
ejpam-3123	120	13	in	in	ADP
ejpam-3123	120	14	the	the	DET
ejpam-3123	120	15	light	light	NOUN
ejpam-3123	120	16	of	of	ADP
ejpam-3123	120	17	[	[	X
ejpam-3123	120	18	4	4	NUM
ejpam-3123	120	19	]	]	PUNCT
ejpam-3123	120	20	,	,	PUNCT
ejpam-3123	120	21	some	some	DET
ejpam-3123	120	22	properties	property	NOUN
ejpam-3123	120	23	of	of	ADP
ejpam-3123	120	24	g	g	NOUN
ejpam-3123	120	25	-	-	PUNCT
ejpam-3123	120	26	weak	weak	ADJ
ejpam-3123	120	27	graded	grade	VERB
ejpam-3123	120	28	rings	ring	NOUN
ejpam-3123	120	29	are	be	AUX
ejpam-3123	120	30	proved	prove	VERB
ejpam-3123	120	31	.	.	PUNCT
ejpam-3123	121	1	proposition	proposition	NOUN
ejpam-3123	121	2	3	3	X
ejpam-3123	121	3	.	.	PUNCT
ejpam-3123	122	1	let	let	VERB
ejpam-3123	122	2	x	x	PRON
ejpam-3123	122	3	be	be	AUX
ejpam-3123	122	4	a	a	DET
ejpam-3123	122	5	group	group	NOUN
ejpam-3123	122	6	,	,	PUNCT
ejpam-3123	122	7	h	h	PROPN
ejpam-3123	122	8	be	be	VERB
ejpam-3123	122	9	a	a	DET
ejpam-3123	122	10	subgroup	subgroup	NOUN
ejpam-3123	122	11	of	of	ADP
ejpam-3123	122	12	x	x	PROPN
ejpam-3123	122	13	,	,	PUNCT
ejpam-3123	122	14	g	g	PROPN
ejpam-3123	122	15	⊂	⊂	PROPN
ejpam-3123	122	16	x	x	VERB
ejpam-3123	122	17	be	be	AUX
ejpam-3123	122	18	a	a	DET
ejpam-3123	122	19	set	set	NOUN
ejpam-3123	122	20	of	of	ADP
ejpam-3123	122	21	left	left	ADJ
ejpam-3123	122	22	coset	coset	NOUN
ejpam-3123	122	23	representatives	representative	NOUN
ejpam-3123	122	24	and	and	CCONJ
ejpam-3123	122	25	r	r	NOUN
ejpam-3123	122	26	be	be	AUX
ejpam-3123	122	27	a	a	DET
ejpam-3123	122	28	g	g	NOUN
ejpam-3123	122	29	-	-	PUNCT
ejpam-3123	122	30	weak	weak	ADJ
ejpam-3123	122	31	graded	grade	VERB
ejpam-3123	122	32	ring	ring	NOUN
ejpam-3123	122	33	.	.	PUNCT
ejpam-3123	123	1	then	then	ADV
ejpam-3123	123	2	for	for	ADP
ejpam-3123	123	3	any	any	DET
ejpam-3123	123	4	s	s	PROPN
ejpam-3123	123	5	,	,	PUNCT
ejpam-3123	123	6	t	t	PROPN
ejpam-3123	123	7	,	,	PUNCT
ejpam-3123	123	8	p	p	PROPN
ejpam-3123	123	9	∈	∈	PROPN
ejpam-3123	123	10	g	g	NOUN
ejpam-3123	123	11	and	and	CCONJ
ejpam-3123	123	12	u	u	NOUN
ejpam-3123	123	13	,	,	PUNCT
ejpam-3123	123	14	v	v	PROPN
ejpam-3123	123	15	∈	∈	PROPN
ejpam-3123	123	16	h	h	NOUN
ejpam-3123	123	17	,	,	PUNCT
ejpam-3123	123	18	the	the	DET
ejpam-3123	123	19	following	follow	VERB
ejpam-3123	123	20	properties	property	NOUN
ejpam-3123	123	21	are	be	AUX
ejpam-3123	123	22	satisfied	satisfied	ADJ
ejpam-3123	123	23	:	:	PUNCT
ejpam-3123	123	24	(	(	PUNCT
ejpam-3123	123	25	i	i	NOUN
ejpam-3123	123	26	)	)	PUNCT
ejpam-3123	123	27	rs.(t.u	rs.(t.u	VERB
ejpam-3123	123	28	)	)	PUNCT
ejpam-3123	124	1	=	=	SYM
ejpam-3123	125	1	r	r	NOUN
ejpam-3123	125	2	f(s	f(	NOUN
ejpam-3123	125	3	,	,	PUNCT
ejpam-3123	125	4	t	t	PROPN
ejpam-3123	125	5	)	)	PUNCT
ejpam-3123	125	6	(	(	PUNCT
ejpam-3123	125	7	(	(	PUNCT
ejpam-3123	125	8	s∗t).u	s∗t).u	PROPN
ejpam-3123	125	9	)	)	PUNCT
ejpam-3123	125	10	f	f	PROPN
ejpam-3123	125	11	(	(	PUNCT
ejpam-3123	125	12	s/(t.u),t	s/(t.u),t	PROPN
ejpam-3123	125	13	/	/	SYM
ejpam-3123	125	14	u	u	NOUN
ejpam-3123	125	15	)	)	PUNCT
ejpam-3123	125	16	−1	−1	NOUN
ejpam-3123	125	17	.	.	PUNCT
ejpam-3123	126	1	(	(	PUNCT
ejpam-3123	126	2	ii	ii	NOUN
ejpam-3123	126	3	)	)	PUNCT
ejpam-3123	126	4	r(s∗t)/u	r(s∗t)/u	NOUN
ejpam-3123	126	5	=	=	SYM
ejpam-3123	126	6	r	r	PROPN
ejpam-3123	126	7	(	(	PUNCT
ejpam-3123	126	8	s/(t.u	s/(t.u	NOUN
ejpam-3123	126	9	)	)	PUNCT
ejpam-3123	126	10	)	)	PUNCT
ejpam-3123	127	1	∗(t	∗(t	NOUN
ejpam-3123	127	2	/	/	SYM
ejpam-3123	127	3	u	u	NOUN
ejpam-3123	127	4	)	)	PUNCT
ejpam-3123	127	5	.	.	PUNCT
ejpam-3123	128	1	(	(	PUNCT
ejpam-3123	128	2	iii	iii	X
ejpam-3123	128	3	)	)	PUNCT
ejpam-3123	128	4	rs.uv	rs.uv	NOUN
ejpam-3123	128	5	=	=	SYM
ejpam-3123	128	6	r	r	NOUN
ejpam-3123	128	7	(	(	PUNCT
ejpam-3123	128	8	s.u	s.u	NOUN
ejpam-3123	128	9	)	)	PUNCT
ejpam-3123	128	10	(	(	PUNCT
ejpam-3123	128	11	(	(	PUNCT
ejpam-3123	128	12	s	s	NOUN
ejpam-3123	128	13	/	/	SYM
ejpam-3123	128	14	u).v	u).v	ADJ
ejpam-3123	128	15	)	)	PUNCT
ejpam-3123	128	16	.	.	PUNCT
ejpam-3123	129	1	n.	n.	PROPN
ejpam-3123	129	2	al	al	PROPN
ejpam-3123	129	3	-	-	PUNCT
ejpam-3123	129	4	subaie	subaie	NOUN
ejpam-3123	129	5	,	,	PUNCT
ejpam-3123	129	6	m.	m.	NOUN
ejpam-3123	129	7	m.	m.	PROPN
ejpam-3123	129	8	al	al	PROPN
ejpam-3123	129	9	-	-	PUNCT
ejpam-3123	129	10	shomrani	shomrani	PROPN
ejpam-3123	129	11	/	/	SYM
ejpam-3123	129	12	eur	eur	NOUN
ejpam-3123	129	13	.	.	PUNCT
ejpam-3123	130	1	j.	j.	PROPN
ejpam-3123	130	2	pure	pure	PROPN
ejpam-3123	130	3	appl	appl	PROPN
ejpam-3123	130	4	.	.	PROPN
ejpam-3123	130	5	math	math	PROPN
ejpam-3123	130	6	,	,	PUNCT
ejpam-3123	130	7	10	10	NUM
ejpam-3123	130	8	(	(	PUNCT
ejpam-3123	130	9	5	5	NUM
ejpam-3123	130	10	)	)	PUNCT
ejpam-3123	130	11	(	(	PUNCT
ejpam-3123	130	12	2017	2017	NUM
ejpam-3123	130	13	)	)	PUNCT
ejpam-3123	130	14	,	,	PUNCT
ejpam-3123	130	15	967	967	NUM
ejpam-3123	130	16	-	-	SYM
ejpam-3123	130	17	980	980	NUM
ejpam-3123	130	18	972	972	NUM
ejpam-3123	130	19	(	(	PUNCT
ejpam-3123	130	20	iv	iv	X
ejpam-3123	130	21	)	)	PUNCT
ejpam-3123	130	22	rs	rs	NOUN
ejpam-3123	130	23	/	/	SYM
ejpam-3123	130	24	uv	uv	NOUN
ejpam-3123	130	25	=	=	PUNCT
ejpam-3123	130	26	r(s	r(s	PROPN
ejpam-3123	130	27	/	/	SYM
ejpam-3123	130	28	u)/v	u)/v	PROPN
ejpam-3123	130	29	.	.	PUNCT
ejpam-3123	131	1	(	(	PUNCT
ejpam-3123	131	2	v	v	NOUN
ejpam-3123	131	3	)	)	PUNCT
ejpam-3123	131	4	rf(p	rf(p	NOUN
ejpam-3123	131	5	,	,	PUNCT
ejpam-3123	131	6	s)f(p∗s	s)f(p∗s	PROPN
ejpam-3123	131	7	,	,	PUNCT
ejpam-3123	131	8	t	t	PROPN
ejpam-3123	131	9	)	)	PUNCT
ejpam-3123	132	1	=	=	SYM
ejpam-3123	132	2	r	r	X
ejpam-3123	132	3	(	(	PUNCT
ejpam-3123	132	4	p.f(s	p.f(s	PROPN
ejpam-3123	132	5	,	,	PUNCT
ejpam-3123	132	6	t	t	PROPN
ejpam-3123	132	7	)	)	PUNCT
ejpam-3123	132	8	)	)	PUNCT
ejpam-3123	133	1	f	f	NOUN
ejpam-3123	133	2	(	(	PUNCT
ejpam-3123	133	3	p	p	X
ejpam-3123	133	4	/	/	SYM
ejpam-3123	133	5	f(s	f(	NOUN
ejpam-3123	133	6	,	,	PUNCT
ejpam-3123	133	7	t),s∗t	t),s∗t	NOUN
ejpam-3123	133	8	)	)	PUNCT
ejpam-3123	133	9	.	.	PUNCT
ejpam-3123	134	1	(	(	PUNCT
ejpam-3123	134	2	vi	vi	NOUN
ejpam-3123	134	3	)	)	PUNCT
ejpam-3123	134	4	r	r	NOUN
ejpam-3123	134	5	(	(	PUNCT
ejpam-3123	134	6	p	p	X
ejpam-3123	134	7	/	/	SYM
ejpam-3123	134	8	f(s	f(	NOUN
ejpam-3123	134	9	,	,	PUNCT
ejpam-3123	134	10	t	t	PROPN
ejpam-3123	134	11	)	)	PUNCT
ejpam-3123	134	12	)	)	PUNCT
ejpam-3123	135	1	∗(s∗t	∗(s∗t	PUNCT
ejpam-3123	135	2	)	)	PUNCT
ejpam-3123	135	3	=	=	PUNCT
ejpam-3123	135	4	r(p∗s)∗t	r(p∗s)∗t	NOUN
ejpam-3123	135	5	.	.	PUNCT
ejpam-3123	136	1	proof	proof	NOUN
ejpam-3123	136	2	.	.	PUNCT
ejpam-3123	137	1	the	the	DET
ejpam-3123	137	2	associativity	associativity	NOUN
ejpam-3123	137	3	of	of	ADP
ejpam-3123	137	4	x	x	PRON
ejpam-3123	137	5	implies	imply	VERB
ejpam-3123	137	6	that	that	SCONJ
ejpam-3123	137	7	r(st)u	r(st)u	PROPN
ejpam-3123	137	8	=	=	SYM
ejpam-3123	137	9	rs(tu	rs(tu	PROPN
ejpam-3123	137	10	)	)	PUNCT
ejpam-3123	137	11	which	which	PRON
ejpam-3123	137	12	is	be	AUX
ejpam-3123	137	13	used	use	VERB
ejpam-3123	137	14	to	to	PART
ejpam-3123	137	15	prove	prove	VERB
ejpam-3123	137	16	relations	relation	NOUN
ejpam-3123	137	17	(	(	PUNCT
ejpam-3123	137	18	i	i	NOUN
ejpam-3123	137	19	)	)	PUNCT
ejpam-3123	137	20	and	and	CCONJ
ejpam-3123	137	21	(	(	PUNCT
ejpam-3123	137	22	ii	ii	NOUN
ejpam-3123	137	23	)	)	PUNCT
ejpam-3123	137	24	as	as	SCONJ
ejpam-3123	137	25	follows	follow	VERB
ejpam-3123	137	26	:	:	PUNCT
ejpam-3123	137	27	r(st)u	r(st)u	NOUN
ejpam-3123	137	28	=	=	PUNCT
ejpam-3123	137	29	rf(s	rf(	NOUN
ejpam-3123	137	30	,	,	PUNCT
ejpam-3123	137	31	t)(s∗t)u	t)(s∗t)u	NOUN
ejpam-3123	138	1	=	=	X
ejpam-3123	138	2	r	r	NOUN
ejpam-3123	138	3	f(s	f(	NOUN
ejpam-3123	138	4	,	,	PUNCT
ejpam-3123	138	5	t	t	PROPN
ejpam-3123	138	6	)	)	PUNCT
ejpam-3123	138	7	(	(	PUNCT
ejpam-3123	138	8	(	(	PUNCT
ejpam-3123	138	9	s∗t).u	s∗t).u	X
ejpam-3123	138	10	)	)	PUNCT
ejpam-3123	138	11	(	(	PUNCT
ejpam-3123	138	12	(	(	PUNCT
ejpam-3123	138	13	s∗t)/u	s∗t)/u	PROPN
ejpam-3123	138	14	)	)	PUNCT
ejpam-3123	138	15	.	.	PUNCT
ejpam-3123	139	1	on	on	ADP
ejpam-3123	139	2	the	the	DET
ejpam-3123	139	3	other	other	ADJ
ejpam-3123	139	4	hand	hand	NOUN
ejpam-3123	139	5	,	,	PUNCT
ejpam-3123	139	6	rs(tu	rs(tu	PROPN
ejpam-3123	139	7	)	)	PUNCT
ejpam-3123	139	8	=	=	SYM
ejpam-3123	139	9	rs(t.u)(t	rs(t.u)(t	NOUN
ejpam-3123	139	10	/	/	SYM
ejpam-3123	139	11	u	u	NOUN
ejpam-3123	139	12	)	)	PUNCT
ejpam-3123	139	13	=	=	SYM
ejpam-3123	139	14	r	r	NOUN
ejpam-3123	139	15	(	(	PUNCT
ejpam-3123	139	16	s.(t.u	s.(t.u	PROPN
ejpam-3123	139	17	)	)	PUNCT
ejpam-3123	139	18	)	)	PUNCT
ejpam-3123	139	19	(	(	PUNCT
ejpam-3123	139	20	s/(t.u	s/(t.u	NOUN
ejpam-3123	139	21	)	)	PUNCT
ejpam-3123	139	22	)	)	PUNCT
ejpam-3123	139	23	(	(	PUNCT
ejpam-3123	139	24	t	t	PROPN
ejpam-3123	139	25	/	/	SYM
ejpam-3123	139	26	u	u	NOUN
ejpam-3123	139	27	)	)	PUNCT
ejpam-3123	139	28	=	=	SYM
ejpam-3123	139	29	r	r	NOUN
ejpam-3123	139	30	(	(	PUNCT
ejpam-3123	139	31	s.(t.u	s.(t.u	PROPN
ejpam-3123	139	32	)	)	PUNCT
ejpam-3123	139	33	)	)	PUNCT
ejpam-3123	140	1	f	f	PROPN
ejpam-3123	140	2	(	(	PUNCT
ejpam-3123	140	3	s/(t.u),t	s/(t.u),t	PROPN
ejpam-3123	140	4	/	/	SYM
ejpam-3123	140	5	u	u	NOUN
ejpam-3123	140	6	)	)	PUNCT
ejpam-3123	140	7	(	(	PUNCT
ejpam-3123	140	8	s/(t.u)∗(t	s/(t.u)∗(t	NOUN
ejpam-3123	140	9	/	/	SYM
ejpam-3123	140	10	u	u	NOUN
ejpam-3123	140	11	)	)	PUNCT
ejpam-3123	140	12	)	)	PUNCT
ejpam-3123	140	13	.	.	PUNCT
ejpam-3123	141	1	thus	thus	ADV
ejpam-3123	141	2	,	,	PUNCT
ejpam-3123	141	3	r	r	NOUN
ejpam-3123	141	4	f(s	f(	NOUN
ejpam-3123	141	5	,	,	PUNCT
ejpam-3123	141	6	t	t	PROPN
ejpam-3123	141	7	)	)	PUNCT
ejpam-3123	141	8	(	(	PUNCT
ejpam-3123	141	9	(	(	PUNCT
ejpam-3123	141	10	s∗t).u	s∗t).u	X
ejpam-3123	141	11	)	)	PUNCT
ejpam-3123	141	12	(	(	PUNCT
ejpam-3123	141	13	(	(	PUNCT
ejpam-3123	141	14	s∗t)/u	s∗t)/u	VERB
ejpam-3123	141	15	)	)	PUNCT
ejpam-3123	142	1	=	=	SYM
ejpam-3123	142	2	r	r	X
ejpam-3123	142	3	(	(	PUNCT
ejpam-3123	142	4	s.(t.u	s.(t.u	PROPN
ejpam-3123	142	5	)	)	PUNCT
ejpam-3123	142	6	)	)	PUNCT
ejpam-3123	143	1	f	f	PROPN
ejpam-3123	143	2	(	(	PUNCT
ejpam-3123	143	3	s/(t.u),t	s/(t.u),t	PROPN
ejpam-3123	143	4	/	/	SYM
ejpam-3123	143	5	u	u	NOUN
ejpam-3123	143	6	)	)	PUNCT
ejpam-3123	143	7	(	(	PUNCT
ejpam-3123	143	8	s/(t.u)∗(t	s/(t.u)∗(t	NOUN
ejpam-3123	143	9	/	/	SYM
ejpam-3123	143	10	u	u	NOUN
ejpam-3123	143	11	)	)	PUNCT
ejpam-3123	143	12	)	)	PUNCT
ejpam-3123	143	13	.	.	PUNCT
ejpam-3123	144	1	as	as	SCONJ
ejpam-3123	144	2	the	the	DET
ejpam-3123	144	3	factorization	factorization	NOUN
ejpam-3123	144	4	is	be	AUX
ejpam-3123	144	5	unique	unique	ADJ
ejpam-3123	144	6	,	,	PUNCT
ejpam-3123	144	7	we	we	PRON
ejpam-3123	144	8	get	get	VERB
ejpam-3123	144	9	:	:	PUNCT
ejpam-3123	144	10	r	r	NOUN
ejpam-3123	144	11	(	(	PUNCT
ejpam-3123	144	12	s.(t.u	s.(t.u	PROPN
ejpam-3123	144	13	)	)	PUNCT
ejpam-3123	144	14	)	)	PUNCT
ejpam-3123	145	1	f	f	PROPN
ejpam-3123	145	2	(	(	PUNCT
ejpam-3123	145	3	s/(t.u),t	s/(t.u),t	PROPN
ejpam-3123	145	4	/	/	SYM
ejpam-3123	145	5	u	u	NOUN
ejpam-3123	145	6	)	)	PUNCT
ejpam-3123	145	7	=	=	SYM
ejpam-3123	146	1	r	r	NOUN
ejpam-3123	146	2	f(s	f(	NOUN
ejpam-3123	146	3	,	,	PUNCT
ejpam-3123	146	4	t	t	PROPN
ejpam-3123	146	5	)	)	PUNCT
ejpam-3123	146	6	(	(	PUNCT
ejpam-3123	146	7	(	(	PUNCT
ejpam-3123	146	8	s∗t).u	s∗t).u	PROPN
ejpam-3123	146	9	)	)	PUNCT
ejpam-3123	146	10	,	,	PUNCT
ejpam-3123	146	11	or	or	CCONJ
ejpam-3123	146	12	equivalently	equivalently	ADV
ejpam-3123	146	13	,	,	PUNCT
ejpam-3123	146	14	rs.(t.u	rs.(t.u	NOUN
ejpam-3123	146	15	)	)	PUNCT
ejpam-3123	146	16	=	=	SYM
ejpam-3123	146	17	r	r	NOUN
ejpam-3123	146	18	f(s	f(	NOUN
ejpam-3123	146	19	,	,	PUNCT
ejpam-3123	146	20	t	t	PROPN
ejpam-3123	146	21	)	)	PUNCT
ejpam-3123	146	22	(	(	PUNCT
ejpam-3123	146	23	(	(	PUNCT
ejpam-3123	146	24	s∗t).u	s∗t).u	PROPN
ejpam-3123	146	25	)	)	PUNCT
ejpam-3123	146	26	f	f	PROPN
ejpam-3123	146	27	(	(	PUNCT
ejpam-3123	146	28	s/(t.u),t	s/(t.u),t	PROPN
ejpam-3123	146	29	/	/	SYM
ejpam-3123	146	30	u	u	NOUN
ejpam-3123	146	31	)	)	PUNCT
ejpam-3123	146	32	−1	−1	NOUN
ejpam-3123	146	33	.	.	PUNCT
ejpam-3123	147	1	also	also	ADV
ejpam-3123	147	2	,	,	PUNCT
ejpam-3123	147	3	r	r	X
ejpam-3123	147	4	(	(	PUNCT
ejpam-3123	147	5	(	(	PUNCT
ejpam-3123	147	6	s∗t)/u	s∗t)/u	NOUN
ejpam-3123	147	7	)	)	PUNCT
ejpam-3123	147	8	=	=	SYM
ejpam-3123	147	9	r	r	NOUN
ejpam-3123	147	10	(	(	PUNCT
ejpam-3123	147	11	s/(t.u)∗(t	s/(t.u)∗(t	NOUN
ejpam-3123	147	12	/	/	SYM
ejpam-3123	147	13	u	u	NOUN
ejpam-3123	147	14	)	)	PUNCT
ejpam-3123	147	15	)	)	PUNCT
ejpam-3123	147	16	.	.	PUNCT
ejpam-3123	148	1	next	next	ADV
ejpam-3123	148	2	,	,	PUNCT
ejpam-3123	148	3	to	to	PART
ejpam-3123	148	4	prove	prove	VERB
ejpam-3123	148	5	relations	relation	NOUN
ejpam-3123	148	6	(	(	PUNCT
ejpam-3123	148	7	iii	iii	NOUN
ejpam-3123	148	8	)	)	PUNCT
ejpam-3123	148	9	and	and	CCONJ
ejpam-3123	148	10	(	(	PUNCT
ejpam-3123	148	11	iv	iv	X
ejpam-3123	148	12	)	)	PUNCT
ejpam-3123	148	13	,	,	PUNCT
ejpam-3123	148	14	we	we	PRON
ejpam-3123	148	15	consider	consider	VERB
ejpam-3123	148	16	rs(uv	rs(uv	NOUN
ejpam-3123	148	17	)	)	PUNCT
ejpam-3123	149	1	=	=	PUNCT
ejpam-3123	149	2	r(su)v	r(su)v	PROPN
ejpam-3123	149	3	,	,	PUNCT
ejpam-3123	149	4	which	which	PRON
ejpam-3123	149	5	is	be	AUX
ejpam-3123	149	6	true	true	ADJ
ejpam-3123	149	7	by	by	ADP
ejpam-3123	149	8	the	the	DET
ejpam-3123	149	9	associativity	associativity	NOUN
ejpam-3123	149	10	of	of	ADP
ejpam-3123	149	11	x	x	PRON
ejpam-3123	149	12	,	,	PUNCT
ejpam-3123	149	13	as	as	SCONJ
ejpam-3123	149	14	follows	follow	VERB
ejpam-3123	149	15	:	:	PUNCT
ejpam-3123	149	16	rs(uv	rs(uv	NOUN
ejpam-3123	149	17	)	)	PUNCT
ejpam-3123	150	1	=	=	PUNCT
ejpam-3123	150	2	r(s.uv)(s	r(s.uv)(s	NOUN
ejpam-3123	150	3	/	/	SYM
ejpam-3123	150	4	uv	uv	NOUN
ejpam-3123	150	5	)	)	PUNCT
ejpam-3123	150	6	.	.	PUNCT
ejpam-3123	151	1	on	on	ADP
ejpam-3123	151	2	the	the	DET
ejpam-3123	151	3	other	other	ADJ
ejpam-3123	151	4	hand	hand	NOUN
ejpam-3123	151	5	,	,	PUNCT
ejpam-3123	151	6	r(su)v	r(su)v	PROPN
ejpam-3123	151	7	=	=	SYM
ejpam-3123	151	8	r(s.u)(s	r(s.u)(s	NOUN
ejpam-3123	151	9	/	/	SYM
ejpam-3123	151	10	u)v	u)v	PUNCT
ejpam-3123	151	11	=	=	SYM
ejpam-3123	151	12	r	r	NOUN
ejpam-3123	151	13	(	(	PUNCT
ejpam-3123	151	14	s.u	s.u	NOUN
ejpam-3123	151	15	)	)	PUNCT
ejpam-3123	151	16	(	(	PUNCT
ejpam-3123	151	17	(	(	PUNCT
ejpam-3123	151	18	s	s	NOUN
ejpam-3123	151	19	/	/	SYM
ejpam-3123	151	20	u).v	u).v	NOUN
ejpam-3123	151	21	)	)	PUNCT
ejpam-3123	151	22	(	(	PUNCT
ejpam-3123	151	23	(	(	PUNCT
ejpam-3123	151	24	s	s	X
ejpam-3123	151	25	/	/	SYM
ejpam-3123	151	26	u)/v	u)/v	PROPN
ejpam-3123	151	27	)	)	PUNCT
ejpam-3123	151	28	.	.	PUNCT
ejpam-3123	152	1	thus	thus	ADV
ejpam-3123	152	2	,	,	PUNCT
ejpam-3123	152	3	r(s.uv)(s	r(s.uv)(s	NOUN
ejpam-3123	152	4	/	/	SYM
ejpam-3123	152	5	uv	uv	NOUN
ejpam-3123	152	6	)	)	PUNCT
ejpam-3123	153	1	=	=	SYM
ejpam-3123	153	2	r	r	NOUN
ejpam-3123	153	3	(	(	PUNCT
ejpam-3123	153	4	s.u	s.u	NOUN
ejpam-3123	153	5	)	)	PUNCT
ejpam-3123	153	6	(	(	PUNCT
ejpam-3123	153	7	(	(	PUNCT
ejpam-3123	153	8	s	s	NOUN
ejpam-3123	153	9	/	/	SYM
ejpam-3123	153	10	u).v	u).v	NOUN
ejpam-3123	153	11	)	)	PUNCT
ejpam-3123	153	12	(	(	PUNCT
ejpam-3123	153	13	(	(	PUNCT
ejpam-3123	153	14	s	s	X
ejpam-3123	153	15	/	/	SYM
ejpam-3123	153	16	u)/v	u)/v	PROPN
ejpam-3123	153	17	)	)	PUNCT
ejpam-3123	153	18	.	.	PUNCT
ejpam-3123	154	1	again	again	ADV
ejpam-3123	154	2	,	,	PUNCT
ejpam-3123	154	3	by	by	ADP
ejpam-3123	154	4	the	the	DET
ejpam-3123	154	5	uniqueness	uniqueness	NOUN
ejpam-3123	154	6	of	of	ADP
ejpam-3123	154	7	factorization	factorization	NOUN
ejpam-3123	154	8	,	,	PUNCT
ejpam-3123	154	9	we	we	PRON
ejpam-3123	154	10	get	get	VERB
ejpam-3123	154	11	:	:	PUNCT
ejpam-3123	154	12	r(s.uv	r(s.uv	X
ejpam-3123	154	13	)	)	PUNCT
ejpam-3123	154	14	=	=	SYM
ejpam-3123	154	15	r	r	NOUN
ejpam-3123	154	16	(	(	PUNCT
ejpam-3123	154	17	s.u	s.u	NOUN
ejpam-3123	154	18	)	)	PUNCT
ejpam-3123	154	19	(	(	PUNCT
ejpam-3123	154	20	(	(	PUNCT
ejpam-3123	154	21	s	s	NOUN
ejpam-3123	154	22	/	/	SYM
ejpam-3123	154	23	u).v	u).v	NOUN
ejpam-3123	154	24	)	)	PUNCT
ejpam-3123	154	25	,	,	PUNCT
ejpam-3123	154	26	n.	n.	PROPN
ejpam-3123	154	27	al	al	PROPN
ejpam-3123	154	28	-	-	PUNCT
ejpam-3123	154	29	subaie	subaie	NOUN
ejpam-3123	154	30	,	,	PUNCT
ejpam-3123	154	31	m.	m.	NOUN
ejpam-3123	154	32	m.	m.	PROPN
ejpam-3123	154	33	al	al	PROPN
ejpam-3123	154	34	-	-	PUNCT
ejpam-3123	154	35	shomrani	shomrani	PROPN
ejpam-3123	154	36	/	/	SYM
ejpam-3123	154	37	eur	eur	NOUN
ejpam-3123	154	38	.	.	PUNCT
ejpam-3123	155	1	j.	j.	PROPN
ejpam-3123	155	2	pure	pure	PROPN
ejpam-3123	155	3	appl	appl	PROPN
ejpam-3123	155	4	.	.	PROPN
ejpam-3123	155	5	math	math	PROPN
ejpam-3123	155	6	,	,	PUNCT
ejpam-3123	155	7	10	10	NUM
ejpam-3123	155	8	(	(	PUNCT
ejpam-3123	155	9	5	5	NUM
ejpam-3123	155	10	)	)	PUNCT
ejpam-3123	155	11	(	(	PUNCT
ejpam-3123	155	12	2017	2017	NUM
ejpam-3123	155	13	)	)	PUNCT
ejpam-3123	155	14	,	,	PUNCT
ejpam-3123	155	15	967	967	NUM
ejpam-3123	155	16	-	-	SYM
ejpam-3123	155	17	980	980	NUM
ejpam-3123	155	18	973	973	NUM
ejpam-3123	155	19	and	and	CCONJ
ejpam-3123	155	20	,	,	PUNCT
ejpam-3123	155	21	r(s	r(s	PROPN
ejpam-3123	155	22	/	/	SYM
ejpam-3123	155	23	uv	uv	NOUN
ejpam-3123	155	24	)	)	PUNCT
ejpam-3123	155	25	=	=	PUNCT
ejpam-3123	156	1	r(s	r(s	NUM
ejpam-3123	156	2	/	/	SYM
ejpam-3123	156	3	u)/v	u)/v	PROPN
ejpam-3123	156	4	.	.	PUNCT
ejpam-3123	157	1	finally	finally	ADV
ejpam-3123	157	2	,	,	PUNCT
ejpam-3123	157	3	as	as	ADP
ejpam-3123	157	4	before	before	ADV
ejpam-3123	157	5	,	,	PUNCT
ejpam-3123	157	6	the	the	DET
ejpam-3123	157	7	associativity	associativity	NOUN
ejpam-3123	157	8	of	of	ADP
ejpam-3123	157	9	x	x	PROPN
ejpam-3123	157	10	yields	yields	PROPN
ejpam-3123	157	11	rp(st	rp(st	PROPN
ejpam-3123	157	12	)	)	PUNCT
ejpam-3123	157	13	=	=	SYM
ejpam-3123	157	14	r(ps)t	r(ps)t	NOUN
ejpam-3123	157	15	which	which	PRON
ejpam-3123	157	16	is	be	AUX
ejpam-3123	157	17	used	use	VERB
ejpam-3123	157	18	to	to	PART
ejpam-3123	157	19	prove	prove	VERB
ejpam-3123	157	20	relations	relation	NOUN
ejpam-3123	157	21	(	(	PUNCT
ejpam-3123	157	22	v	v	NOUN
ejpam-3123	157	23	)	)	PUNCT
ejpam-3123	157	24	and	and	CCONJ
ejpam-3123	157	25	(	(	PUNCT
ejpam-3123	157	26	vi	vi	X
ejpam-3123	157	27	)	)	PUNCT
ejpam-3123	157	28	as	as	SCONJ
ejpam-3123	157	29	follows	follow	VERB
ejpam-3123	157	30	:	:	PUNCT
ejpam-3123	157	31	rp(st	rp(st	NOUN
ejpam-3123	157	32	)	)	PUNCT
ejpam-3123	158	1	=	=	PUNCT
ejpam-3123	158	2	rpf(s	rpf(	NOUN
ejpam-3123	158	3	,	,	PUNCT
ejpam-3123	158	4	t)(s∗t	t)(s∗t	X
ejpam-3123	158	5	)	)	PUNCT
ejpam-3123	158	6	=	=	SYM
ejpam-3123	159	1	r	r	X
ejpam-3123	159	2	(	(	PUNCT
ejpam-3123	159	3	p.f(s	p.f(s	PROPN
ejpam-3123	159	4	,	,	PUNCT
ejpam-3123	159	5	t	t	PROPN
ejpam-3123	159	6	)	)	PUNCT
ejpam-3123	159	7	)	)	PUNCT
ejpam-3123	160	1	(	(	PUNCT
ejpam-3123	160	2	p	p	X
ejpam-3123	160	3	/	/	SYM
ejpam-3123	160	4	f(s	f(	NOUN
ejpam-3123	160	5	,	,	PUNCT
ejpam-3123	160	6	t	t	PROPN
ejpam-3123	160	7	)	)	PUNCT
ejpam-3123	160	8	)	)	PUNCT
ejpam-3123	160	9	(	(	PUNCT
ejpam-3123	160	10	s∗t	s∗t	X
ejpam-3123	160	11	)	)	PUNCT
ejpam-3123	160	12	=	=	SYM
ejpam-3123	160	13	r	r	X
ejpam-3123	160	14	(	(	PUNCT
ejpam-3123	160	15	p.f(s	p.f(s	PROPN
ejpam-3123	160	16	,	,	PUNCT
ejpam-3123	160	17	t	t	PROPN
ejpam-3123	160	18	)	)	PUNCT
ejpam-3123	160	19	)	)	PUNCT
ejpam-3123	161	1	f	f	NOUN
ejpam-3123	161	2	(	(	PUNCT
ejpam-3123	161	3	p	p	X
ejpam-3123	161	4	/	/	SYM
ejpam-3123	161	5	f(s	f(	NOUN
ejpam-3123	161	6	,	,	PUNCT
ejpam-3123	161	7	t),(s∗t	t),(s∗t	NOUN
ejpam-3123	161	8	)	)	PUNCT
ejpam-3123	161	9	)	)	PUNCT
ejpam-3123	161	10	(	(	PUNCT
ejpam-3123	161	11	(	(	PUNCT
ejpam-3123	161	12	p	p	X
ejpam-3123	161	13	/	/	SYM
ejpam-3123	161	14	f(s	f(	NOUN
ejpam-3123	161	15	,	,	PUNCT
ejpam-3123	161	16	t))∗(s∗t	t))∗(s∗t	NUM
ejpam-3123	161	17	)	)	PUNCT
ejpam-3123	161	18	)	)	PUNCT
ejpam-3123	161	19	.	.	PUNCT
ejpam-3123	162	1	on	on	ADP
ejpam-3123	162	2	the	the	DET
ejpam-3123	162	3	other	other	ADJ
ejpam-3123	162	4	hand	hand	NOUN
ejpam-3123	162	5	,	,	PUNCT
ejpam-3123	162	6	r(ps)t	r(ps)t	NOUN
ejpam-3123	162	7	=	=	SYM
ejpam-3123	162	8	rf(p	rf(p	X
ejpam-3123	162	9	,	,	PUNCT
ejpam-3123	162	10	s)(p∗s)t	s)(p∗s)t	NOUN
ejpam-3123	162	11	=	=	SYM
ejpam-3123	162	12	r	r	NOUN
ejpam-3123	162	13	f(p	f(p	PROPN
ejpam-3123	162	14	,	,	PUNCT
ejpam-3123	162	15	s)f	s)f	NUM
ejpam-3123	162	16	(	(	PUNCT
ejpam-3123	162	17	(	(	PUNCT
ejpam-3123	162	18	p∗s),t	p∗s),t	X
ejpam-3123	162	19	)	)	PUNCT
ejpam-3123	162	20	(	(	PUNCT
ejpam-3123	162	21	(	(	PUNCT
ejpam-3123	162	22	p∗s)∗t	p∗s)∗t	NOUN
ejpam-3123	162	23	)	)	PUNCT
ejpam-3123	162	24	.	.	PUNCT
ejpam-3123	163	1	thus	thus	ADV
ejpam-3123	163	2	,	,	PUNCT
ejpam-3123	163	3	r	r	NOUN
ejpam-3123	163	4	f(p	f(p	NOUN
ejpam-3123	163	5	,	,	PUNCT
ejpam-3123	163	6	s)f	s)f	NUM
ejpam-3123	163	7	(	(	PUNCT
ejpam-3123	163	8	(	(	PUNCT
ejpam-3123	163	9	p∗s),t	p∗s),t	X
ejpam-3123	163	10	)	)	PUNCT
ejpam-3123	163	11	(	(	PUNCT
ejpam-3123	163	12	(	(	PUNCT
ejpam-3123	163	13	p∗s)∗t	p∗s)∗t	NOUN
ejpam-3123	163	14	)	)	PUNCT
ejpam-3123	164	1	=	=	PUNCT
ejpam-3123	164	2	r	r	X
ejpam-3123	164	3	(	(	PUNCT
ejpam-3123	164	4	p.f(s	p.f(s	PROPN
ejpam-3123	164	5	,	,	PUNCT
ejpam-3123	164	6	t	t	PROPN
ejpam-3123	164	7	)	)	PUNCT
ejpam-3123	164	8	)	)	PUNCT
ejpam-3123	165	1	f	f	NOUN
ejpam-3123	165	2	(	(	PUNCT
ejpam-3123	165	3	p	p	X
ejpam-3123	165	4	/	/	SYM
ejpam-3123	165	5	f(s	f(	NOUN
ejpam-3123	165	6	,	,	PUNCT
ejpam-3123	165	7	t),(s∗t	t),(s∗t	NOUN
ejpam-3123	165	8	)	)	PUNCT
ejpam-3123	165	9	)	)	PUNCT
ejpam-3123	165	10	(	(	PUNCT
ejpam-3123	165	11	(	(	PUNCT
ejpam-3123	165	12	p	p	X
ejpam-3123	165	13	/	/	SYM
ejpam-3123	165	14	f(s	f(	NOUN
ejpam-3123	165	15	,	,	PUNCT
ejpam-3123	165	16	t))∗(s∗t	t))∗(s∗t	NUM
ejpam-3123	165	17	)	)	PUNCT
ejpam-3123	165	18	)	)	PUNCT
ejpam-3123	165	19	.	.	PUNCT
ejpam-3123	166	1	the	the	DET
ejpam-3123	166	2	uniqueness	uniqueness	NOUN
ejpam-3123	166	3	of	of	ADP
ejpam-3123	166	4	factorization	factorization	NOUN
ejpam-3123	166	5	yields	yield	NOUN
ejpam-3123	166	6	:	:	PUNCT
ejpam-3123	166	7	r	r	NOUN
ejpam-3123	166	8	f(p	f(p	PROPN
ejpam-3123	166	9	,	,	PUNCT
ejpam-3123	166	10	s)f	s)f	NUM
ejpam-3123	166	11	(	(	PUNCT
ejpam-3123	166	12	(	(	PUNCT
ejpam-3123	166	13	p∗s),t	p∗s),t	X
ejpam-3123	166	14	)	)	PUNCT
ejpam-3123	167	1	=	=	SYM
ejpam-3123	167	2	r	r	X
ejpam-3123	167	3	(	(	PUNCT
ejpam-3123	167	4	p.f(s	p.f(s	PROPN
ejpam-3123	167	5	,	,	PUNCT
ejpam-3123	167	6	t	t	PROPN
ejpam-3123	167	7	)	)	PUNCT
ejpam-3123	167	8	)	)	PUNCT
ejpam-3123	168	1	f	f	NOUN
ejpam-3123	168	2	(	(	PUNCT
ejpam-3123	168	3	p	p	X
ejpam-3123	168	4	/	/	SYM
ejpam-3123	168	5	f(s	f(	NOUN
ejpam-3123	168	6	,	,	PUNCT
ejpam-3123	168	7	t),(s∗t	t),(s∗t	NOUN
ejpam-3123	168	8	)	)	PUNCT
ejpam-3123	168	9	)	)	PUNCT
ejpam-3123	168	10	,	,	PUNCT
ejpam-3123	168	11	and	and	CCONJ
ejpam-3123	168	12	r	r	X
ejpam-3123	168	13	(	(	PUNCT
ejpam-3123	168	14	(	(	PUNCT
ejpam-3123	168	15	p∗s)∗t	p∗s)∗t	NOUN
ejpam-3123	168	16	)	)	PUNCT
ejpam-3123	169	1	=	=	PUNCT
ejpam-3123	169	2	r	r	X
ejpam-3123	169	3	(	(	PUNCT
ejpam-3123	169	4	p	p	X
ejpam-3123	169	5	/	/	SYM
ejpam-3123	169	6	f(s	f(	NOUN
ejpam-3123	169	7	,	,	PUNCT
ejpam-3123	169	8	t	t	PROPN
ejpam-3123	169	9	)	)	PUNCT
ejpam-3123	169	10	)	)	PUNCT
ejpam-3123	170	1	∗(s∗t	∗(s∗t	VERB
ejpam-3123	170	2	)	)	PUNCT
ejpam-3123	170	3	.	.	PUNCT
ejpam-3123	171	1	proposition	proposition	NOUN
ejpam-3123	171	2	4	4	NUM
ejpam-3123	171	3	.	.	PUNCT
ejpam-3123	172	1	let	let	VERB
ejpam-3123	172	2	x	x	PRON
ejpam-3123	172	3	be	be	AUX
ejpam-3123	172	4	a	a	DET
ejpam-3123	172	5	group	group	NOUN
ejpam-3123	172	6	,	,	PUNCT
ejpam-3123	172	7	h	h	PROPN
ejpam-3123	172	8	be	be	VERB
ejpam-3123	172	9	a	a	DET
ejpam-3123	172	10	subgroup	subgroup	NOUN
ejpam-3123	172	11	of	of	ADP
ejpam-3123	172	12	x	x	PROPN
ejpam-3123	172	13	,	,	PUNCT
ejpam-3123	172	14	g	g	PROPN
ejpam-3123	172	15	⊂	⊂	PROPN
ejpam-3123	172	16	x	x	VERB
ejpam-3123	172	17	be	be	AUX
ejpam-3123	172	18	a	a	DET
ejpam-3123	172	19	set	set	NOUN
ejpam-3123	172	20	of	of	ADP
ejpam-3123	172	21	left	left	ADJ
ejpam-3123	172	22	coset	coset	NOUN
ejpam-3123	172	23	representatives	representative	NOUN
ejpam-3123	172	24	and	and	CCONJ
ejpam-3123	172	25	r	r	NOUN
ejpam-3123	172	26	be	be	AUX
ejpam-3123	172	27	a	a	DET
ejpam-3123	172	28	g	g	NOUN
ejpam-3123	172	29	-	-	PUNCT
ejpam-3123	172	30	weak	weak	ADJ
ejpam-3123	172	31	graded	grade	VERB
ejpam-3123	172	32	ring	ring	NOUN
ejpam-3123	172	33	.	.	PUNCT
ejpam-3123	173	1	then	then	ADV
ejpam-3123	173	2	for	for	ADP
ejpam-3123	173	3	any	any	DET
ejpam-3123	173	4	t	t	NOUN
ejpam-3123	173	5	∈	∈	PROPN
ejpam-3123	173	6	g	g	PROPN
ejpam-3123	173	7	and	and	CCONJ
ejpam-3123	173	8	v	v	ADP
ejpam-3123	173	9	∈	∈	PROPN
ejpam-3123	173	10	h	h	NOUN
ejpam-3123	173	11	,	,	PUNCT
ejpam-3123	173	12	the	the	DET
ejpam-3123	173	13	following	follow	VERB
ejpam-3123	173	14	properties	property	NOUN
ejpam-3123	173	15	are	be	AUX
ejpam-3123	173	16	satisfied	satisfied	ADJ
ejpam-3123	173	17	:	:	PUNCT
ejpam-3123	173	18	(	(	PUNCT
ejpam-3123	173	19	i	i	NOUN
ejpam-3123	173	20	)	)	PUNCT
ejpam-3123	173	21	reg	reg	PROPN
ejpam-3123	173	22	/	/	SYM
ejpam-3123	173	23	v	v	NOUN
ejpam-3123	173	24	=	=	NOUN
ejpam-3123	173	25	reg	reg	NOUN
ejpam-3123	173	26	,	,	PUNCT
ejpam-3123	173	27	and	and	CCONJ
ejpam-3123	173	28	reg.v	reg.v	PROPN
ejpam-3123	173	29	=	=	SYM
ejpam-3123	173	30	regve−1	regve−1	PROPN
ejpam-3123	173	31	g	g	NOUN
ejpam-3123	173	32	.	.	PUNCT
ejpam-3123	174	1	(	(	PUNCT
ejpam-3123	174	2	ii	ii	NOUN
ejpam-3123	174	3	)	)	PUNCT
ejpam-3123	174	4	rt.e	rt.e	NOUN
ejpam-3123	174	5	=	=	SYM
ejpam-3123	174	6	re	re	PROPN
ejpam-3123	174	7	,	,	PUNCT
ejpam-3123	174	8	and	and	CCONJ
ejpam-3123	174	9	rt	rt	PROPN
ejpam-3123	174	10	/	/	SYM
ejpam-3123	174	11	e	e	PROPN
ejpam-3123	174	12	=	=	PROPN
ejpam-3123	174	13	rt	rt	PROPN
ejpam-3123	174	14	.	.	PUNCT
ejpam-3123	174	15	(	(	PUNCT
ejpam-3123	174	16	iii	iii	NOUN
ejpam-3123	174	17	)	)	PUNCT
ejpam-3123	174	18	rf(eg	rf(eg	PROPN
ejpam-3123	174	19	,	,	PUNCT
ejpam-3123	174	20	t	t	PROPN
ejpam-3123	174	21	)	)	PUNCT
ejpam-3123	174	22	=	=	SYM
ejpam-3123	175	1	reg	reg	NOUN
ejpam-3123	175	2	.	.	PUNCT
ejpam-3123	176	1	(	(	PUNCT
ejpam-3123	176	2	iv	iv	X
ejpam-3123	176	3	)	)	PUNCT
ejpam-3123	176	4	rt.e−1	rt.e−1	NOUN
ejpam-3123	176	5	g	g	NOUN
ejpam-3123	176	6	=	=	SYM
ejpam-3123	176	7	r	r	NOUN
ejpam-3123	176	8	f	f	X
ejpam-3123	176	9	(	(	PUNCT
ejpam-3123	176	10	t	t	PROPN
ejpam-3123	176	11	/	/	SYM
ejpam-3123	176	12	e−1	e−1	PROPN
ejpam-3123	176	13	g	g	PROPN
ejpam-3123	176	14	,	,	PUNCT
ejpam-3123	176	15	eg	eg	NOUN
ejpam-3123	176	16	)	)	PUNCT
ejpam-3123	176	17	−1	−1	NOUN
ejpam-3123	176	18	,	,	PUNCT
ejpam-3123	176	19	and	and	CCONJ
ejpam-3123	176	20	r	r	NOUN
ejpam-3123	176	21	(	(	PUNCT
ejpam-3123	176	22	t	t	PROPN
ejpam-3123	176	23	/	/	SYM
ejpam-3123	176	24	e−1	e−1	PROPN
ejpam-3123	176	25	g	g	NOUN
ejpam-3123	176	26	)	)	PUNCT
ejpam-3123	176	27	∗eg	∗eg	PUNCT
ejpam-3123	176	28	=	=	SYM
ejpam-3123	176	29	rt	rt	PROPN
ejpam-3123	176	30	.	.	PUNCT
ejpam-3123	176	31	proof	proof	NOUN
ejpam-3123	176	32	.	.	PUNCT
ejpam-3123	177	1	to	to	PART
ejpam-3123	177	2	prove	prove	VERB
ejpam-3123	177	3	(	(	PUNCT
ejpam-3123	177	4	i	i	NOUN
ejpam-3123	177	5	)	)	PUNCT
ejpam-3123	177	6	we	we	PRON
ejpam-3123	177	7	consider	consider	VERB
ejpam-3123	177	8	regv	regv	NOUN
ejpam-3123	177	9	=	=	NUM
ejpam-3123	177	10	r(egv)e−1	r(egv)e−1	NOUN
ejpam-3123	177	11	g	g	NOUN
ejpam-3123	177	12	eg	eg	NOUN
ejpam-3123	177	13	=	=	SYM
ejpam-3123	177	14	r(egve−1	r(egve−1	PROPN
ejpam-3123	177	15	g	g	NOUN
ejpam-3123	177	16	)	)	PUNCT
ejpam-3123	177	17	eg	eg	NOUN
ejpam-3123	177	18	,	,	PUNCT
ejpam-3123	177	19	by	by	ADP
ejpam-3123	177	20	the	the	DET
ejpam-3123	177	21	associativity	associativity	NOUN
ejpam-3123	177	22	of	of	ADP
ejpam-3123	177	23	x	x	PRON
ejpam-3123	177	24	,	,	PUNCT
ejpam-3123	177	25	where	where	SCONJ
ejpam-3123	177	26	eg	eg	PROPN
ejpam-3123	177	27	∈	∈	PROPN
ejpam-3123	177	28	g	g	PROPN
ejpam-3123	177	29	and	and	CCONJ
ejpam-3123	177	30	egve	egve	VERB
ejpam-3123	177	31	−1	−1	NOUN
ejpam-3123	177	32	g	g	PROPN
ejpam-3123	177	33	∈	∈	PROPN
ejpam-3123	177	34	h.	h.	NOUN
ejpam-3123	177	35	but	but	CCONJ
ejpam-3123	177	36	regv	regv	NOUN
ejpam-3123	177	37	=	=	SYM
ejpam-3123	177	38	r(eg.v)(eg	r(eg.v)(eg	NOUN
ejpam-3123	177	39	/	/	SYM
ejpam-3123	177	40	v	v	NOUN
ejpam-3123	177	41	)	)	PUNCT
ejpam-3123	177	42	.	.	PUNCT
ejpam-3123	178	1	as	as	SCONJ
ejpam-3123	178	2	the	the	DET
ejpam-3123	178	3	factorization	factorization	NOUN
ejpam-3123	178	4	is	be	AUX
ejpam-3123	178	5	unique	unique	ADJ
ejpam-3123	178	6	we	we	PRON
ejpam-3123	178	7	get	get	VERB
ejpam-3123	178	8	:	:	PUNCT
ejpam-3123	178	9	reg	reg	PROPN
ejpam-3123	178	10	/	/	SYM
ejpam-3123	178	11	v	v	NOUN
ejpam-3123	178	12	=	=	NOUN
ejpam-3123	178	13	reg	reg	NOUN
ejpam-3123	178	14	,	,	PUNCT
ejpam-3123	178	15	and	and	CCONJ
ejpam-3123	178	16	reg.v	reg.v	PROPN
ejpam-3123	178	17	=	=	SYM
ejpam-3123	178	18	regve−1	regve−1	PROPN
ejpam-3123	178	19	g	g	NOUN
ejpam-3123	178	20	.	.	PUNCT
ejpam-3123	179	1	now	now	ADV
ejpam-3123	179	2	for	for	ADP
ejpam-3123	179	3	(	(	PUNCT
ejpam-3123	179	4	ii	ii	NOUN
ejpam-3123	179	5	)	)	PUNCT
ejpam-3123	179	6	,	,	PUNCT
ejpam-3123	179	7	as	as	SCONJ
ejpam-3123	179	8	x	x	PRON
ejpam-3123	179	9	is	be	AUX
ejpam-3123	179	10	a	a	DET
ejpam-3123	179	11	group	group	NOUN
ejpam-3123	179	12	,	,	PUNCT
ejpam-3123	179	13	we	we	PRON
ejpam-3123	179	14	have	have	VERB
ejpam-3123	179	15	rte	rte	NOUN
ejpam-3123	179	16	=	=	SYM
ejpam-3123	179	17	ret	ret	PROPN
ejpam-3123	179	18	where	where	SCONJ
ejpam-3123	179	19	e	e	X
ejpam-3123	179	20	∈	∈	PROPN
ejpam-3123	179	21	h	h	NOUN
ejpam-3123	179	22	is	be	AUX
ejpam-3123	179	23	the	the	DET
ejpam-3123	179	24	identity	identity	NOUN
ejpam-3123	179	25	and	and	CCONJ
ejpam-3123	179	26	t	t	PROPN
ejpam-3123	179	27	∈	∈	PROPN
ejpam-3123	179	28	g.	g.	PROPN
ejpam-3123	179	29	also	also	ADV
ejpam-3123	179	30	,	,	PUNCT
ejpam-3123	179	31	rt	rt	PROPN
ejpam-3123	179	32	=	=	SYM
ejpam-3123	179	33	rte	rte	PROPN
ejpam-3123	179	34	=	=	PUNCT
ejpam-3123	179	35	r(t.e)(t	r(t.e)(t	PROPN
ejpam-3123	179	36	/	/	SYM
ejpam-3123	179	37	e	e	NOUN
ejpam-3123	179	38	)	)	PUNCT
ejpam-3123	179	39	which	which	PRON
ejpam-3123	179	40	can	can	AUX
ejpam-3123	179	41	be	be	AUX
ejpam-3123	179	42	written	write	VERB
ejpam-3123	179	43	as	as	ADP
ejpam-3123	179	44	ret	ret	NOUN
ejpam-3123	179	45	=	=	NOUN
ejpam-3123	179	46	r(t.e)(t	r(t.e)(t	PROPN
ejpam-3123	179	47	/	/	SYM
ejpam-3123	179	48	e	e	NOUN
ejpam-3123	179	49	)	)	PUNCT
ejpam-3123	179	50	.	.	PUNCT
ejpam-3123	180	1	the	the	DET
ejpam-3123	180	2	uniqueness	uniqueness	NOUN
ejpam-3123	180	3	of	of	ADP
ejpam-3123	180	4	factorization	factorization	NOUN
ejpam-3123	180	5	implies	imply	VERB
ejpam-3123	180	6	re	re	NOUN
ejpam-3123	180	7	=	=	NOUN
ejpam-3123	180	8	r(t.e	r(t.e	PROPN
ejpam-3123	180	9	)	)	PUNCT
ejpam-3123	180	10	,	,	PUNCT
ejpam-3123	180	11	and	and	CCONJ
ejpam-3123	180	12	rt	rt	PROPN
ejpam-3123	180	13	=	=	PUNCT
ejpam-3123	180	14	r(t	r(t	PROPN
ejpam-3123	180	15	/	/	SYM
ejpam-3123	180	16	e	e	NOUN
ejpam-3123	180	17	)	)	PUNCT
ejpam-3123	180	18	.	.	PUNCT
ejpam-3123	181	1	n.	n.	PROPN
ejpam-3123	181	2	al	al	PROPN
ejpam-3123	181	3	-	-	PUNCT
ejpam-3123	181	4	subaie	subaie	NOUN
ejpam-3123	181	5	,	,	PUNCT
ejpam-3123	181	6	m.	m.	NOUN
ejpam-3123	181	7	m.	m.	PROPN
ejpam-3123	181	8	al	al	PROPN
ejpam-3123	181	9	-	-	PUNCT
ejpam-3123	181	10	shomrani	shomrani	PROPN
ejpam-3123	181	11	/	/	SYM
ejpam-3123	181	12	eur	eur	NOUN
ejpam-3123	181	13	.	.	PUNCT
ejpam-3123	182	1	j.	j.	PROPN
ejpam-3123	182	2	pure	pure	PROPN
ejpam-3123	182	3	appl	appl	PROPN
ejpam-3123	182	4	.	.	PROPN
ejpam-3123	182	5	math	math	PROPN
ejpam-3123	182	6	,	,	PUNCT
ejpam-3123	182	7	10	10	NUM
ejpam-3123	182	8	(	(	PUNCT
ejpam-3123	182	9	5	5	NUM
ejpam-3123	182	10	)	)	PUNCT
ejpam-3123	182	11	(	(	PUNCT
ejpam-3123	182	12	2017	2017	NUM
ejpam-3123	182	13	)	)	PUNCT
ejpam-3123	182	14	,	,	PUNCT
ejpam-3123	182	15	967	967	NUM
ejpam-3123	182	16	-	-	SYM
ejpam-3123	182	17	980	980	NUM
ejpam-3123	182	18	974	974	NUM
ejpam-3123	182	19	next	next	ADV
ejpam-3123	182	20	,	,	PUNCT
ejpam-3123	182	21	for	for	ADP
ejpam-3123	182	22	(	(	PUNCT
ejpam-3123	182	23	iii	iii	NOUN
ejpam-3123	182	24	)	)	PUNCT
ejpam-3123	182	25	consider	consider	VERB
ejpam-3123	182	26	regt	regt	NOUN
ejpam-3123	182	27	=	=	PUNCT
ejpam-3123	182	28	rf(eg	rf(eg	NOUN
ejpam-3123	182	29	,	,	PUNCT
ejpam-3123	182	30	t)(eg∗t	t)(eg∗t	NOUN
ejpam-3123	182	31	)	)	PUNCT
ejpam-3123	182	32	=	=	SYM
ejpam-3123	183	1	rf(eg	rf(eg	NOUN
ejpam-3123	183	2	,	,	PUNCT
ejpam-3123	183	3	t)t	t)t	NOUN
ejpam-3123	183	4	which	which	PRON
ejpam-3123	183	5	is	be	AUX
ejpam-3123	183	6	true	true	ADJ
ejpam-3123	183	7	by	by	ADP
ejpam-3123	183	8	the	the	DET
ejpam-3123	183	9	definitions	definition	NOUN
ejpam-3123	183	10	of	of	ADP
ejpam-3123	183	11	∗	∗	NOUN
ejpam-3123	183	12	and	and	CCONJ
ejpam-3123	183	13	f	f	PROPN
ejpam-3123	183	14	.	.	PUNCT
ejpam-3123	184	1	hence	hence	ADV
ejpam-3123	184	2	,	,	PUNCT
ejpam-3123	184	3	the	the	DET
ejpam-3123	184	4	uniqueness	uniqueness	NOUN
ejpam-3123	184	5	of	of	ADP
ejpam-3123	184	6	factorization	factorization	NOUN
ejpam-3123	184	7	gives	give	VERB
ejpam-3123	184	8	reg	reg	NOUN
ejpam-3123	184	9	=	=	SYM
ejpam-3123	184	10	rf(eg	rf(eg	PROPN
ejpam-3123	184	11	,	,	PUNCT
ejpam-3123	184	12	t	t	PROPN
ejpam-3123	184	13	)	)	PUNCT
ejpam-3123	184	14	.	.	PUNCT
ejpam-3123	185	1	finally	finally	ADV
ejpam-3123	185	2	,	,	PUNCT
ejpam-3123	185	3	to	to	PART
ejpam-3123	185	4	prove	prove	VERB
ejpam-3123	185	5	(	(	PUNCT
ejpam-3123	185	6	iv	iv	X
ejpam-3123	185	7	)	)	PUNCT
ejpam-3123	185	8	we	we	PRON
ejpam-3123	185	9	consider	consider	VERB
ejpam-3123	185	10	:	:	PUNCT
ejpam-3123	185	11	ret	ret	PROPN
ejpam-3123	185	12	=	=	PROPN
ejpam-3123	185	13	rt	rt	PROPN
ejpam-3123	186	1	=	=	SYM
ejpam-3123	186	2	rte−1	rte−1	PROPN
ejpam-3123	186	3	g	g	PROPN
ejpam-3123	186	4	eg	eg	NOUN
ejpam-3123	186	5	=	=	SYM
ejpam-3123	186	6	r(t.e−1	r(t.e−1	NOUN
ejpam-3123	186	7	g	g	NOUN
ejpam-3123	186	8	)	)	PUNCT
ejpam-3123	186	9	(	(	PUNCT
ejpam-3123	186	10	t	t	PROPN
ejpam-3123	186	11	/	/	SYM
ejpam-3123	186	12	e−1	e−1	PROPN
ejpam-3123	186	13	g	g	NOUN
ejpam-3123	186	14	)	)	PUNCT
ejpam-3123	186	15	eg	eg	NOUN
ejpam-3123	186	16	=	=	SYM
ejpam-3123	186	17	r	r	NOUN
ejpam-3123	186	18	(	(	PUNCT
ejpam-3123	186	19	t.e−1	t.e−1	NOUN
ejpam-3123	186	20	g	g	NOUN
ejpam-3123	186	21	)	)	PUNCT
ejpam-3123	186	22	f	f	PROPN
ejpam-3123	186	23	(	(	PUNCT
ejpam-3123	186	24	(	(	PUNCT
ejpam-3123	186	25	t	t	PROPN
ejpam-3123	186	26	/	/	SYM
ejpam-3123	186	27	e−1	e−1	PROPN
ejpam-3123	186	28	g	g	PROPN
ejpam-3123	186	29	)	)	PUNCT
ejpam-3123	186	30	,	,	PUNCT
ejpam-3123	186	31	eg	eg	NOUN
ejpam-3123	186	32	)	)	PUNCT
ejpam-3123	186	33	(	(	PUNCT
ejpam-3123	186	34	(	(	PUNCT
ejpam-3123	186	35	t	t	PROPN
ejpam-3123	186	36	/	/	SYM
ejpam-3123	186	37	e−1	e−1	PROPN
ejpam-3123	186	38	g	g	PROPN
ejpam-3123	186	39	)	)	PUNCT
ejpam-3123	186	40	∗eg	∗eg	PUNCT
ejpam-3123	186	41	)	)	PUNCT
ejpam-3123	186	42	,	,	PUNCT
ejpam-3123	186	43	which	which	PRON
ejpam-3123	186	44	implies	imply	VERB
ejpam-3123	186	45	,	,	PUNCT
ejpam-3123	186	46	re	re	ADP
ejpam-3123	186	47	=	=	SYM
ejpam-3123	186	48	r	r	NOUN
ejpam-3123	186	49	(	(	PUNCT
ejpam-3123	186	50	t.e−1	t.e−1	NOUN
ejpam-3123	186	51	g	g	NOUN
ejpam-3123	186	52	)	)	PUNCT
ejpam-3123	186	53	f	f	PROPN
ejpam-3123	186	54	(	(	PUNCT
ejpam-3123	186	55	(	(	PUNCT
ejpam-3123	186	56	t	t	PROPN
ejpam-3123	186	57	/	/	SYM
ejpam-3123	186	58	e−1	e−1	PROPN
ejpam-3123	186	59	g	g	PROPN
ejpam-3123	186	60	)	)	PUNCT
ejpam-3123	186	61	,	,	PUNCT
ejpam-3123	186	62	eg	eg	NOUN
ejpam-3123	186	63	)	)	PUNCT
ejpam-3123	186	64	,	,	PUNCT
ejpam-3123	186	65	or	or	CCONJ
ejpam-3123	186	66	equivalently	equivalently	ADV
ejpam-3123	186	67	,	,	PUNCT
ejpam-3123	186	68	r(t.e−1	r(t.e−1	NOUN
ejpam-3123	186	69	g	g	NOUN
ejpam-3123	186	70	)	)	PUNCT
ejpam-3123	187	1	=	=	PUNCT
ejpam-3123	187	2	r	r	NOUN
ejpam-3123	187	3	f	f	X
ejpam-3123	187	4	(	(	PUNCT
ejpam-3123	187	5	(	(	PUNCT
ejpam-3123	187	6	t	t	PROPN
ejpam-3123	187	7	/	/	SYM
ejpam-3123	187	8	e−1	e−1	PROPN
ejpam-3123	187	9	g	g	PROPN
ejpam-3123	187	10	)	)	PUNCT
ejpam-3123	187	11	,	,	PUNCT
ejpam-3123	187	12	eg	eg	NOUN
ejpam-3123	187	13	)	)	PUNCT
ejpam-3123	187	14	−1	−1	NOUN
ejpam-3123	187	15	,	,	PUNCT
ejpam-3123	187	16	and	and	CCONJ
ejpam-3123	187	17	,	,	PUNCT
ejpam-3123	187	18	rt	rt	PROPN
ejpam-3123	187	19	=	=	PUNCT
ejpam-3123	187	20	r(t	r(t	PROPN
ejpam-3123	187	21	/	/	SYM
ejpam-3123	187	22	e−1	e−1	PROPN
ejpam-3123	187	23	g	g	PROPN
ejpam-3123	187	24	)	)	PUNCT
ejpam-3123	187	25	∗eg	∗eg	PUNCT
ejpam-3123	187	26	.	.	PUNCT
ejpam-3123	187	27	example	example	NOUN
ejpam-3123	187	28	2	2	NUM
ejpam-3123	187	29	.	.	X
ejpam-3123	188	1	consider	consider	VERB
ejpam-3123	188	2	the	the	DET
ejpam-3123	188	3	morita	morita	PROPN
ejpam-3123	188	4	ring	ring	PROPN
ejpam-3123	188	5	t	t	PROPN
ejpam-3123	188	6	=	=	PUNCT
ejpam-3123	188	7	(	(	PUNCT
ejpam-3123	188	8	r	r	NOUN
ejpam-3123	188	9	m	m	VERB
ejpam-3123	188	10	n	n	PRON
ejpam-3123	188	11	s	s	PRON
ejpam-3123	188	12	)	)	PUNCT
ejpam-3123	188	13	mentioned	mention	VERB
ejpam-3123	188	14	in	in	ADP
ejpam-3123	188	15	example	example	NOUN
ejpam-3123	188	16	1	1	NUM
ejpam-3123	188	17	with	with	ADP
ejpam-3123	188	18	x	x	X
ejpam-3123	188	19	=	=	SYM
ejpam-3123	188	20	z2×z3	z2×z3	PROPN
ejpam-3123	188	21	,	,	PUNCT
ejpam-3123	188	22	h	h	NOUN
ejpam-3123	188	23	=	=	PRON
ejpam-3123	188	24	{	{	PUNCT
ejpam-3123	188	25	(	(	PUNCT
ejpam-3123	188	26	0	0	NUM
ejpam-3123	188	27	,	,	PUNCT
ejpam-3123	188	28	0	0	NUM
ejpam-3123	188	29	)	)	PUNCT
ejpam-3123	188	30	,	,	PUNCT
ejpam-3123	188	31	(	(	PUNCT
ejpam-3123	188	32	1	1	NUM
ejpam-3123	188	33	,	,	PUNCT
ejpam-3123	188	34	0	0	NUM
ejpam-3123	188	35	)	)	PUNCT
ejpam-3123	188	36	}	}	PUNCT
ejpam-3123	188	37	and	and	CCONJ
ejpam-3123	188	38	a	a	DET
ejpam-3123	188	39	set	set	NOUN
ejpam-3123	188	40	of	of	ADP
ejpam-3123	188	41	left	left	ADJ
ejpam-3123	188	42	coset	coset	NOUN
ejpam-3123	188	43	representatives	representative	NOUN
ejpam-3123	188	44	g	g	NOUN
ejpam-3123	188	45	=	=	SYM
ejpam-3123	188	46	{	{	PUNCT
ejpam-3123	188	47	(	(	PUNCT
ejpam-3123	188	48	1	1	NUM
ejpam-3123	188	49	,	,	PUNCT
ejpam-3123	188	50	0	0	NUM
ejpam-3123	188	51	)	)	PUNCT
ejpam-3123	188	52	,	,	PUNCT
ejpam-3123	188	53	(	(	PUNCT
ejpam-3123	188	54	0	0	NUM
ejpam-3123	188	55	,	,	PUNCT
ejpam-3123	188	56	1	1	NUM
ejpam-3123	188	57	)	)	PUNCT
ejpam-3123	188	58	,	,	PUNCT
ejpam-3123	188	59	(	(	PUNCT
ejpam-3123	188	60	1	1	NUM
ejpam-3123	188	61	,	,	PUNCT
ejpam-3123	188	62	2	2	NUM
ejpam-3123	188	63	)	)	PUNCT
ejpam-3123	188	64	}	}	PUNCT
ejpam-3123	188	65	.	.	PUNCT
ejpam-3123	189	1	as	as	ADP
ejpam-3123	189	2	before	before	ADP
ejpam-3123	189	3	t	t	PROPN
ejpam-3123	189	4	=	=	SYM
ejpam-3123	189	5	t(1,0	t(1,0	X
ejpam-3123	189	6	)	)	PUNCT
ejpam-3123	189	7	⊕	⊕	PROPN
ejpam-3123	189	8	t(0,1	t(0,1	ADP
ejpam-3123	189	9	)	)	PUNCT
ejpam-3123	189	10	⊕	⊕	PROPN
ejpam-3123	189	11	t(1,2	t(1,2	PROPN
ejpam-3123	189	12	)	)	PUNCT
ejpam-3123	189	13	is	be	AUX
ejpam-3123	189	14	a	a	DET
ejpam-3123	189	15	g	g	NOUN
ejpam-3123	189	16	-	-	PUNCT
ejpam-3123	189	17	weak	weak	ADJ
ejpam-3123	189	18	graded	grade	VERB
ejpam-3123	189	19	ring	ring	NOUN
ejpam-3123	189	20	where	where	SCONJ
ejpam-3123	189	21	,	,	PUNCT
ejpam-3123	189	22	t(1,0	t(1,0	NUM
ejpam-3123	189	23	)	)	PUNCT
ejpam-3123	189	24	=	=	SYM
ejpam-3123	190	1	(	(	PUNCT
ejpam-3123	190	2	r	r	NOUN
ejpam-3123	190	3	0	0	NUM
ejpam-3123	190	4	0	0	NUM
ejpam-3123	190	5	s	s	PART
ejpam-3123	190	6	)	)	PUNCT
ejpam-3123	190	7	=	=	SYM
ejpam-3123	190	8	{	{	PUNCT
ejpam-3123	190	9	(	(	PUNCT
ejpam-3123	190	10	r	r	NOUN
ejpam-3123	190	11	0	0	NUM
ejpam-3123	190	12	0	0	NUM
ejpam-3123	190	13	s	s	NOUN
ejpam-3123	190	14	)	)	PUNCT
ejpam-3123	190	15	:	:	PUNCT
ejpam-3123	191	1	r	r	NOUN
ejpam-3123	191	2	∈	∈	PROPN
ejpam-3123	191	3	r	r	NOUN
ejpam-3123	191	4	,	,	PUNCT
ejpam-3123	191	5	and	and	CCONJ
ejpam-3123	191	6	s	s	VERB
ejpam-3123	191	7	∈	∈	NOUN
ejpam-3123	191	8	s	s	PART
ejpam-3123	191	9	}	}	PUNCT
ejpam-3123	191	10	,	,	PUNCT
ejpam-3123	191	11	t(0,1	t(0,1	ADP
ejpam-3123	191	12	)	)	PUNCT
ejpam-3123	191	13	=	=	SYM
ejpam-3123	191	14	(	(	PUNCT
ejpam-3123	191	15	0	0	NUM
ejpam-3123	191	16	m	m	NOUN
ejpam-3123	191	17	0	0	NUM
ejpam-3123	191	18	0	0	NUM
ejpam-3123	191	19	)	)	PUNCT
ejpam-3123	192	1	=	=	PRON
ejpam-3123	192	2	{	{	PUNCT
ejpam-3123	192	3	(	(	PUNCT
ejpam-3123	192	4	0	0	NUM
ejpam-3123	192	5	m	m	NOUN
ejpam-3123	192	6	0	0	NUM
ejpam-3123	192	7	0	0	NUM
ejpam-3123	192	8	)	)	PUNCT
ejpam-3123	192	9	:	:	PUNCT
ejpam-3123	192	10	m	m	VERB
ejpam-3123	192	11	∈m	∈m	NOUN
ejpam-3123	192	12	}	}	PUNCT
ejpam-3123	192	13	and	and	CCONJ
ejpam-3123	192	14	t(1,2	t(1,2	NUM
ejpam-3123	192	15	)	)	PUNCT
ejpam-3123	192	16	=	=	SYM
ejpam-3123	192	17	(	(	PUNCT
ejpam-3123	192	18	0	0	NUM
ejpam-3123	192	19	0	0	NUM
ejpam-3123	192	20	n	n	NOUN
ejpam-3123	192	21	0	0	NUM
ejpam-3123	192	22	)	)	PUNCT
ejpam-3123	193	1	=	=	PRON
ejpam-3123	193	2	{	{	PUNCT
ejpam-3123	193	3	(	(	PUNCT
ejpam-3123	193	4	0	0	NUM
ejpam-3123	193	5	0	0	NUM
ejpam-3123	193	6	n	n	NOUN
ejpam-3123	193	7	0	0	NUM
ejpam-3123	193	8	)	)	PUNCT
ejpam-3123	193	9	:	:	PUNCT
ejpam-3123	193	10	n	n	X
ejpam-3123	193	11	∈	∈	PROPN
ejpam-3123	193	12	n	n	CCONJ
ejpam-3123	193	13	}	}	PUNCT
ejpam-3123	193	14	.	.	PUNCT
ejpam-3123	194	1	now	now	ADV
ejpam-3123	194	2	put	put	VERB
ejpam-3123	194	3	s	s	NOUN
ejpam-3123	194	4	=	=	PUNCT
ejpam-3123	194	5	(	(	PUNCT
ejpam-3123	194	6	0	0	NUM
ejpam-3123	194	7	,	,	PUNCT
ejpam-3123	194	8	1	1	NUM
ejpam-3123	194	9	)	)	PUNCT
ejpam-3123	194	10	,	,	PUNCT
ejpam-3123	194	11	t	t	PROPN
ejpam-3123	194	12	=	=	PUNCT
ejpam-3123	194	13	(	(	PUNCT
ejpam-3123	194	14	1	1	NUM
ejpam-3123	194	15	,	,	PUNCT
ejpam-3123	194	16	2	2	NUM
ejpam-3123	194	17	)	)	PUNCT
ejpam-3123	194	18	,	,	PUNCT
ejpam-3123	194	19	p	p	NOUN
ejpam-3123	194	20	=	=	PUNCT
ejpam-3123	194	21	(	(	PUNCT
ejpam-3123	194	22	1	1	NUM
ejpam-3123	194	23	,	,	PUNCT
ejpam-3123	194	24	0	0	NUM
ejpam-3123	194	25	)	)	PUNCT
ejpam-3123	194	26	in	in	ADP
ejpam-3123	194	27	g	g	PROPN
ejpam-3123	194	28	and	and	CCONJ
ejpam-3123	194	29	u	u	NOUN
ejpam-3123	194	30	=	=	SYM
ejpam-3123	194	31	(	(	PUNCT
ejpam-3123	194	32	0	0	NUM
ejpam-3123	194	33	,	,	PUNCT
ejpam-3123	194	34	0	0	NUM
ejpam-3123	194	35	)	)	PUNCT
ejpam-3123	194	36	,	,	PUNCT
ejpam-3123	194	37	v	v	X
ejpam-3123	194	38	=	=	SYM
ejpam-3123	194	39	(	(	PUNCT
ejpam-3123	194	40	1	1	NUM
ejpam-3123	194	41	,	,	PUNCT
ejpam-3123	194	42	0	0	NUM
ejpam-3123	194	43	)	)	PUNCT
ejpam-3123	194	44	in	in	ADP
ejpam-3123	194	45	h	h	NOUN
ejpam-3123	194	46	,	,	PUNCT
ejpam-3123	194	47	then	then	ADV
ejpam-3123	194	48	the	the	DET
ejpam-3123	194	49	above	above	ADJ
ejpam-3123	194	50	properties	property	NOUN
ejpam-3123	194	51	can	can	AUX
ejpam-3123	194	52	be	be	AUX
ejpam-3123	194	53	illustrated	illustrate	VERB
ejpam-3123	194	54	one	one	NUM
ejpam-3123	194	55	by	by	ADP
ejpam-3123	194	56	one	one	NUM
ejpam-3123	194	57	as	as	SCONJ
ejpam-3123	194	58	follows	follow	VERB
ejpam-3123	194	59	:	:	PUNCT
ejpam-3123	194	60	(	(	PUNCT
ejpam-3123	194	61	i	i	NOUN
ejpam-3123	194	62	)	)	PUNCT
ejpam-3123	194	63	t(s∗t)/u	t(s∗t)/u	PROPN
ejpam-3123	194	64	=	=	PROPN
ejpam-3123	194	65	t	t	PROPN
ejpam-3123	194	66	(	(	PUNCT
ejpam-3123	194	67	s/(t.u	s/(t.u	PROPN
ejpam-3123	194	68	)	)	PUNCT
ejpam-3123	194	69	)	)	PUNCT
ejpam-3123	195	1	∗(t	∗(t	NOUN
ejpam-3123	195	2	/	/	SYM
ejpam-3123	195	3	u	u	NOUN
ejpam-3123	195	4	)	)	PUNCT
ejpam-3123	195	5	.	.	PUNCT
ejpam-3123	196	1	we	we	PRON
ejpam-3123	196	2	start	start	VERB
ejpam-3123	196	3	with	with	ADP
ejpam-3123	196	4	the	the	DET
ejpam-3123	196	5	left	left	ADJ
ejpam-3123	196	6	hand	hand	NOUN
ejpam-3123	196	7	side	side	NOUN
ejpam-3123	196	8	as	as	SCONJ
ejpam-3123	196	9	follows	follow	VERB
ejpam-3123	196	10	:	:	PUNCT
ejpam-3123	196	11	t(s∗t)/u	t(s∗t)/u	PROPN
ejpam-3123	196	12	=	=	PROPN
ejpam-3123	196	13	t	t	PROPN
ejpam-3123	196	14	(	(	PUNCT
ejpam-3123	196	15	(	(	PUNCT
ejpam-3123	196	16	0,1)∗(1,2	0,1)∗(1,2	NUM
ejpam-3123	196	17	)	)	PUNCT
ejpam-3123	196	18	)	)	PUNCT
ejpam-3123	196	19	/(0,0	/(0,0	X
ejpam-3123	196	20	)	)	PUNCT
ejpam-3123	196	21	=	=	SYM
ejpam-3123	196	22	t(1,0)/(0,0	t(1,0)/(0,0	NOUN
ejpam-3123	196	23	)	)	PUNCT
ejpam-3123	196	24	=	=	SYM
ejpam-3123	196	25	t(1,0	t(1,0	NUM
ejpam-3123	196	26	)	)	PUNCT
ejpam-3123	196	27	.	.	PUNCT
ejpam-3123	197	1	on	on	ADP
ejpam-3123	197	2	the	the	DET
ejpam-3123	197	3	other	other	ADJ
ejpam-3123	197	4	hand	hand	NOUN
ejpam-3123	197	5	,	,	PUNCT
ejpam-3123	197	6	t	t	PROPN
ejpam-3123	197	7	(	(	PUNCT
ejpam-3123	197	8	s/(t.u	s/(t.u	PROPN
ejpam-3123	197	9	)	)	PUNCT
ejpam-3123	197	10	)	)	PUNCT
ejpam-3123	197	11	∗(t	∗(t	NOUN
ejpam-3123	197	12	/	/	SYM
ejpam-3123	197	13	u	u	NOUN
ejpam-3123	197	14	)	)	PUNCT
ejpam-3123	197	15	=	=	SYM
ejpam-3123	197	16	t	t	PROPN
ejpam-3123	197	17	(	(	PUNCT
ejpam-3123	197	18	(	(	PUNCT
ejpam-3123	197	19	0,1)/	0,1)/	NOUN
ejpam-3123	197	20	(	(	PUNCT
ejpam-3123	197	21	(	(	PUNCT
ejpam-3123	197	22	1,2).(0,0	1,2).(0,0	NOUN
ejpam-3123	197	23	)	)	PUNCT
ejpam-3123	197	24	)	)	PUNCT
ejpam-3123	197	25	)	)	PUNCT
ejpam-3123	197	26	∗	∗	NOUN
ejpam-3123	197	27	(	(	PUNCT
ejpam-3123	197	28	(	(	PUNCT
ejpam-3123	197	29	1,2)/(0,0	1,2)/(0,0	NUM
ejpam-3123	197	30	)	)	PUNCT
ejpam-3123	197	31	)	)	PUNCT
ejpam-3123	198	1	=	=	SYM
ejpam-3123	198	2	t	t	PROPN
ejpam-3123	198	3	(	(	PUNCT
ejpam-3123	198	4	(	(	PUNCT
ejpam-3123	198	5	0,1)/(0,0	0,1)/(0,0	NUM
ejpam-3123	198	6	)	)	PUNCT
ejpam-3123	198	7	)	)	PUNCT
ejpam-3123	198	8	∗(12	∗(12	NOUN
ejpam-3123	198	9	)	)	PUNCT
ejpam-3123	198	10	=	=	SYM
ejpam-3123	198	11	t(0,1)∗(1,2	t(0,1)∗(1,2	X
ejpam-3123	198	12	)	)	PUNCT
ejpam-3123	198	13	=	=	PUNCT
ejpam-3123	198	14	t(1,0	t(1,0	NUM
ejpam-3123	198	15	)	)	PUNCT
ejpam-3123	198	16	.	.	PUNCT
ejpam-3123	199	1	hence	hence	ADV
ejpam-3123	199	2	,	,	PUNCT
ejpam-3123	199	3	the	the	DET
ejpam-3123	199	4	equality	equality	NOUN
ejpam-3123	199	5	is	be	AUX
ejpam-3123	199	6	satisfied	satisfied	ADJ
ejpam-3123	199	7	.	.	PUNCT
ejpam-3123	200	1	n.	n.	PROPN
ejpam-3123	200	2	al	al	PROPN
ejpam-3123	200	3	-	-	PUNCT
ejpam-3123	200	4	subaie	subaie	NOUN
ejpam-3123	200	5	,	,	PUNCT
ejpam-3123	200	6	m.	m.	NOUN
ejpam-3123	200	7	m.	m.	PROPN
ejpam-3123	200	8	al	al	PROPN
ejpam-3123	200	9	-	-	PUNCT
ejpam-3123	200	10	shomrani	shomrani	PROPN
ejpam-3123	200	11	/	/	SYM
ejpam-3123	200	12	eur	eur	NOUN
ejpam-3123	200	13	.	.	PUNCT
ejpam-3123	201	1	j.	j.	PROPN
ejpam-3123	201	2	pure	pure	PROPN
ejpam-3123	201	3	appl	appl	PROPN
ejpam-3123	201	4	.	.	PROPN
ejpam-3123	201	5	math	math	PROPN
ejpam-3123	201	6	,	,	PUNCT
ejpam-3123	201	7	10	10	NUM
ejpam-3123	201	8	(	(	PUNCT
ejpam-3123	201	9	5	5	NUM
ejpam-3123	201	10	)	)	PUNCT
ejpam-3123	201	11	(	(	PUNCT
ejpam-3123	201	12	2017	2017	NUM
ejpam-3123	201	13	)	)	PUNCT
ejpam-3123	201	14	,	,	PUNCT
ejpam-3123	201	15	967	967	NUM
ejpam-3123	201	16	-	-	SYM
ejpam-3123	201	17	980	980	NUM
ejpam-3123	201	18	975	975	NUM
ejpam-3123	201	19	(	(	PUNCT
ejpam-3123	201	20	ii	ii	NOUN
ejpam-3123	201	21	)	)	PUNCT
ejpam-3123	201	22	ts.(t.u	ts.(t.u	PROPN
ejpam-3123	201	23	)	)	PUNCT
ejpam-3123	201	24	=	=	SYM
ejpam-3123	202	1	t	t	PROPN
ejpam-3123	202	2	f(s	f(s	PROPN
ejpam-3123	202	3	,	,	PUNCT
ejpam-3123	202	4	t	t	PROPN
ejpam-3123	202	5	)	)	PUNCT
ejpam-3123	202	6	(	(	PUNCT
ejpam-3123	202	7	(	(	PUNCT
ejpam-3123	202	8	s∗t).u	s∗t).u	PROPN
ejpam-3123	202	9	)	)	PUNCT
ejpam-3123	202	10	f	f	PROPN
ejpam-3123	202	11	(	(	PUNCT
ejpam-3123	202	12	s/(t.u),t	s/(t.u),t	PROPN
ejpam-3123	202	13	/	/	SYM
ejpam-3123	202	14	u	u	NOUN
ejpam-3123	202	15	)	)	PUNCT
ejpam-3123	202	16	−1	−1	NOUN
ejpam-3123	202	17	.	.	PUNCT
ejpam-3123	203	1	we	we	PRON
ejpam-3123	203	2	start	start	VERB
ejpam-3123	203	3	with	with	ADP
ejpam-3123	203	4	the	the	DET
ejpam-3123	203	5	left	left	ADJ
ejpam-3123	203	6	hand	hand	NOUN
ejpam-3123	203	7	side	side	NOUN
ejpam-3123	203	8	as	as	SCONJ
ejpam-3123	203	9	follows	follow	VERB
ejpam-3123	203	10	:	:	PUNCT
ejpam-3123	203	11	ts.(t.u	ts.(t.u	NUM
ejpam-3123	203	12	)	)	PUNCT
ejpam-3123	203	13	=	=	SYM
ejpam-3123	203	14	t	t	PROPN
ejpam-3123	203	15	(	(	PUNCT
ejpam-3123	203	16	0,1	0,1	NUM
ejpam-3123	203	17	)	)	PUNCT
ejpam-3123	203	18	.	.	PUNCT
ejpam-3123	204	1	(	(	PUNCT
ejpam-3123	204	2	(	(	PUNCT
ejpam-3123	204	3	1,2).(0,0	1,2).(0,0	NOUN
ejpam-3123	204	4	)	)	PUNCT
ejpam-3123	204	5	)	)	PUNCT
ejpam-3123	205	1	=	=	SYM
ejpam-3123	205	2	t(0,1).(0,0	t(0,1).(0,0	NOUN
ejpam-3123	205	3	)	)	PUNCT
ejpam-3123	205	4	=	=	PUNCT
ejpam-3123	205	5	t(0,0	t(0,0	NOUN
ejpam-3123	205	6	)	)	PUNCT
ejpam-3123	205	7	.	.	PUNCT
ejpam-3123	206	1	on	on	ADP
ejpam-3123	206	2	the	the	DET
ejpam-3123	206	3	other	other	ADJ
ejpam-3123	206	4	hand	hand	NOUN
ejpam-3123	206	5	,	,	PUNCT
ejpam-3123	206	6	t	t	PROPN
ejpam-3123	206	7	f(s	f(s	PROPN
ejpam-3123	206	8	,	,	PUNCT
ejpam-3123	206	9	t	t	PROPN
ejpam-3123	206	10	)	)	PUNCT
ejpam-3123	206	11	(	(	PUNCT
ejpam-3123	206	12	(	(	PUNCT
ejpam-3123	206	13	s∗t).u	s∗t).u	PROPN
ejpam-3123	206	14	)	)	PUNCT
ejpam-3123	206	15	f	f	PROPN
ejpam-3123	206	16	(	(	PUNCT
ejpam-3123	206	17	s/(t.u),t	s/(t.u),t	PROPN
ejpam-3123	206	18	/	/	SYM
ejpam-3123	206	19	u	u	NOUN
ejpam-3123	206	20	)	)	PUNCT
ejpam-3123	206	21	−1	−1	NOUN
ejpam-3123	207	1	=	=	SYM
ejpam-3123	207	2	t	t	PROPN
ejpam-3123	207	3	f	f	X
ejpam-3123	207	4	(	(	PUNCT
ejpam-3123	207	5	(	(	PUNCT
ejpam-3123	207	6	0,1),(1,2	0,1),(1,2	NOUN
ejpam-3123	207	7	)	)	PUNCT
ejpam-3123	207	8	)	)	PUNCT
ejpam-3123	207	9	(	(	PUNCT
ejpam-3123	207	10	(	(	PUNCT
ejpam-3123	207	11	(	(	PUNCT
ejpam-3123	207	12	0,1)∗(1,2	0,1)∗(1,2	NUM
ejpam-3123	207	13	)	)	PUNCT
ejpam-3123	207	14	)	)	PUNCT
ejpam-3123	207	15	.(0,0	.(0,0	NOUN
ejpam-3123	207	16	)	)	PUNCT
ejpam-3123	207	17	)	)	PUNCT
ejpam-3123	208	1	f	f	X
ejpam-3123	208	2	(	(	PUNCT
ejpam-3123	208	3	(	(	PUNCT
ejpam-3123	208	4	0,1)/	0,1)/	NOUN
ejpam-3123	208	5	(	(	PUNCT
ejpam-3123	208	6	(	(	PUNCT
ejpam-3123	208	7	1,2).(0,0	1,2).(0,0	NOUN
ejpam-3123	208	8	)	)	PUNCT
ejpam-3123	208	9	)	)	PUNCT
ejpam-3123	208	10	,	,	PUNCT
ejpam-3123	208	11	(	(	PUNCT
ejpam-3123	208	12	1,2)/(0,0	1,2)/(0,0	NUM
ejpam-3123	208	13	)	)	PUNCT
ejpam-3123	208	14	)	)	PUNCT
ejpam-3123	208	15	−1	−1	NOUN
ejpam-3123	209	1	=	=	SYM
ejpam-3123	209	2	t	t	PROPN
ejpam-3123	209	3	(	(	PUNCT
ejpam-3123	209	4	0,0	0,0	NOUN
ejpam-3123	209	5	)	)	PUNCT
ejpam-3123	209	6	(	(	PUNCT
ejpam-3123	209	7	(	(	PUNCT
ejpam-3123	209	8	1,0).(0,0	1,0).(0,0	NOUN
ejpam-3123	209	9	)	)	PUNCT
ejpam-3123	209	10	)	)	PUNCT
ejpam-3123	210	1	f	f	X
ejpam-3123	210	2	(	(	PUNCT
ejpam-3123	210	3	(	(	PUNCT
ejpam-3123	210	4	0,1)/(0,0	0,1)/(0,0	NOUN
ejpam-3123	210	5	)	)	PUNCT
ejpam-3123	210	6	(	(	PUNCT
ejpam-3123	210	7	1,2	1,2	NUM
ejpam-3123	210	8	)	)	PUNCT
ejpam-3123	210	9	)	)	PUNCT
ejpam-3123	210	10	−1	−1	NOUN
ejpam-3123	211	1	=	=	SYM
ejpam-3123	211	2	t	t	PROPN
ejpam-3123	211	3	(	(	PUNCT
ejpam-3123	211	4	0,0)f	0,0)f	X
ejpam-3123	211	5	(	(	PUNCT
ejpam-3123	211	6	(	(	PUNCT
ejpam-3123	211	7	0,1	0,1	NUM
ejpam-3123	211	8	)	)	PUNCT
ejpam-3123	211	9	(	(	PUNCT
ejpam-3123	211	10	1,2	1,2	NUM
ejpam-3123	211	11	)	)	PUNCT
ejpam-3123	211	12	)	)	PUNCT
ejpam-3123	211	13	−1	−1	NOUN
ejpam-3123	211	14	=	=	SYM
ejpam-3123	211	15	t	t	PROPN
ejpam-3123	211	16	(	(	PUNCT
ejpam-3123	211	17	0,0	0,0	NOUN
ejpam-3123	211	18	)	)	PUNCT
ejpam-3123	211	19	(	(	PUNCT
ejpam-3123	211	20	(	(	PUNCT
ejpam-3123	211	21	1,0).(0,0	1,0).(0,0	NOUN
ejpam-3123	211	22	)	)	PUNCT
ejpam-3123	211	23	)	)	PUNCT
ejpam-3123	212	1	f	f	X
ejpam-3123	212	2	(	(	PUNCT
ejpam-3123	212	3	(	(	PUNCT
ejpam-3123	212	4	0,1)/(0,0	0,1)/(0,0	NOUN
ejpam-3123	212	5	)	)	PUNCT
ejpam-3123	212	6	(	(	PUNCT
ejpam-3123	212	7	1,2	1,2	NUM
ejpam-3123	212	8	)	)	PUNCT
ejpam-3123	212	9	)	)	PUNCT
ejpam-3123	212	10	−1	−1	NOUN
ejpam-3123	213	1	=	=	SYM
ejpam-3123	213	2	t	t	PROPN
ejpam-3123	213	3	f	f	X
ejpam-3123	213	4	(	(	PUNCT
ejpam-3123	213	5	(	(	PUNCT
ejpam-3123	213	6	0,1	0,1	NOUN
ejpam-3123	213	7	)	)	PUNCT
ejpam-3123	213	8	,	,	PUNCT
ejpam-3123	213	9	(	(	PUNCT
ejpam-3123	213	10	1,2	1,2	NUM
ejpam-3123	213	11	)	)	PUNCT
ejpam-3123	213	12	)	)	PUNCT
ejpam-3123	213	13	−1	−1	NOUN
ejpam-3123	213	14	=	=	NOUN
ejpam-3123	213	15	t(0,0)−1	t(0,0)−1	NUM
ejpam-3123	213	16	=	=	SYM
ejpam-3123	213	17	t(0,0	t(0,0	NOUN
ejpam-3123	213	18	)	)	PUNCT
ejpam-3123	213	19	.	.	PUNCT
ejpam-3123	214	1	hence	hence	ADV
ejpam-3123	214	2	,	,	PUNCT
ejpam-3123	214	3	the	the	DET
ejpam-3123	214	4	equality	equality	NOUN
ejpam-3123	214	5	is	be	AUX
ejpam-3123	214	6	satisfied	satisfied	ADJ
ejpam-3123	214	7	.	.	PUNCT
ejpam-3123	215	1	(	(	PUNCT
ejpam-3123	215	2	iii	iii	X
ejpam-3123	215	3	)	)	PUNCT
ejpam-3123	215	4	ts.uv	ts.uv	X
ejpam-3123	215	5	=	=	SYM
ejpam-3123	215	6	t	t	PROPN
ejpam-3123	215	7	(	(	PUNCT
ejpam-3123	215	8	s.u	s.u	PROPN
ejpam-3123	215	9	)	)	PUNCT
ejpam-3123	215	10	(	(	PUNCT
ejpam-3123	215	11	(	(	PUNCT
ejpam-3123	215	12	s	s	NOUN
ejpam-3123	215	13	/	/	SYM
ejpam-3123	215	14	u).v	u).v	ADJ
ejpam-3123	215	15	)	)	PUNCT
ejpam-3123	215	16	.	.	PUNCT
ejpam-3123	216	1	we	we	PRON
ejpam-3123	216	2	start	start	VERB
ejpam-3123	216	3	with	with	ADP
ejpam-3123	216	4	the	the	DET
ejpam-3123	216	5	left	left	ADJ
ejpam-3123	216	6	hand	hand	NOUN
ejpam-3123	216	7	side	side	NOUN
ejpam-3123	216	8	as	as	SCONJ
ejpam-3123	216	9	follows	follow	VERB
ejpam-3123	216	10	:	:	PUNCT
ejpam-3123	216	11	ts.uv	ts.uv	X
ejpam-3123	216	12	=	=	SYM
ejpam-3123	216	13	t	t	PROPN
ejpam-3123	216	14	(	(	PUNCT
ejpam-3123	216	15	0,1	0,1	NUM
ejpam-3123	216	16	)	)	PUNCT
ejpam-3123	216	17	.	.	PUNCT
ejpam-3123	217	1	(	(	PUNCT
ejpam-3123	217	2	(	(	PUNCT
ejpam-3123	217	3	0,0)+(1,0	0,0)+(1,0	NOUN
ejpam-3123	217	4	)	)	PUNCT
ejpam-3123	217	5	)	)	PUNCT
ejpam-3123	218	1	=	=	SYM
ejpam-3123	218	2	t(0,1).(1,0	t(0,1).(1,0	X
ejpam-3123	218	3	)	)	PUNCT
ejpam-3123	218	4	=	=	SYM
ejpam-3123	218	5	t(1,0	t(1,0	NUM
ejpam-3123	218	6	)	)	PUNCT
ejpam-3123	218	7	.	.	PUNCT
ejpam-3123	219	1	on	on	ADP
ejpam-3123	219	2	the	the	DET
ejpam-3123	219	3	other	other	ADJ
ejpam-3123	219	4	hand	hand	NOUN
ejpam-3123	219	5	,	,	PUNCT
ejpam-3123	219	6	t	t	PROPN
ejpam-3123	219	7	(	(	PUNCT
ejpam-3123	219	8	s.u	s.u	PROPN
ejpam-3123	219	9	)	)	PUNCT
ejpam-3123	219	10	(	(	PUNCT
ejpam-3123	219	11	(	(	PUNCT
ejpam-3123	219	12	s	s	NOUN
ejpam-3123	219	13	/	/	SYM
ejpam-3123	219	14	u).v	u).v	ADJ
ejpam-3123	219	15	)	)	PUNCT
ejpam-3123	220	1	=	=	SYM
ejpam-3123	220	2	t	t	PROPN
ejpam-3123	220	3	(	(	PUNCT
ejpam-3123	220	4	(	(	PUNCT
ejpam-3123	220	5	0,1).(0,0	0,1).(0,0	NOUN
ejpam-3123	220	6	)	)	PUNCT
ejpam-3123	220	7	)	)	PUNCT
ejpam-3123	220	8	(	(	PUNCT
ejpam-3123	220	9	(	(	PUNCT
ejpam-3123	220	10	(	(	PUNCT
ejpam-3123	220	11	0,1)/(0,0	0,1)/(0,0	NOUN
ejpam-3123	220	12	)	)	PUNCT
ejpam-3123	220	13	)	)	PUNCT
ejpam-3123	220	14	.(1,0	.(1,0	PROPN
ejpam-3123	220	15	)	)	PUNCT
ejpam-3123	220	16	)	)	PUNCT
ejpam-3123	221	1	=	=	SYM
ejpam-3123	221	2	t	t	PROPN
ejpam-3123	221	3	(	(	PUNCT
ejpam-3123	221	4	0,0	0,0	NOUN
ejpam-3123	221	5	)	)	PUNCT
ejpam-3123	221	6	(	(	PUNCT
ejpam-3123	221	7	(	(	PUNCT
ejpam-3123	221	8	0,1)/(1,0	0,1)/(1,0	NUM
ejpam-3123	221	9	)	)	PUNCT
ejpam-3123	221	10	)	)	PUNCT
ejpam-3123	222	1	=	=	SYM
ejpam-3123	222	2	t(0,0)+(1,0	t(0,0)+(1,0	ADV
ejpam-3123	222	3	)	)	PUNCT
ejpam-3123	222	4	=	=	SYM
ejpam-3123	222	5	t(1,0	t(1,0	NUM
ejpam-3123	222	6	)	)	PUNCT
ejpam-3123	222	7	.	.	PUNCT
ejpam-3123	223	1	hence	hence	ADV
ejpam-3123	223	2	,	,	PUNCT
ejpam-3123	223	3	the	the	DET
ejpam-3123	223	4	equality	equality	NOUN
ejpam-3123	223	5	is	be	AUX
ejpam-3123	223	6	satisfied	satisfied	ADJ
ejpam-3123	223	7	.	.	PUNCT
ejpam-3123	224	1	(	(	PUNCT
ejpam-3123	224	2	iv	iv	X
ejpam-3123	224	3	)	)	PUNCT
ejpam-3123	224	4	ts	ts	NOUN
ejpam-3123	224	5	/	/	SYM
ejpam-3123	224	6	uv	uv	NOUN
ejpam-3123	224	7	=	=	PUNCT
ejpam-3123	224	8	t(s	t(s	PROPN
ejpam-3123	224	9	/	/	SYM
ejpam-3123	224	10	u)/v	u)/v	PROPN
ejpam-3123	224	11	.	.	PUNCT
ejpam-3123	225	1	we	we	PRON
ejpam-3123	225	2	start	start	VERB
ejpam-3123	225	3	with	with	ADP
ejpam-3123	225	4	the	the	DET
ejpam-3123	225	5	left	left	ADJ
ejpam-3123	225	6	hand	hand	NOUN
ejpam-3123	225	7	side	side	NOUN
ejpam-3123	225	8	as	as	SCONJ
ejpam-3123	225	9	follows	follow	VERB
ejpam-3123	225	10	:	:	PUNCT
ejpam-3123	225	11	ts	ts	X
ejpam-3123	225	12	/	/	SYM
ejpam-3123	225	13	uv	uv	PROPN
ejpam-3123	225	14	=	=	SYM
ejpam-3123	225	15	t	t	PROPN
ejpam-3123	225	16	(	(	PUNCT
ejpam-3123	225	17	0,1)/	0,1)/	NOUN
ejpam-3123	225	18	(	(	PUNCT
ejpam-3123	225	19	(	(	PUNCT
ejpam-3123	225	20	0,0)+(1,0	0,0)+(1,0	NOUN
ejpam-3123	225	21	)	)	PUNCT
ejpam-3123	225	22	)	)	PUNCT
ejpam-3123	226	1	=	=	SYM
ejpam-3123	226	2	t(0,1)/(1,0	t(0,1)/(1,0	PROPN
ejpam-3123	226	3	)	)	PUNCT
ejpam-3123	226	4	=	=	SYM
ejpam-3123	227	1	t(0,1	t(0,1	NOUN
ejpam-3123	227	2	)	)	PUNCT
ejpam-3123	227	3	.	.	PUNCT
ejpam-3123	228	1	on	on	ADP
ejpam-3123	228	2	the	the	DET
ejpam-3123	228	3	other	other	ADJ
ejpam-3123	228	4	hand	hand	NOUN
ejpam-3123	228	5	,	,	PUNCT
ejpam-3123	228	6	t(s	t(s	PROPN
ejpam-3123	228	7	/	/	SYM
ejpam-3123	228	8	u)/v	u)/v	PROPN
ejpam-3123	228	9	=	=	SYM
ejpam-3123	228	10	t	t	PROPN
ejpam-3123	228	11	(	(	PUNCT
ejpam-3123	228	12	(	(	PUNCT
ejpam-3123	228	13	0,1)/(0,0	0,1)/(0,0	NUM
ejpam-3123	228	14	)	)	PUNCT
ejpam-3123	228	15	)	)	PUNCT
ejpam-3123	228	16	/(1,0	/(1,0	PUNCT
ejpam-3123	228	17	)	)	PUNCT
ejpam-3123	229	1	=	=	SYM
ejpam-3123	229	2	t(0,1)/(1,0	t(0,1)/(1,0	PROPN
ejpam-3123	229	3	)	)	PUNCT
ejpam-3123	229	4	=	=	SYM
ejpam-3123	230	1	t(0,1	t(0,1	NOUN
ejpam-3123	230	2	)	)	PUNCT
ejpam-3123	230	3	.	.	PUNCT
ejpam-3123	231	1	hence	hence	ADV
ejpam-3123	231	2	,	,	PUNCT
ejpam-3123	231	3	the	the	DET
ejpam-3123	231	4	equality	equality	NOUN
ejpam-3123	231	5	is	be	AUX
ejpam-3123	231	6	satisfied	satisfied	ADJ
ejpam-3123	231	7	.	.	PUNCT
ejpam-3123	232	1	(	(	PUNCT
ejpam-3123	232	2	v	v	NOUN
ejpam-3123	232	3	)	)	PUNCT
ejpam-3123	232	4	tf(p	tf(p	NUM
ejpam-3123	232	5	,	,	PUNCT
ejpam-3123	232	6	s)f(p∗s	s)f(p∗s	PROPN
ejpam-3123	232	7	,	,	PUNCT
ejpam-3123	232	8	t	t	PROPN
ejpam-3123	232	9	)	)	PUNCT
ejpam-3123	233	1	=	=	SYM
ejpam-3123	233	2	t	t	PROPN
ejpam-3123	233	3	(	(	PUNCT
ejpam-3123	233	4	p.f(s	p.f(s	PROPN
ejpam-3123	233	5	,	,	PUNCT
ejpam-3123	233	6	t	t	PROPN
ejpam-3123	233	7	)	)	PUNCT
ejpam-3123	233	8	)	)	PUNCT
ejpam-3123	234	1	f	f	NOUN
ejpam-3123	234	2	(	(	PUNCT
ejpam-3123	234	3	p	p	X
ejpam-3123	234	4	/	/	SYM
ejpam-3123	234	5	f(s	f(	NOUN
ejpam-3123	234	6	,	,	PUNCT
ejpam-3123	234	7	t),s∗t	t),s∗t	NOUN
ejpam-3123	234	8	)	)	PUNCT
ejpam-3123	234	9	.	.	PUNCT
ejpam-3123	235	1	we	we	PRON
ejpam-3123	235	2	start	start	VERB
ejpam-3123	235	3	with	with	ADP
ejpam-3123	235	4	the	the	DET
ejpam-3123	235	5	left	left	ADJ
ejpam-3123	235	6	hand	hand	NOUN
ejpam-3123	235	7	side	side	NOUN
ejpam-3123	235	8	as	as	SCONJ
ejpam-3123	235	9	follows	follow	VERB
ejpam-3123	235	10	:	:	PUNCT
ejpam-3123	235	11	tf(p	tf(p	NUM
ejpam-3123	235	12	,	,	PUNCT
ejpam-3123	235	13	s)f(p∗s	s)f(p∗s	PROPN
ejpam-3123	235	14	,	,	PUNCT
ejpam-3123	235	15	t	t	PROPN
ejpam-3123	235	16	)	)	PUNCT
ejpam-3123	235	17	=	=	SYM
ejpam-3123	236	1	t	t	PROPN
ejpam-3123	236	2	f	f	X
ejpam-3123	236	3	(	(	PUNCT
ejpam-3123	236	4	(	(	PUNCT
ejpam-3123	236	5	1,0),(0,1	1,0),(0,1	NOUN
ejpam-3123	236	6	)	)	PUNCT
ejpam-3123	236	7	)	)	PUNCT
ejpam-3123	237	1	f	f	X
ejpam-3123	237	2	(	(	PUNCT
ejpam-3123	237	3	(	(	PUNCT
ejpam-3123	237	4	1,0)∗(0,1),(1,2	1,0)∗(0,1),(1,2	NUM
ejpam-3123	237	5	)	)	PUNCT
ejpam-3123	237	6	)	)	PUNCT
ejpam-3123	238	1	=	=	SYM
ejpam-3123	238	2	t	t	PROPN
ejpam-3123	238	3	(	(	PUNCT
ejpam-3123	238	4	1,0)f	1,0)f	NUM
ejpam-3123	238	5	(	(	PUNCT
ejpam-3123	238	6	(	(	PUNCT
ejpam-3123	238	7	0,1),(1,2	0,1),(1,2	NOUN
ejpam-3123	238	8	)	)	PUNCT
ejpam-3123	238	9	)	)	PUNCT
ejpam-3123	239	1	=	=	SYM
ejpam-3123	239	2	t(1,0)(0,0	t(1,0)(0,0	NOUN
ejpam-3123	239	3	)	)	PUNCT
ejpam-3123	239	4	=	=	SYM
ejpam-3123	239	5	t(1,0	t(1,0	NUM
ejpam-3123	239	6	)	)	PUNCT
ejpam-3123	239	7	.	.	PUNCT
ejpam-3123	240	1	n.	n.	PROPN
ejpam-3123	240	2	al	al	PROPN
ejpam-3123	240	3	-	-	PUNCT
ejpam-3123	240	4	subaie	subaie	NOUN
ejpam-3123	240	5	,	,	PUNCT
ejpam-3123	240	6	m.	m.	NOUN
ejpam-3123	240	7	m.	m.	PROPN
ejpam-3123	240	8	al	al	PROPN
ejpam-3123	240	9	-	-	PUNCT
ejpam-3123	240	10	shomrani	shomrani	PROPN
ejpam-3123	240	11	/	/	SYM
ejpam-3123	240	12	eur	eur	NOUN
ejpam-3123	240	13	.	.	PUNCT
ejpam-3123	241	1	j.	j.	PROPN
ejpam-3123	241	2	pure	pure	PROPN
ejpam-3123	241	3	appl	appl	PROPN
ejpam-3123	241	4	.	.	PROPN
ejpam-3123	241	5	math	math	PROPN
ejpam-3123	241	6	,	,	PUNCT
ejpam-3123	241	7	10	10	NUM
ejpam-3123	241	8	(	(	PUNCT
ejpam-3123	241	9	5	5	NUM
ejpam-3123	241	10	)	)	PUNCT
ejpam-3123	241	11	(	(	PUNCT
ejpam-3123	241	12	2017	2017	NUM
ejpam-3123	241	13	)	)	PUNCT
ejpam-3123	241	14	,	,	PUNCT
ejpam-3123	241	15	967	967	NUM
ejpam-3123	241	16	-	-	SYM
ejpam-3123	241	17	980	980	NUM
ejpam-3123	241	18	976	976	NUM
ejpam-3123	241	19	on	on	ADP
ejpam-3123	241	20	the	the	DET
ejpam-3123	241	21	other	other	ADJ
ejpam-3123	241	22	hand	hand	NOUN
ejpam-3123	241	23	,	,	PUNCT
ejpam-3123	241	24	t	t	PROPN
ejpam-3123	241	25	(	(	PUNCT
ejpam-3123	241	26	p.f(s	p.f(s	PROPN
ejpam-3123	241	27	,	,	PUNCT
ejpam-3123	241	28	t	t	PROPN
ejpam-3123	241	29	)	)	PUNCT
ejpam-3123	241	30	)	)	PUNCT
ejpam-3123	242	1	f	f	NOUN
ejpam-3123	242	2	(	(	PUNCT
ejpam-3123	242	3	p	p	X
ejpam-3123	242	4	/	/	SYM
ejpam-3123	242	5	f(s	f(	NOUN
ejpam-3123	242	6	,	,	PUNCT
ejpam-3123	242	7	t),s∗t	t),s∗t	X
ejpam-3123	242	8	)	)	PUNCT
ejpam-3123	242	9	=	=	SYM
ejpam-3123	242	10	t	t	PROPN
ejpam-3123	242	11	(	(	PUNCT
ejpam-3123	242	12	(	(	PUNCT
ejpam-3123	242	13	1,0).f	1,0).f	X
ejpam-3123	242	14	(	(	PUNCT
ejpam-3123	242	15	(	(	PUNCT
ejpam-3123	242	16	0,1),(1,2	0,1),(1,2	NOUN
ejpam-3123	242	17	)	)	PUNCT
ejpam-3123	242	18	)	)	PUNCT
ejpam-3123	242	19	)	)	PUNCT
ejpam-3123	243	1	f	f	X
ejpam-3123	243	2	(	(	PUNCT
ejpam-3123	243	3	(	(	PUNCT
ejpam-3123	243	4	1,0)/f	1,0)/f	NUM
ejpam-3123	243	5	(	(	PUNCT
ejpam-3123	243	6	(	(	PUNCT
ejpam-3123	243	7	0,1),(1,2	0,1),(1,2	NOUN
ejpam-3123	243	8	)	)	PUNCT
ejpam-3123	243	9	)	)	PUNCT
ejpam-3123	243	10	,	,	PUNCT
ejpam-3123	243	11	(	(	PUNCT
ejpam-3123	243	12	0,1)∗(1,2	0,1)∗(1,2	NUM
ejpam-3123	243	13	)	)	PUNCT
ejpam-3123	243	14	)	)	PUNCT
ejpam-3123	244	1	=	=	SYM
ejpam-3123	244	2	t	t	PROPN
ejpam-3123	244	3	(	(	PUNCT
ejpam-3123	244	4	(	(	PUNCT
ejpam-3123	244	5	1,0).(0,0	1,0).(0,0	NOUN
ejpam-3123	244	6	)	)	PUNCT
ejpam-3123	244	7	)	)	PUNCT
ejpam-3123	245	1	f	f	X
ejpam-3123	245	2	(	(	PUNCT
ejpam-3123	245	3	(	(	PUNCT
ejpam-3123	245	4	1,0)/(0,0),(1,0	1,0)/(0,0),(1,0	NUM
ejpam-3123	245	5	)	)	PUNCT
ejpam-3123	245	6	)	)	PUNCT
ejpam-3123	246	1	=	=	SYM
ejpam-3123	246	2	t	t	PROPN
ejpam-3123	246	3	(	(	PUNCT
ejpam-3123	246	4	0,0)f	0,0)f	X
ejpam-3123	246	5	(	(	PUNCT
ejpam-3123	246	6	(	(	PUNCT
ejpam-3123	246	7	1,0),(1,0	1,0),(1,0	NUM
ejpam-3123	246	8	)	)	PUNCT
ejpam-3123	246	9	)	)	PUNCT
ejpam-3123	247	1	=	=	PUNCT
ejpam-3123	247	2	t(1,0	t(1,0	NUM
ejpam-3123	247	3	)	)	PUNCT
ejpam-3123	247	4	.	.	PUNCT
ejpam-3123	248	1	hence	hence	ADV
ejpam-3123	248	2	,	,	PUNCT
ejpam-3123	248	3	the	the	DET
ejpam-3123	248	4	equality	equality	NOUN
ejpam-3123	248	5	is	be	AUX
ejpam-3123	248	6	satisfied	satisfied	ADJ
ejpam-3123	248	7	.	.	PUNCT
ejpam-3123	249	1	(	(	PUNCT
ejpam-3123	249	2	vi	vi	NOUN
ejpam-3123	249	3	)	)	PUNCT
ejpam-3123	249	4	t	t	PROPN
ejpam-3123	249	5	(	(	PUNCT
ejpam-3123	249	6	p	p	X
ejpam-3123	249	7	/	/	SYM
ejpam-3123	249	8	f(s	f(	NOUN
ejpam-3123	249	9	,	,	PUNCT
ejpam-3123	249	10	t	t	PROPN
ejpam-3123	249	11	)	)	PUNCT
ejpam-3123	249	12	)	)	PUNCT
ejpam-3123	250	1	∗(s∗t	∗(s∗t	PUNCT
ejpam-3123	250	2	)	)	PUNCT
ejpam-3123	251	1	=	=	PUNCT
ejpam-3123	251	2	t(p∗s)∗t	t(p∗s)∗t	NOUN
ejpam-3123	251	3	.	.	PUNCT
ejpam-3123	252	1	we	we	PRON
ejpam-3123	252	2	start	start	VERB
ejpam-3123	252	3	with	with	ADP
ejpam-3123	252	4	the	the	DET
ejpam-3123	252	5	left	left	ADJ
ejpam-3123	252	6	hand	hand	NOUN
ejpam-3123	252	7	side	side	NOUN
ejpam-3123	252	8	as	as	SCONJ
ejpam-3123	252	9	follows	follow	VERB
ejpam-3123	252	10	:	:	PUNCT
ejpam-3123	252	11	t	t	X
ejpam-3123	252	12	(	(	PUNCT
ejpam-3123	252	13	p	p	X
ejpam-3123	252	14	/	/	SYM
ejpam-3123	252	15	f(s	f(	NOUN
ejpam-3123	252	16	,	,	PUNCT
ejpam-3123	252	17	t	t	PROPN
ejpam-3123	252	18	)	)	PUNCT
ejpam-3123	252	19	)	)	PUNCT
ejpam-3123	253	1	∗(s∗t	∗(s∗t	X
ejpam-3123	253	2	)	)	PUNCT
ejpam-3123	254	1	=	=	SYM
ejpam-3123	254	2	t	t	PROPN
ejpam-3123	254	3	(	(	PUNCT
ejpam-3123	254	4	(	(	PUNCT
ejpam-3123	254	5	1,0)/f	1,0)/f	NUM
ejpam-3123	254	6	(	(	PUNCT
ejpam-3123	254	7	(	(	PUNCT
ejpam-3123	254	8	0,1),(1,2	0,1),(1,2	NOUN
ejpam-3123	254	9	)	)	PUNCT
ejpam-3123	254	10	)	)	PUNCT
ejpam-3123	254	11	)	)	PUNCT
ejpam-3123	255	1	∗	∗	NOUN
ejpam-3123	255	2	(	(	PUNCT
ejpam-3123	255	3	(	(	PUNCT
ejpam-3123	255	4	0,1)∗(1,2	0,1)∗(1,2	NUM
ejpam-3123	255	5	)	)	PUNCT
ejpam-3123	255	6	)	)	PUNCT
ejpam-3123	256	1	=	=	SYM
ejpam-3123	256	2	t	t	PROPN
ejpam-3123	256	3	(	(	PUNCT
ejpam-3123	256	4	(	(	PUNCT
ejpam-3123	256	5	1,0)/(0,0	1,0)/(0,0	NUM
ejpam-3123	256	6	)	)	PUNCT
ejpam-3123	256	7	)	)	PUNCT
ejpam-3123	257	1	∗(1,0	∗(1,0	X
ejpam-3123	257	2	)	)	PUNCT
ejpam-3123	257	3	=	=	SYM
ejpam-3123	257	4	t(1,0)∗(1,0	t(1,0)∗(1,0	X
ejpam-3123	257	5	)	)	PUNCT
ejpam-3123	257	6	=	=	SYM
ejpam-3123	257	7	t(1,0	t(1,0	NUM
ejpam-3123	257	8	)	)	PUNCT
ejpam-3123	257	9	.	.	PUNCT
ejpam-3123	258	1	on	on	ADP
ejpam-3123	258	2	the	the	DET
ejpam-3123	258	3	other	other	ADJ
ejpam-3123	258	4	hand	hand	NOUN
ejpam-3123	258	5	,	,	PUNCT
ejpam-3123	258	6	t(p∗s)∗t	t(p∗s)∗t	PROPN
ejpam-3123	258	7	=	=	SYM
ejpam-3123	258	8	t	t	PROPN
ejpam-3123	258	9	(	(	PUNCT
ejpam-3123	258	10	(	(	PUNCT
ejpam-3123	258	11	1,0)∗(0,1	1,0)∗(0,1	NOUN
ejpam-3123	258	12	)	)	PUNCT
ejpam-3123	258	13	)	)	PUNCT
ejpam-3123	259	1	∗(1,2	∗(1,2	PUNCT
ejpam-3123	259	2	)	)	PUNCT
ejpam-3123	259	3	=	=	SYM
ejpam-3123	259	4	t(0,1)∗(1,2	t(0,1)∗(1,2	NOUN
ejpam-3123	259	5	)	)	PUNCT
ejpam-3123	259	6	=	=	PUNCT
ejpam-3123	259	7	t(1,0	t(1,0	NUM
ejpam-3123	259	8	)	)	PUNCT
ejpam-3123	259	9	.	.	PUNCT
ejpam-3123	260	1	hence	hence	ADV
ejpam-3123	260	2	,	,	PUNCT
ejpam-3123	260	3	the	the	DET
ejpam-3123	260	4	equality	equality	NOUN
ejpam-3123	260	5	is	be	AUX
ejpam-3123	260	6	satisfied	satisfied	ADJ
ejpam-3123	260	7	.	.	PUNCT
ejpam-3123	261	1	in	in	ADP
ejpam-3123	261	2	addition	addition	NOUN
ejpam-3123	261	3	,	,	PUNCT
ejpam-3123	261	4	to	to	PART
ejpam-3123	261	5	illustrate	illustrate	VERB
ejpam-3123	261	6	the	the	DET
ejpam-3123	261	7	proposition	proposition	NOUN
ejpam-3123	261	8	in	in	ADP
ejpam-3123	261	9	4	4	NUM
ejpam-3123	261	10	,	,	PUNCT
ejpam-3123	261	11	let	let	VERB
ejpam-3123	261	12	t	t	NOUN
ejpam-3123	261	13	=	=	SYM
ejpam-3123	261	14	(	(	PUNCT
ejpam-3123	261	15	1	1	NUM
ejpam-3123	261	16	,	,	PUNCT
ejpam-3123	261	17	2	2	NUM
ejpam-3123	261	18	)	)	PUNCT
ejpam-3123	261	19	∈	∈	PROPN
ejpam-3123	261	20	g	g	NOUN
ejpam-3123	261	21	and	and	CCONJ
ejpam-3123	261	22	v	v	NOUN
ejpam-3123	261	23	=	=	SYM
ejpam-3123	261	24	(	(	PUNCT
ejpam-3123	261	25	0	0	NUM
ejpam-3123	261	26	,	,	PUNCT
ejpam-3123	261	27	0	0	NUM
ejpam-3123	261	28	)	)	PUNCT
ejpam-3123	261	29	∈	∈	PROPN
ejpam-3123	261	30	h	h	NOUN
ejpam-3123	261	31	where	where	SCONJ
ejpam-3123	261	32	eg	eg	NOUN
ejpam-3123	261	33	=	=	SYM
ejpam-3123	261	34	(	(	PUNCT
ejpam-3123	261	35	1	1	NUM
ejpam-3123	261	36	,	,	PUNCT
ejpam-3123	261	37	0	0	NUM
ejpam-3123	261	38	)	)	PUNCT
ejpam-3123	261	39	∈	∈	PROPN
ejpam-3123	261	40	h	h	NOUN
ejpam-3123	261	41	∩g	∩g	PROPN
ejpam-3123	261	42	.	.	PUNCT
ejpam-3123	262	1	then	then	ADV
ejpam-3123	262	2	(	(	PUNCT
ejpam-3123	262	3	i	i	NOUN
ejpam-3123	262	4	)	)	PUNCT
ejpam-3123	262	5	teg	teg	PROPN
ejpam-3123	262	6	/	/	SYM
ejpam-3123	262	7	v	v	NOUN
ejpam-3123	262	8	=	=	SYM
ejpam-3123	262	9	t(1,0)/(0,0	t(1,0)/(0,0	NOUN
ejpam-3123	262	10	)	)	PUNCT
ejpam-3123	262	11	=	=	SYM
ejpam-3123	262	12	t(1,0	t(1,0	X
ejpam-3123	262	13	)	)	PUNCT
ejpam-3123	262	14	=	=	SYM
ejpam-3123	262	15	teg	teg	NOUN
ejpam-3123	262	16	,	,	PUNCT
ejpam-3123	262	17	as	as	SCONJ
ejpam-3123	262	18	required	require	VERB
ejpam-3123	262	19	.	.	PUNCT
ejpam-3123	263	1	(	(	PUNCT
ejpam-3123	263	2	ii	ii	X
ejpam-3123	263	3	)	)	PUNCT
ejpam-3123	263	4	tt	tt	PROPN
ejpam-3123	263	5	/	/	SYM
ejpam-3123	263	6	e	e	NOUN
ejpam-3123	263	7	=	=	X
ejpam-3123	263	8	t(1,2)/e	t(1,2)/e	X
ejpam-3123	263	9	=	=	SYM
ejpam-3123	263	10	t(1,2	t(1,2	NOUN
ejpam-3123	263	11	)	)	PUNCT
ejpam-3123	263	12	=	=	SYM
ejpam-3123	263	13	tt	tt	PROPN
ejpam-3123	263	14	,	,	PUNCT
ejpam-3123	263	15	as	as	SCONJ
ejpam-3123	263	16	required	require	VERB
ejpam-3123	263	17	.	.	PUNCT
ejpam-3123	264	1	(	(	PUNCT
ejpam-3123	264	2	iii	iii	NOUN
ejpam-3123	264	3	)	)	PUNCT
ejpam-3123	264	4	t(t	t(t	NOUN
ejpam-3123	264	5	/	/	SYM
ejpam-3123	264	6	e−1	e−1	PROPN
ejpam-3123	264	7	g	g	NOUN
ejpam-3123	264	8	)	)	PUNCT
ejpam-3123	264	9	∗eg	∗eg	PUNCT
ejpam-3123	264	10	=	=	SYM
ejpam-3123	264	11	t	t	PROPN
ejpam-3123	264	12	(	(	PUNCT
ejpam-3123	264	13	(	(	PUNCT
ejpam-3123	264	14	1,2)/(1,0)−1	1,2)/(1,0)−1	PROPN
ejpam-3123	264	15	)	)	PUNCT
ejpam-3123	264	16	∗(1,0	∗(1,0	PROPN
ejpam-3123	264	17	)	)	PUNCT
ejpam-3123	264	18	=	=	SYM
ejpam-3123	264	19	t(1,2)∗(1,0	t(1,2)∗(1,0	NOUN
ejpam-3123	264	20	)	)	PUNCT
ejpam-3123	264	21	=	=	SYM
ejpam-3123	264	22	t(1,2	t(1,2	X
ejpam-3123	264	23	)	)	PUNCT
ejpam-3123	264	24	=	=	SYM
ejpam-3123	264	25	tt	tt	PROPN
ejpam-3123	264	26	,	,	PUNCT
ejpam-3123	264	27	as	as	SCONJ
ejpam-3123	264	28	required	require	VERB
ejpam-3123	264	29	.	.	PUNCT
ejpam-3123	265	1	5	5	X
ejpam-3123	265	2	.	.	X
ejpam-3123	265	3	grading	grade	VERB
ejpam-3123	265	4	by	by	ADP
ejpam-3123	265	5	h	h	PROPN
ejpam-3123	265	6	×g	×g	PROPN
ejpam-3123	265	7	definition	definition	NOUN
ejpam-3123	265	8	4	4	NUM
ejpam-3123	265	9	.	.	PUNCT
ejpam-3123	266	1	let	let	VERB
ejpam-3123	266	2	x	x	PRON
ejpam-3123	266	3	be	be	AUX
ejpam-3123	266	4	a	a	DET
ejpam-3123	266	5	group	group	NOUN
ejpam-3123	266	6	,	,	PUNCT
ejpam-3123	266	7	h	h	PROPN
ejpam-3123	266	8	be	be	VERB
ejpam-3123	266	9	a	a	DET
ejpam-3123	266	10	subgroup	subgroup	NOUN
ejpam-3123	266	11	of	of	ADP
ejpam-3123	266	12	x	x	PUNCT
ejpam-3123	266	13	and	and	CCONJ
ejpam-3123	266	14	(	(	PUNCT
ejpam-3123	266	15	g	g	NOUN
ejpam-3123	266	16	,	,	PUNCT
ejpam-3123	266	17	∗	∗	NOUN
ejpam-3123	266	18	)	)	PUNCT
ejpam-3123	266	19	be	be	VERB
ejpam-3123	266	20	a	a	DET
ejpam-3123	266	21	fixed	fix	VERB
ejpam-3123	266	22	set	set	NOUN
ejpam-3123	266	23	of	of	ADP
ejpam-3123	266	24	left	left	ADJ
ejpam-3123	266	25	coset	coset	NOUN
ejpam-3123	266	26	representatives	representative	NOUN
ejpam-3123	266	27	for	for	ADP
ejpam-3123	266	28	the	the	DET
ejpam-3123	266	29	subgroup	subgroup	PROPN
ejpam-3123	266	30	h	h	NOUN
ejpam-3123	266	31	with	with	ADP
ejpam-3123	266	32	the	the	DET
ejpam-3123	266	33	binary	binary	PROPN
ejpam-3123	266	34	operation	operation	NOUN
ejpam-3123	266	35	∗	∗	NOUN
ejpam-3123	266	36	which	which	PRON
ejpam-3123	266	37	is	be	AUX
ejpam-3123	266	38	defined	define	VERB
ejpam-3123	266	39	as	as	ADP
ejpam-3123	266	40	in	in	ADP
ejpam-3123	266	41	2	2	NUM
ejpam-3123	266	42	.	.	PUNCT
ejpam-3123	267	1	a	a	DET
ejpam-3123	267	2	ring	ring	NOUN
ejpam-3123	267	3	r	r	NOUN
ejpam-3123	267	4	is	be	AUX
ejpam-3123	267	5	called	call	VERB
ejpam-3123	267	6	a	a	DET
ejpam-3123	267	7	h	h	NOUN
ejpam-3123	267	8	×g	×g	NOUN
ejpam-3123	267	9	-	-	PUNCT
ejpam-3123	267	10	graded	grade	VERB
ejpam-3123	267	11	ring	ring	NOUN
ejpam-3123	267	12	if	if	SCONJ
ejpam-3123	267	13	r	r	NOUN
ejpam-3123	267	14	=	=	SYM
ejpam-3123	267	15	⊕	⊕	PROPN
ejpam-3123	267	16	(	(	PUNCT
ejpam-3123	267	17	u	u	NOUN
ejpam-3123	267	18	,	,	PUNCT
ejpam-3123	267	19	s)∈h×g	s)∈h×g	ADV
ejpam-3123	267	20	r(u	r(u	PROPN
ejpam-3123	267	21	,	,	PUNCT
ejpam-3123	267	22	s	s	AUX
ejpam-3123	267	23	)	)	PUNCT
ejpam-3123	267	24	(	(	PUNCT
ejpam-3123	267	25	4	4	NUM
ejpam-3123	267	26	)	)	PUNCT
ejpam-3123	267	27	and	and	CCONJ
ejpam-3123	267	28	r(u	r(u	PROPN
ejpam-3123	267	29	,	,	PUNCT
ejpam-3123	267	30	s)r(v	s)r(v	PROPN
ejpam-3123	267	31	,	,	PUNCT
ejpam-3123	267	32	t	t	PROPN
ejpam-3123	267	33	)	)	PUNCT
ejpam-3123	267	34	⊆	⊆	NUM
ejpam-3123	267	35	r(u	r(u	PROPN
ejpam-3123	267	36	,	,	PUNCT
ejpam-3123	267	37	s)(v	s)(v	PROPN
ejpam-3123	267	38	,	,	PUNCT
ejpam-3123	267	39	t	t	PROPN
ejpam-3123	267	40	)	)	PUNCT
ejpam-3123	267	41	for	for	ADP
ejpam-3123	267	42	all	all	DET
ejpam-3123	267	43	(	(	PUNCT
ejpam-3123	267	44	u	u	NOUN
ejpam-3123	267	45	,	,	PUNCT
ejpam-3123	267	46	s	s	PART
ejpam-3123	267	47	)	)	PUNCT
ejpam-3123	267	48	,	,	PUNCT
ejpam-3123	267	49	(	(	PUNCT
ejpam-3123	267	50	v	v	NOUN
ejpam-3123	267	51	,	,	PUNCT
ejpam-3123	267	52	t	t	PROPN
ejpam-3123	267	53	)	)	PUNCT
ejpam-3123	267	54	∈	∈	PROPN
ejpam-3123	267	55	h	h	NOUN
ejpam-3123	267	56	×g	×g	NOUN
ejpam-3123	267	57	,	,	PUNCT
ejpam-3123	267	58	where	where	SCONJ
ejpam-3123	267	59	u	u	NOUN
ejpam-3123	267	60	,	,	PUNCT
ejpam-3123	267	61	v	v	PROPN
ejpam-3123	267	62	∈	∈	PROPN
ejpam-3123	267	63	h	h	NOUN
ejpam-3123	267	64	and	and	CCONJ
ejpam-3123	267	65	s	s	PROPN
ejpam-3123	267	66	,	,	PUNCT
ejpam-3123	267	67	t	t	PROPN
ejpam-3123	267	68	∈	∈	PROPN
ejpam-3123	267	69	g	g	PROPN
ejpam-3123	267	70	,	,	PUNCT
ejpam-3123	267	71	(	(	PUNCT
ejpam-3123	267	72	5	5	NUM
ejpam-3123	267	73	)	)	PUNCT
ejpam-3123	267	74	where	where	SCONJ
ejpam-3123	267	75	r(u	r(u	PROPN
ejpam-3123	267	76	,	,	PUNCT
ejpam-3123	267	77	s	s	PART
ejpam-3123	267	78	)	)	PUNCT
ejpam-3123	267	79	is	be	AUX
ejpam-3123	267	80	an	an	DET
ejpam-3123	267	81	additive	additive	ADJ
ejpam-3123	267	82	subgroup	subgroup	NOUN
ejpam-3123	267	83	for	for	ADP
ejpam-3123	267	84	each	each	DET
ejpam-3123	267	85	(	(	PUNCT
ejpam-3123	267	86	u	u	NOUN
ejpam-3123	267	87	,	,	PUNCT
ejpam-3123	267	88	s	s	PART
ejpam-3123	267	89	)	)	PUNCT
ejpam-3123	267	90	∈	∈	PROPN
ejpam-3123	267	91	h	h	NOUN
ejpam-3123	267	92	×g	×g	NOUN
ejpam-3123	267	93	.	.	PUNCT
ejpam-3123	268	1	if	if	SCONJ
ejpam-3123	268	2	(	(	PUNCT
ejpam-3123	268	3	5	5	X
ejpam-3123	268	4	)	)	PUNCT
ejpam-3123	268	5	is	be	AUX
ejpam-3123	268	6	replaced	replace	VERB
ejpam-3123	268	7	by	by	ADP
ejpam-3123	268	8	r(u	r(u	PROPN
ejpam-3123	268	9	,	,	PUNCT
ejpam-3123	268	10	s)r(v	s)r(v	PROPN
ejpam-3123	268	11	,	,	PUNCT
ejpam-3123	268	12	t	t	PROPN
ejpam-3123	268	13	)	)	PUNCT
ejpam-3123	268	14	=	=	SYM
ejpam-3123	269	1	r(u	r(u	PROPN
ejpam-3123	269	2	,	,	PUNCT
ejpam-3123	269	3	s)(v	s)(v	PROPN
ejpam-3123	269	4	,	,	PUNCT
ejpam-3123	269	5	t	t	PROPN
ejpam-3123	269	6	)	)	PUNCT
ejpam-3123	269	7	for	for	ADP
ejpam-3123	269	8	all	all	DET
ejpam-3123	269	9	(	(	PUNCT
ejpam-3123	269	10	u	u	NOUN
ejpam-3123	269	11	,	,	PUNCT
ejpam-3123	269	12	s	s	PART
ejpam-3123	269	13	)	)	PUNCT
ejpam-3123	269	14	,	,	PUNCT
ejpam-3123	269	15	(	(	PUNCT
ejpam-3123	269	16	v	v	NOUN
ejpam-3123	269	17	,	,	PUNCT
ejpam-3123	269	18	t	t	PROPN
ejpam-3123	269	19	)	)	PUNCT
ejpam-3123	269	20	∈	∈	PROPN
ejpam-3123	269	21	h	h	NOUN
ejpam-3123	269	22	×g	×g	NOUN
ejpam-3123	269	23	,	,	PUNCT
ejpam-3123	269	24	where	where	SCONJ
ejpam-3123	269	25	u	u	NOUN
ejpam-3123	269	26	,	,	PUNCT
ejpam-3123	269	27	v	v	PROPN
ejpam-3123	269	28	∈	∈	PROPN
ejpam-3123	269	29	h	h	NOUN
ejpam-3123	269	30	and	and	CCONJ
ejpam-3123	269	31	s	s	PROPN
ejpam-3123	269	32	,	,	PUNCT
ejpam-3123	269	33	t	t	PROPN
ejpam-3123	269	34	∈	∈	PROPN
ejpam-3123	269	35	g	g	PROPN
ejpam-3123	269	36	,	,	PUNCT
ejpam-3123	269	37	(	(	PUNCT
ejpam-3123	269	38	6	6	NUM
ejpam-3123	269	39	)	)	PUNCT
ejpam-3123	269	40	then	then	ADV
ejpam-3123	269	41	r	r	NOUN
ejpam-3123	269	42	is	be	AUX
ejpam-3123	269	43	called	call	VERB
ejpam-3123	269	44	a	a	DET
ejpam-3123	269	45	fully	fully	ADV
ejpam-3123	269	46	(	(	PUNCT
ejpam-3123	269	47	or	or	CCONJ
ejpam-3123	269	48	strongly	strongly	ADV
ejpam-3123	269	49	)	)	PUNCT
ejpam-3123	269	50	h	h	NOUN
ejpam-3123	269	51	×g	×g	NOUN
ejpam-3123	269	52	-	-	PUNCT
ejpam-3123	269	53	graded	grade	VERB
ejpam-3123	269	54	ring	ring	NOUN
ejpam-3123	269	55	.	.	PUNCT
ejpam-3123	270	1	n.	n.	PROPN
ejpam-3123	270	2	al	al	PROPN
ejpam-3123	270	3	-	-	PUNCT
ejpam-3123	270	4	subaie	subaie	NOUN
ejpam-3123	270	5	,	,	PUNCT
ejpam-3123	270	6	m.	m.	NOUN
ejpam-3123	270	7	m.	m.	PROPN
ejpam-3123	270	8	al	al	PROPN
ejpam-3123	270	9	-	-	PUNCT
ejpam-3123	270	10	shomrani	shomrani	PROPN
ejpam-3123	270	11	/	/	SYM
ejpam-3123	270	12	eur	eur	NOUN
ejpam-3123	270	13	.	.	PUNCT
ejpam-3123	271	1	j.	j.	PROPN
ejpam-3123	271	2	pure	pure	PROPN
ejpam-3123	271	3	appl	appl	PROPN
ejpam-3123	271	4	.	.	PROPN
ejpam-3123	271	5	math	math	PROPN
ejpam-3123	271	6	,	,	PUNCT
ejpam-3123	271	7	10	10	NUM
ejpam-3123	271	8	(	(	PUNCT
ejpam-3123	271	9	5	5	NUM
ejpam-3123	271	10	)	)	PUNCT
ejpam-3123	271	11	(	(	PUNCT
ejpam-3123	271	12	2017	2017	NUM
ejpam-3123	271	13	)	)	PUNCT
ejpam-3123	271	14	,	,	PUNCT
ejpam-3123	271	15	967	967	NUM
ejpam-3123	271	16	-	-	SYM
ejpam-3123	271	17	980	980	NUM
ejpam-3123	271	18	977	977	NUM
ejpam-3123	271	19	theorem	theorem	NOUN
ejpam-3123	271	20	1	1	X
ejpam-3123	271	21	.	.	PUNCT
ejpam-3123	272	1	let	let	VERB
ejpam-3123	272	2	x	x	PRON
ejpam-3123	272	3	be	be	AUX
ejpam-3123	272	4	a	a	DET
ejpam-3123	272	5	group	group	NOUN
ejpam-3123	272	6	,	,	PUNCT
ejpam-3123	272	7	h	h	PROPN
ejpam-3123	272	8	be	be	VERB
ejpam-3123	272	9	a	a	DET
ejpam-3123	272	10	subgroup	subgroup	NOUN
ejpam-3123	272	11	of	of	ADP
ejpam-3123	272	12	x	x	PROPN
ejpam-3123	272	13	and	and	CCONJ
ejpam-3123	272	14	g	g	PROPN
ejpam-3123	272	15	⊂	⊂	PROPN
ejpam-3123	272	16	x	x	X
ejpam-3123	272	17	be	be	AUX
ejpam-3123	272	18	a	a	DET
ejpam-3123	272	19	set	set	NOUN
ejpam-3123	272	20	of	of	ADP
ejpam-3123	272	21	left	left	ADJ
ejpam-3123	272	22	coset	coset	NOUN
ejpam-3123	272	23	representatives	representative	NOUN
ejpam-3123	272	24	.	.	PUNCT
ejpam-3123	273	1	then	then	ADV
ejpam-3123	273	2	the	the	DET
ejpam-3123	273	3	equality	equality	NOUN
ejpam-3123	273	4	r(u	r(u	PROPN
ejpam-3123	273	5	,	,	PUNCT
ejpam-3123	273	6	s)(v	s)(v	PROPN
ejpam-3123	273	7	,	,	PUNCT
ejpam-3123	273	8	t	t	NOUN
ejpam-3123	273	9	)	)	PUNCT
ejpam-3123	273	10	=	=	SYM
ejpam-3123	274	1	r	r	X
ejpam-3123	274	2	(	(	PUNCT
ejpam-3123	274	3	u(s.v)f((s	u(s.v)f((s	ADJ
ejpam-3123	274	4	/	/	SYM
ejpam-3123	274	5	v),t),(s	v),t),(s	ADJ
ejpam-3123	274	6	/	/	SYM
ejpam-3123	274	7	v)∗t	v)∗t	NOUN
ejpam-3123	274	8	)	)	PUNCT
ejpam-3123	274	9	for	for	ADP
ejpam-3123	274	10	s	s	PROPN
ejpam-3123	274	11	,	,	PUNCT
ejpam-3123	274	12	t	t	PROPN
ejpam-3123	274	13	∈	∈	PROPN
ejpam-3123	274	14	g	g	PROPN
ejpam-3123	274	15	and	and	CCONJ
ejpam-3123	274	16	u	u	NOUN
ejpam-3123	274	17	,	,	PUNCT
ejpam-3123	274	18	v	v	PROPN
ejpam-3123	274	19	∈	∈	PROPN
ejpam-3123	274	20	h	h	NOUN
ejpam-3123	274	21	,	,	PUNCT
ejpam-3123	274	22	makes	make	VERB
ejpam-3123	274	23	r	r	NOUN
ejpam-3123	274	24	into	into	ADP
ejpam-3123	274	25	a	a	DET
ejpam-3123	274	26	h	h	NOUN
ejpam-3123	274	27	×g	×g	NOUN
ejpam-3123	274	28	-	-	PUNCT
ejpam-3123	274	29	graded	grade	VERB
ejpam-3123	274	30	ring	ring	NOUN
ejpam-3123	274	31	where	where	SCONJ
ejpam-3123	274	32	the	the	DET
ejpam-3123	274	33	functions	function	NOUN
ejpam-3123	274	34	.	.	PUNCT
ejpam-3123	275	1	:	:	PUNCT
ejpam-3123	275	2	g	g	PROPN
ejpam-3123	275	3	×	×	PROPN
ejpam-3123	275	4	h	h	NOUN
ejpam-3123	275	5	→	→	SYM
ejpam-3123	275	6	h	h	NOUN
ejpam-3123	275	7	,	,	PUNCT
ejpam-3123	275	8	/	/	SYM
ejpam-3123	275	9	:	:	PUNCT
ejpam-3123	275	10	g×h	g×h	PROPN
ejpam-3123	275	11	→	→	SYM
ejpam-3123	275	12	g	g	PROPN
ejpam-3123	275	13	and	and	CCONJ
ejpam-3123	275	14	f	f	PROPN
ejpam-3123	275	15	:	:	PUNCT
ejpam-3123	275	16	g×g→	g×g→	PROPN
ejpam-3123	275	17	h	h	NOUN
ejpam-3123	275	18	are	be	AUX
ejpam-3123	275	19	supposed	suppose	VERB
ejpam-3123	275	20	to	to	PART
ejpam-3123	275	21	satisfy	satisfy	VERB
ejpam-3123	275	22	the	the	DET
ejpam-3123	275	23	identities	identity	NOUN
ejpam-3123	275	24	in	in	ADP
ejpam-3123	275	25	proposition	proposition	NOUN
ejpam-3123	275	26	1	1	NUM
ejpam-3123	275	27	.	.	PUNCT
ejpam-3123	276	1	proof	proof	NOUN
ejpam-3123	276	2	.	.	PUNCT
ejpam-3123	277	1	the	the	DET
ejpam-3123	277	2	proof	proof	NOUN
ejpam-3123	277	3	of	of	ADP
ejpam-3123	277	4	the	the	DET
ejpam-3123	277	5	theorem	theorem	NOUN
ejpam-3123	277	6	follows	follow	VERB
ejpam-3123	277	7	from	from	ADP
ejpam-3123	277	8	the	the	DET
ejpam-3123	277	9	next	next	ADJ
ejpam-3123	277	10	three	three	NUM
ejpam-3123	277	11	lemmas	lemmas	ADJ
ejpam-3123	277	12	.	.	PUNCT
ejpam-3123	278	1	lemma	lemma	PROPN
ejpam-3123	278	2	1	1	X
ejpam-3123	278	3	.	.	PUNCT
ejpam-3123	279	1	let	let	VERB
ejpam-3123	279	2	x	x	PRON
ejpam-3123	279	3	be	be	AUX
ejpam-3123	279	4	a	a	DET
ejpam-3123	279	5	group	group	NOUN
ejpam-3123	279	6	,	,	PUNCT
ejpam-3123	279	7	h	h	PROPN
ejpam-3123	279	8	be	be	VERB
ejpam-3123	279	9	a	a	DET
ejpam-3123	279	10	subgroup	subgroup	NOUN
ejpam-3123	279	11	of	of	ADP
ejpam-3123	279	12	x	x	PROPN
ejpam-3123	279	13	,	,	PUNCT
ejpam-3123	279	14	g	g	PROPN
ejpam-3123	279	15	⊂	⊂	PROPN
ejpam-3123	279	16	x	x	VERB
ejpam-3123	279	17	be	be	AUX
ejpam-3123	279	18	a	a	DET
ejpam-3123	279	19	set	set	NOUN
ejpam-3123	279	20	of	of	ADP
ejpam-3123	279	21	left	left	ADJ
ejpam-3123	279	22	coset	coset	NOUN
ejpam-3123	279	23	representatives	representative	NOUN
ejpam-3123	279	24	and	and	CCONJ
ejpam-3123	279	25	r(u	r(u	PROPN
ejpam-3123	279	26	,	,	PUNCT
ejpam-3123	279	27	s)(v	s)(v	PROPN
ejpam-3123	279	28	,	,	PUNCT
ejpam-3123	279	29	t	t	NOUN
ejpam-3123	279	30	)	)	PUNCT
ejpam-3123	279	31	=	=	SYM
ejpam-3123	280	1	r	r	X
ejpam-3123	280	2	(	(	PUNCT
ejpam-3123	280	3	u(s.v)f((s	u(s.v)f((s	ADJ
ejpam-3123	280	4	/	/	SYM
ejpam-3123	280	5	v),t),(s	v),t),(s	ADJ
ejpam-3123	280	6	/	/	SYM
ejpam-3123	280	7	v)∗t	v)∗t	NOUN
ejpam-3123	280	8	)	)	PUNCT
ejpam-3123	280	9	.	.	PUNCT
ejpam-3123	281	1	then	then	ADV
ejpam-3123	281	2	the	the	DET
ejpam-3123	281	3	equality	equality	NOUN
ejpam-3123	281	4	r	r	NOUN
ejpam-3123	281	5	(	(	PUNCT
ejpam-3123	281	6	u	u	NOUN
ejpam-3123	281	7	,	,	PUNCT
ejpam-3123	281	8	s	s	PART
ejpam-3123	281	9	)	)	PUNCT
ejpam-3123	281	10	(	(	PUNCT
ejpam-3123	281	11	(	(	PUNCT
ejpam-3123	281	12	v	v	NOUN
ejpam-3123	281	13	,	,	PUNCT
ejpam-3123	281	14	t)(w	t)(w	NOUN
ejpam-3123	281	15	,	,	PUNCT
ejpam-3123	281	16	p	p	NOUN
ejpam-3123	281	17	)	)	PUNCT
ejpam-3123	281	18	)	)	PUNCT
ejpam-3123	282	1	=	=	SYM
ejpam-3123	282	2	r	r	X
ejpam-3123	282	3	(	(	PUNCT
ejpam-3123	282	4	(	(	PUNCT
ejpam-3123	282	5	u	u	NOUN
ejpam-3123	282	6	,	,	PUNCT
ejpam-3123	282	7	s)(v	s)(v	PROPN
ejpam-3123	282	8	,	,	PUNCT
ejpam-3123	282	9	t	t	PROPN
ejpam-3123	282	10	)	)	PUNCT
ejpam-3123	282	11	)	)	PUNCT
ejpam-3123	283	1	(	(	PUNCT
ejpam-3123	283	2	w	w	X
ejpam-3123	283	3	,	,	PUNCT
ejpam-3123	283	4	p	p	NOUN
ejpam-3123	283	5	)	)	PUNCT
ejpam-3123	283	6	is	be	AUX
ejpam-3123	283	7	satisfied	satisfied	ADJ
ejpam-3123	283	8	for	for	ADP
ejpam-3123	283	9	all	all	DET
ejpam-3123	283	10	(	(	PUNCT
ejpam-3123	283	11	u	u	NOUN
ejpam-3123	283	12	,	,	PUNCT
ejpam-3123	283	13	s	s	PART
ejpam-3123	283	14	)	)	PUNCT
ejpam-3123	283	15	,	,	PUNCT
ejpam-3123	283	16	(	(	PUNCT
ejpam-3123	283	17	v	v	NOUN
ejpam-3123	283	18	,	,	PUNCT
ejpam-3123	283	19	t	t	PROPN
ejpam-3123	283	20	)	)	PUNCT
ejpam-3123	283	21	and	and	CCONJ
ejpam-3123	283	22	(	(	PUNCT
ejpam-3123	283	23	w	w	PROPN
ejpam-3123	283	24	,	,	PUNCT
ejpam-3123	283	25	p	p	NOUN
ejpam-3123	283	26	)	)	PUNCT
ejpam-3123	283	27	in	in	ADP
ejpam-3123	283	28	h	h	NUM
ejpam-3123	283	29	×	×	NOUN
ejpam-3123	283	30	g	g	NOUN
ejpam-3123	283	31	where	where	SCONJ
ejpam-3123	283	32	the	the	DET
ejpam-3123	283	33	functions	function	NOUN
ejpam-3123	283	34	.	.	PUNCT
ejpam-3123	284	1	:	:	PUNCT
ejpam-3123	284	2	g×h	g×h	VERB
ejpam-3123	284	3	→	→	SYM
ejpam-3123	284	4	h	h	NOUN
ejpam-3123	284	5	,	,	PUNCT
ejpam-3123	284	6	/	/	SYM
ejpam-3123	284	7	:	:	PUNCT
ejpam-3123	284	8	g×h	g×h	PROPN
ejpam-3123	284	9	→	→	SYM
ejpam-3123	284	10	g	g	PROPN
ejpam-3123	284	11	and	and	CCONJ
ejpam-3123	284	12	f	f	PROPN
ejpam-3123	284	13	:	:	PUNCT
ejpam-3123	284	14	g×g→	g×g→	PROPN
ejpam-3123	284	15	h	h	NOUN
ejpam-3123	284	16	are	be	AUX
ejpam-3123	284	17	supposed	suppose	VERB
ejpam-3123	284	18	to	to	PART
ejpam-3123	284	19	satisfy	satisfy	VERB
ejpam-3123	284	20	the	the	DET
ejpam-3123	284	21	identities	identity	NOUN
ejpam-3123	284	22	in	in	ADP
ejpam-3123	284	23	proposition	proposition	NOUN
ejpam-3123	284	24	1	1	NUM
ejpam-3123	284	25	.	.	PUNCT
ejpam-3123	285	1	proof	proof	NOUN
ejpam-3123	285	2	.	.	PUNCT
ejpam-3123	286	1	for	for	ADP
ejpam-3123	286	2	s	s	PROPN
ejpam-3123	286	3	,	,	PUNCT
ejpam-3123	286	4	t	t	PROPN
ejpam-3123	286	5	,	,	PUNCT
ejpam-3123	286	6	p	p	PROPN
ejpam-3123	286	7	∈	∈	PROPN
ejpam-3123	286	8	g	g	NOUN
ejpam-3123	286	9	and	and	CCONJ
ejpam-3123	286	10	u	u	NOUN
ejpam-3123	286	11	,	,	PUNCT
ejpam-3123	286	12	v	v	NOUN
ejpam-3123	286	13	,	,	PUNCT
ejpam-3123	286	14	w	w	PROPN
ejpam-3123	286	15	∈	∈	PROPN
ejpam-3123	286	16	h	h	NOUN
ejpam-3123	286	17	,	,	PUNCT
ejpam-3123	286	18	we	we	PRON
ejpam-3123	286	19	start	start	VERB
ejpam-3123	286	20	with	with	ADP
ejpam-3123	286	21	the	the	DET
ejpam-3123	286	22	left	left	ADJ
ejpam-3123	286	23	hand	hand	NOUN
ejpam-3123	286	24	side	side	NOUN
ejpam-3123	286	25	as	as	SCONJ
ejpam-3123	286	26	follows	follow	VERB
ejpam-3123	286	27	:	:	PUNCT
ejpam-3123	286	28	r	r	NOUN
ejpam-3123	286	29	(	(	PUNCT
ejpam-3123	286	30	u	u	NOUN
ejpam-3123	286	31	,	,	PUNCT
ejpam-3123	286	32	s	s	PART
ejpam-3123	286	33	)	)	PUNCT
ejpam-3123	286	34	(	(	PUNCT
ejpam-3123	286	35	(	(	PUNCT
ejpam-3123	286	36	v	v	NOUN
ejpam-3123	286	37	,	,	PUNCT
ejpam-3123	286	38	t)(w	t)(w	NOUN
ejpam-3123	286	39	,	,	PUNCT
ejpam-3123	286	40	p	p	NOUN
ejpam-3123	286	41	)	)	PUNCT
ejpam-3123	286	42	)	)	PUNCT
ejpam-3123	287	1	=	=	SYM
ejpam-3123	287	2	r	r	NOUN
ejpam-3123	287	3	(	(	PUNCT
ejpam-3123	287	4	u	u	NOUN
ejpam-3123	287	5	,	,	PUNCT
ejpam-3123	287	6	s	s	PART
ejpam-3123	287	7	)	)	PUNCT
ejpam-3123	287	8	(	(	PUNCT
ejpam-3123	287	9	v(t.w)f	v(t.w)f	X
ejpam-3123	287	10	(	(	PUNCT
ejpam-3123	287	11	(	(	PUNCT
ejpam-3123	287	12	t	t	NOUN
ejpam-3123	287	13	/	/	SYM
ejpam-3123	287	14	w),p	w),p	PROPN
ejpam-3123	287	15	)	)	PUNCT
ejpam-3123	287	16	,	,	PUNCT
ejpam-3123	287	17	(	(	PUNCT
ejpam-3123	287	18	t	t	NOUN
ejpam-3123	287	19	/	/	SYM
ejpam-3123	287	20	w)∗p	w)∗p	NOUN
ejpam-3123	287	21	)	)	PUNCT
ejpam-3123	288	1	=	=	SYM
ejpam-3123	288	2	r	r	X
ejpam-3123	288	3	(	(	PUNCT
ejpam-3123	288	4	(	(	PUNCT
ejpam-3123	288	5	u	u	X
ejpam-3123	288	6	(	(	PUNCT
ejpam-3123	288	7	s.(v(t.w)f((t	s.(v(t.w)f((t	NOUN
ejpam-3123	288	8	/	/	SYM
ejpam-3123	288	9	w),p	w),p	NOUN
ejpam-3123	288	10	)	)	PUNCT
ejpam-3123	288	11	)	)	PUNCT
ejpam-3123	288	12	)	)	PUNCT
ejpam-3123	289	1	f	f	PROPN
ejpam-3123	289	2	(	(	PUNCT
ejpam-3123	289	3	s/(v(t.w)f((t	s/(v(t.w)f((t	NOUN
ejpam-3123	289	4	/	/	SYM
ejpam-3123	289	5	w),p)),(t	w),p)),(t	PROPN
ejpam-3123	289	6	/	/	SYM
ejpam-3123	289	7	w)∗p	w)∗p	NOUN
ejpam-3123	289	8	)	)	PUNCT
ejpam-3123	289	9	)	)	PUNCT
ejpam-3123	289	10	,	,	PUNCT
ejpam-3123	289	11	(	(	PUNCT
ejpam-3123	289	12	(	(	PUNCT
ejpam-3123	289	13	s/(v(t.w)f((t	s/(v(t.w)f((t	X
ejpam-3123	289	14	/	/	SYM
ejpam-3123	289	15	w),p)))∗((t	w),p)))∗((t	NOUN
ejpam-3123	289	16	/	/	SYM
ejpam-3123	289	17	w)∗p	w)∗p	NOUN
ejpam-3123	289	18	)	)	PUNCT
ejpam-3123	289	19	)	)	PUNCT
ejpam-3123	289	20	)	)	PUNCT
ejpam-3123	289	21	.	.	PUNCT
ejpam-3123	290	1	(	(	PUNCT
ejpam-3123	290	2	7	7	X
ejpam-3123	290	3	)	)	PUNCT
ejpam-3123	290	4	now	now	ADV
ejpam-3123	290	5	,	,	PUNCT
ejpam-3123	290	6	we	we	PRON
ejpam-3123	290	7	simplify	simplify	VERB
ejpam-3123	290	8	(	(	PUNCT
ejpam-3123	290	9	7	7	X
ejpam-3123	290	10	)	)	PUNCT
ejpam-3123	290	11	using	use	VERB
ejpam-3123	290	12	the	the	DET
ejpam-3123	290	13	proposition	proposition	NOUN
ejpam-3123	290	14	in	in	ADP
ejpam-3123	290	15	1	1	NUM
ejpam-3123	290	16	as	as	SCONJ
ejpam-3123	290	17	follows	follow	VERB
ejpam-3123	290	18	:	:	PUNCT
ejpam-3123	290	19	u	u	NOUN
ejpam-3123	290	20	(	(	PUNCT
ejpam-3123	290	21	s	s	X
ejpam-3123	290	22	.	.	PUNCT
ejpam-3123	291	1	(	(	PUNCT
ejpam-3123	291	2	v(t	v(t	NOUN
ejpam-3123	291	3	.	.	PUNCT
ejpam-3123	291	4	w)f	w)f	PUNCT
ejpam-3123	292	1	(	(	PUNCT
ejpam-3123	292	2	(	(	PUNCT
ejpam-3123	292	3	t	t	PROPN
ejpam-3123	292	4	/	/	SYM
ejpam-3123	292	5	w	w	PROPN
ejpam-3123	292	6	)	)	PUNCT
ejpam-3123	292	7	,	,	PUNCT
ejpam-3123	292	8	p	p	NOUN
ejpam-3123	292	9	)	)	PUNCT
ejpam-3123	292	10	)	)	PUNCT
ejpam-3123	292	11	)	)	PUNCT
ejpam-3123	293	1	f	f	PROPN
ejpam-3123	293	2	(	(	PUNCT
ejpam-3123	293	3	s	s	AUX
ejpam-3123	293	4	/	/	PUNCT
ejpam-3123	293	5	(	(	PUNCT
ejpam-3123	293	6	v(t	v(t	X
ejpam-3123	293	7	.	.	PUNCT
ejpam-3123	293	8	w)f	w)f	PUNCT
ejpam-3123	293	9	(	(	PUNCT
ejpam-3123	293	10	(	(	PUNCT
ejpam-3123	293	11	t	t	PROPN
ejpam-3123	293	12	/	/	SYM
ejpam-3123	293	13	w	w	PROPN
ejpam-3123	293	14	)	)	PUNCT
ejpam-3123	293	15	,	,	PUNCT
ejpam-3123	293	16	p	p	NOUN
ejpam-3123	293	17	)	)	PUNCT
ejpam-3123	293	18	)	)	PUNCT
ejpam-3123	293	19	,	,	PUNCT
ejpam-3123	293	20	(	(	PUNCT
ejpam-3123	293	21	t	t	PROPN
ejpam-3123	293	22	/	/	SYM
ejpam-3123	293	23	w	w	PROPN
ejpam-3123	293	24	)	)	PUNCT
ejpam-3123	293	25	∗	∗	NOUN
ejpam-3123	293	26	p	p	NOUN
ejpam-3123	293	27	)	)	PUNCT
ejpam-3123	294	1	=	=	SYM
ejpam-3123	294	2	u	u	NOUN
ejpam-3123	294	3	(	(	PUNCT
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ejpam-3123	298	17	∗	∗	NOUN
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ejpam-3123	304	18	∗	∗	NOUN
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ejpam-3123	305	5	)	)	PUNCT
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ejpam-3123	335	8	∗	∗	NOUN
ejpam-3123	335	9	p	p	NOUN
ejpam-3123	335	10	)	)	PUNCT
ejpam-3123	335	11	=	=	PUNCT
ejpam-3123	335	12	(	(	PUNCT
ejpam-3123	335	13	(	(	PUNCT
ejpam-3123	335	14	s	s	AUX
ejpam-3123	335	15	/	/	SYM
ejpam-3123	335	16	(	(	PUNCT
ejpam-3123	335	17	v(t	v(t	X
ejpam-3123	335	18	.	.	PUNCT
ejpam-3123	336	1	w	w	NOUN
ejpam-3123	336	2	)	)	PUNCT
ejpam-3123	336	3	)	)	PUNCT
ejpam-3123	336	4	)	)	PUNCT
ejpam-3123	337	1	/	/	SYM
ejpam-3123	337	2	f	f	NOUN
ejpam-3123	337	3	(	(	PUNCT
ejpam-3123	337	4	(	(	PUNCT
ejpam-3123	337	5	t	t	PROPN
ejpam-3123	337	6	/	/	SYM
ejpam-3123	337	7	w	w	PROPN
ejpam-3123	337	8	)	)	PUNCT
ejpam-3123	337	9	,	,	PUNCT
ejpam-3123	337	10	p	p	NOUN
ejpam-3123	337	11	)	)	PUNCT
ejpam-3123	337	12	)	)	PUNCT
ejpam-3123	337	13	∗	∗	NOUN
ejpam-3123	337	14	(	(	PUNCT
ejpam-3123	337	15	(	(	PUNCT
ejpam-3123	337	16	t	t	PROPN
ejpam-3123	337	17	/	/	SYM
ejpam-3123	337	18	w	w	PROPN
ejpam-3123	337	19	)	)	PUNCT
ejpam-3123	337	20	∗	∗	NOUN
ejpam-3123	337	21	p	p	NOUN
ejpam-3123	337	22	)	)	PUNCT
ejpam-3123	337	23	=	=	PUNCT
ejpam-3123	337	24	(	(	PUNCT
ejpam-3123	337	25	(	(	PUNCT
ejpam-3123	337	26	s	s	AUX
ejpam-3123	337	27	/	/	SYM
ejpam-3123	337	28	(	(	PUNCT
ejpam-3123	337	29	v(t	v(t	X
ejpam-3123	337	30	.	.	PUNCT
ejpam-3123	337	31	w	w	NOUN
ejpam-3123	337	32	)	)	PUNCT
ejpam-3123	337	33	)	)	PUNCT
ejpam-3123	337	34	)	)	PUNCT
ejpam-3123	338	1	∗	∗	NOUN
ejpam-3123	338	2	(	(	PUNCT
ejpam-3123	338	3	t	t	PROPN
ejpam-3123	338	4	/	/	SYM
ejpam-3123	338	5	w	w	PROPN
ejpam-3123	338	6	)	)	PUNCT
ejpam-3123	338	7	)	)	PUNCT
ejpam-3123	339	1	∗	∗	NOUN
ejpam-3123	339	2	p	p	NOUN
ejpam-3123	339	3	=	=	X
ejpam-3123	339	4	(	(	PUNCT
ejpam-3123	339	5	(	(	PUNCT
ejpam-3123	339	6	(	(	PUNCT
ejpam-3123	339	7	s	s	NOUN
ejpam-3123	339	8	/	/	SYM
ejpam-3123	339	9	v	v	NOUN
ejpam-3123	339	10	)	)	PUNCT
ejpam-3123	339	11	/	/	PUNCT
ejpam-3123	340	1	(	(	PUNCT
ejpam-3123	340	2	t	t	PROPN
ejpam-3123	340	3	.	.	PUNCT
ejpam-3123	341	1	w	w	X
ejpam-3123	341	2	)	)	PUNCT
ejpam-3123	341	3	)	)	PUNCT
ejpam-3123	342	1	∗	∗	NOUN
ejpam-3123	342	2	(	(	PUNCT
ejpam-3123	342	3	t	t	PROPN
ejpam-3123	342	4	/	/	SYM
ejpam-3123	342	5	w	w	PROPN
ejpam-3123	342	6	)	)	PUNCT
ejpam-3123	342	7	)	)	PUNCT
ejpam-3123	343	1	∗	∗	NOUN
ejpam-3123	343	2	p	p	NOUN
ejpam-3123	343	3	=	=	X
ejpam-3123	343	4	(	(	PUNCT
ejpam-3123	343	5	(	(	PUNCT
ejpam-3123	343	6	(	(	PUNCT
ejpam-3123	343	7	s	s	NOUN
ejpam-3123	343	8	/	/	SYM
ejpam-3123	343	9	v	v	NOUN
ejpam-3123	343	10	)	)	PUNCT
ejpam-3123	343	11	∗	∗	NOUN
ejpam-3123	343	12	t	t	NOUN
ejpam-3123	343	13	)	)	PUNCT
ejpam-3123	343	14	/	/	SYM
ejpam-3123	344	1	w	w	NOUN
ejpam-3123	344	2	)	)	PUNCT
ejpam-3123	344	3	∗	∗	NOUN
ejpam-3123	344	4	p.	p.	NOUN
ejpam-3123	344	5	hence	hence	ADV
ejpam-3123	344	6	,	,	PUNCT
ejpam-3123	344	7	equation	equation	NOUN
ejpam-3123	344	8	(	(	PUNCT
ejpam-3123	344	9	7	7	X
ejpam-3123	344	10	)	)	PUNCT
ejpam-3123	344	11	can	can	AUX
ejpam-3123	344	12	be	be	AUX
ejpam-3123	344	13	rewritten	rewrite	VERB
ejpam-3123	344	14	as	as	ADP
ejpam-3123	344	15	r	r	NOUN
ejpam-3123	344	16	(	(	PUNCT
ejpam-3123	344	17	u	u	NOUN
ejpam-3123	344	18	,	,	PUNCT
ejpam-3123	344	19	s	s	PART
ejpam-3123	344	20	)	)	PUNCT
ejpam-3123	344	21	(	(	PUNCT
ejpam-3123	344	22	(	(	PUNCT
ejpam-3123	344	23	v	v	NOUN
ejpam-3123	344	24	,	,	PUNCT
ejpam-3123	344	25	t)(w	t)(w	NOUN
ejpam-3123	344	26	,	,	PUNCT
ejpam-3123	344	27	p	p	NOUN
ejpam-3123	344	28	)	)	PUNCT
ejpam-3123	344	29	)	)	PUNCT
ejpam-3123	345	1	=	=	SYM
ejpam-3123	345	2	r	r	NOUN
ejpam-3123	345	3	(	(	PUNCT
ejpam-3123	345	4	u	u	NOUN
ejpam-3123	345	5	,	,	PUNCT
ejpam-3123	345	6	s	s	PART
ejpam-3123	345	7	)	)	PUNCT
ejpam-3123	345	8	(	(	PUNCT
ejpam-3123	345	9	v(t.w)f	v(t.w)f	X
ejpam-3123	345	10	(	(	PUNCT
ejpam-3123	345	11	(	(	PUNCT
ejpam-3123	345	12	t	t	NOUN
ejpam-3123	345	13	/	/	SYM
ejpam-3123	345	14	w),p	w),p	PROPN
ejpam-3123	345	15	)	)	PUNCT
ejpam-3123	345	16	,	,	PUNCT
ejpam-3123	345	17	(	(	PUNCT
ejpam-3123	345	18	t	t	NOUN
ejpam-3123	345	19	/	/	SYM
ejpam-3123	345	20	w)∗p	w)∗p	NOUN
ejpam-3123	345	21	)	)	PUNCT
ejpam-3123	346	1	=	=	SYM
ejpam-3123	346	2	r	r	X
ejpam-3123	346	3	(	(	PUNCT
ejpam-3123	346	4	(	(	PUNCT
ejpam-3123	346	5	u(s.v)f((s	u(s.v)f((s	ADJ
ejpam-3123	346	6	/	/	SYM
ejpam-3123	346	7	v),t	v),t	NUM
ejpam-3123	346	8	)	)	PUNCT
ejpam-3123	346	9	)	)	PUNCT
ejpam-3123	346	10	(	(	PUNCT
ejpam-3123	346	11	(	(	PUNCT
ejpam-3123	346	12	(	(	PUNCT
ejpam-3123	346	13	s	s	X
ejpam-3123	346	14	/	/	SYM
ejpam-3123	346	15	v)∗t).w	v)∗t).w	ADJ
ejpam-3123	346	16	)	)	PUNCT
ejpam-3123	347	1	f	f	PROPN
ejpam-3123	347	2	(	(	PUNCT
ejpam-3123	347	3	(	(	PUNCT
ejpam-3123	347	4	(	(	PUNCT
ejpam-3123	347	5	s	s	X
ejpam-3123	347	6	/	/	SYM
ejpam-3123	347	7	v)∗t)/w	v)∗t)/w	PROPN
ejpam-3123	347	8	,	,	PUNCT
ejpam-3123	347	9	p	p	NOUN
ejpam-3123	347	10	)	)	PUNCT
ejpam-3123	347	11	,	,	PUNCT
ejpam-3123	347	12	(	(	PUNCT
ejpam-3123	347	13	(	(	PUNCT
ejpam-3123	347	14	(	(	PUNCT
ejpam-3123	347	15	s	s	NOUN
ejpam-3123	347	16	/	/	SYM
ejpam-3123	347	17	v)∗t)/w	v)∗t)/w	NOUN
ejpam-3123	347	18	)	)	PUNCT
ejpam-3123	347	19	∗p	∗p	PROPN
ejpam-3123	347	20	)	)	PUNCT
ejpam-3123	347	21	.	.	PUNCT
ejpam-3123	348	1	(	(	PUNCT
ejpam-3123	348	2	8)	8)	NUM
ejpam-3123	348	3	n.	n.	PROPN
ejpam-3123	348	4	al	al	PROPN
ejpam-3123	348	5	-	-	PUNCT
ejpam-3123	348	6	subaie	subaie	NOUN
ejpam-3123	348	7	,	,	PUNCT
ejpam-3123	348	8	m.	m.	NOUN
ejpam-3123	348	9	m.	m.	PROPN
ejpam-3123	348	10	al	al	PROPN
ejpam-3123	348	11	-	-	PUNCT
ejpam-3123	348	12	shomrani	shomrani	PROPN
ejpam-3123	348	13	/	/	SYM
ejpam-3123	348	14	eur	eur	NOUN
ejpam-3123	348	15	.	.	PUNCT
ejpam-3123	349	1	j.	j.	PROPN
ejpam-3123	349	2	pure	pure	PROPN
ejpam-3123	349	3	appl	appl	PROPN
ejpam-3123	349	4	.	.	PROPN
ejpam-3123	349	5	math	math	PROPN
ejpam-3123	349	6	,	,	PUNCT
ejpam-3123	349	7	10	10	NUM
ejpam-3123	349	8	(	(	PUNCT
ejpam-3123	349	9	5	5	NUM
ejpam-3123	349	10	)	)	PUNCT
ejpam-3123	349	11	(	(	PUNCT
ejpam-3123	349	12	2017	2017	NUM
ejpam-3123	349	13	)	)	PUNCT
ejpam-3123	349	14	,	,	PUNCT
ejpam-3123	349	15	967	967	NUM
ejpam-3123	349	16	-	-	SYM
ejpam-3123	349	17	980	980	NUM
ejpam-3123	349	18	978	978	NUM
ejpam-3123	349	19	on	on	ADP
ejpam-3123	349	20	the	the	DET
ejpam-3123	349	21	other	other	ADJ
ejpam-3123	349	22	hand	hand	NOUN
ejpam-3123	349	23	,	,	PUNCT
ejpam-3123	349	24	r	r	X
ejpam-3123	349	25	(	(	PUNCT
ejpam-3123	349	26	(	(	PUNCT
ejpam-3123	349	27	u	u	NOUN
ejpam-3123	349	28	,	,	PUNCT
ejpam-3123	349	29	s)(v	s)(v	PROPN
ejpam-3123	349	30	,	,	PUNCT
ejpam-3123	349	31	t	t	PROPN
ejpam-3123	349	32	)	)	PUNCT
ejpam-3123	349	33	)	)	PUNCT
ejpam-3123	350	1	(	(	PUNCT
ejpam-3123	350	2	w	w	X
ejpam-3123	350	3	,	,	PUNCT
ejpam-3123	350	4	p	p	NOUN
ejpam-3123	350	5	)	)	PUNCT
ejpam-3123	350	6	=	=	SYM
ejpam-3123	351	1	r	r	NOUN
ejpam-3123	351	2	(	(	PUNCT
ejpam-3123	351	3	u(s.v)f((s	u(s.v)f((s	ADJ
ejpam-3123	351	4	/	/	SYM
ejpam-3123	351	5	v),t),(s	v),t),(s	ADJ
ejpam-3123	351	6	/	/	SYM
ejpam-3123	351	7	v)∗t	v)∗t	NOUN
ejpam-3123	351	8	)	)	PUNCT
ejpam-3123	351	9	(	(	PUNCT
ejpam-3123	351	10	w	w	X
ejpam-3123	351	11	,	,	PUNCT
ejpam-3123	351	12	p	p	NOUN
ejpam-3123	351	13	)	)	PUNCT
ejpam-3123	351	14	=	=	SYM
ejpam-3123	352	1	r	r	X
ejpam-3123	352	2	(	(	PUNCT
ejpam-3123	352	3	(	(	PUNCT
ejpam-3123	352	4	u(s.v)f((s	u(s.v)f((s	ADJ
ejpam-3123	352	5	/	/	SYM
ejpam-3123	352	6	v),t	v),t	NUM
ejpam-3123	352	7	)	)	PUNCT
ejpam-3123	352	8	)	)	PUNCT
ejpam-3123	352	9	(	(	PUNCT
ejpam-3123	352	10	(	(	PUNCT
ejpam-3123	352	11	(	(	PUNCT
ejpam-3123	352	12	s	s	X
ejpam-3123	352	13	/	/	SYM
ejpam-3123	352	14	v)∗t).w	v)∗t).w	ADJ
ejpam-3123	352	15	)	)	PUNCT
ejpam-3123	353	1	f	f	PROPN
ejpam-3123	354	1	(	(	PUNCT
ejpam-3123	354	2	(	(	PUNCT
ejpam-3123	354	3	(	(	PUNCT
ejpam-3123	354	4	s	s	X
ejpam-3123	354	5	/	/	SYM
ejpam-3123	354	6	v)∗t)/w	v)∗t)/w	PROPN
ejpam-3123	354	7	,	,	PUNCT
ejpam-3123	354	8	p	p	NOUN
ejpam-3123	354	9	)	)	PUNCT
ejpam-3123	354	10	,	,	PUNCT
ejpam-3123	354	11	(	(	PUNCT
ejpam-3123	354	12	(	(	PUNCT
ejpam-3123	354	13	(	(	PUNCT
ejpam-3123	354	14	s	s	NOUN
ejpam-3123	354	15	/	/	SYM
ejpam-3123	354	16	v)∗t)/w	v)∗t)/w	NOUN
ejpam-3123	354	17	)	)	PUNCT
ejpam-3123	354	18	∗p	∗p	PROPN
ejpam-3123	354	19	)	)	PUNCT
ejpam-3123	354	20	.	.	PUNCT
ejpam-3123	355	1	(	(	PUNCT
ejpam-3123	355	2	9	9	NUM
ejpam-3123	355	3	)	)	PUNCT
ejpam-3123	355	4	thus	thus	ADV
ejpam-3123	355	5	,	,	PUNCT
ejpam-3123	355	6	equations	equation	NOUN
ejpam-3123	355	7	(	(	PUNCT
ejpam-3123	355	8	8)	8)	NUM
ejpam-3123	355	9	and	and	CCONJ
ejpam-3123	355	10	(	(	PUNCT
ejpam-3123	355	11	9	9	X
ejpam-3123	355	12	)	)	PUNCT
ejpam-3123	355	13	show	show	VERB
ejpam-3123	355	14	that	that	SCONJ
ejpam-3123	355	15	the	the	DET
ejpam-3123	355	16	equality	equality	NOUN
ejpam-3123	355	17	is	be	AUX
ejpam-3123	355	18	satisfied	satisfied	ADJ
ejpam-3123	355	19	.	.	PUNCT
ejpam-3123	356	1	lemma	lemma	PROPN
ejpam-3123	356	2	2	2	X
ejpam-3123	356	3	.	.	PUNCT
ejpam-3123	357	1	let	let	VERB
ejpam-3123	357	2	x	x	PRON
ejpam-3123	357	3	be	be	AUX
ejpam-3123	357	4	a	a	DET
ejpam-3123	357	5	group	group	NOUN
ejpam-3123	357	6	,	,	PUNCT
ejpam-3123	357	7	h	h	PROPN
ejpam-3123	357	8	be	be	VERB
ejpam-3123	357	9	a	a	DET
ejpam-3123	357	10	subgroup	subgroup	NOUN
ejpam-3123	357	11	of	of	ADP
ejpam-3123	357	12	x	x	PROPN
ejpam-3123	357	13	,	,	PUNCT
ejpam-3123	357	14	g	g	PROPN
ejpam-3123	357	15	⊂	⊂	PROPN
ejpam-3123	357	16	x	x	VERB
ejpam-3123	357	17	be	be	AUX
ejpam-3123	357	18	a	a	DET
ejpam-3123	357	19	set	set	NOUN
ejpam-3123	357	20	of	of	ADP
ejpam-3123	357	21	left	left	ADJ
ejpam-3123	357	22	coset	coset	NOUN
ejpam-3123	357	23	representatives	representative	NOUN
ejpam-3123	357	24	and	and	CCONJ
ejpam-3123	357	25	r(u	r(u	PROPN
ejpam-3123	357	26	,	,	PUNCT
ejpam-3123	357	27	s)(v	s)(v	PROPN
ejpam-3123	357	28	,	,	PUNCT
ejpam-3123	357	29	t	t	NOUN
ejpam-3123	357	30	)	)	PUNCT
ejpam-3123	357	31	=	=	SYM
ejpam-3123	358	1	r	r	X
ejpam-3123	358	2	(	(	PUNCT
ejpam-3123	358	3	u(s.v)f((s	u(s.v)f((s	ADJ
ejpam-3123	358	4	/	/	SYM
ejpam-3123	358	5	v),t),(s	v),t),(s	ADJ
ejpam-3123	358	6	/	/	SYM
ejpam-3123	358	7	v)∗t	v)∗t	NOUN
ejpam-3123	358	8	)	)	PUNCT
ejpam-3123	358	9	for	for	ADP
ejpam-3123	358	10	all	all	DET
ejpam-3123	358	11	(	(	PUNCT
ejpam-3123	358	12	u	u	NOUN
ejpam-3123	358	13	,	,	PUNCT
ejpam-3123	358	14	s	s	PART
ejpam-3123	358	15	)	)	PUNCT
ejpam-3123	358	16	and	and	CCONJ
ejpam-3123	358	17	(	(	PUNCT
ejpam-3123	358	18	v	v	NOUN
ejpam-3123	358	19	,	,	PUNCT
ejpam-3123	358	20	t	t	PROPN
ejpam-3123	358	21	)	)	PUNCT
ejpam-3123	358	22	in	in	ADP
ejpam-3123	358	23	h	h	NOUN
ejpam-3123	358	24	×g	×g	NOUN
ejpam-3123	358	25	.	.	PUNCT
ejpam-3123	358	26	suppose	suppose	VERB
ejpam-3123	358	27	that	that	SCONJ
ejpam-3123	358	28	there	there	PRON
ejpam-3123	358	29	is	be	VERB
ejpam-3123	358	30	an	an	DET
ejpam-3123	358	31	element	element	NOUN
ejpam-3123	358	32	eh	eh	INTJ
ejpam-3123	358	33	∈	∈	PROPN
ejpam-3123	358	34	h	h	NOUN
ejpam-3123	358	35	such	such	ADJ
ejpam-3123	358	36	that	that	PRON
ejpam-3123	358	37	for	for	ADP
ejpam-3123	358	38	all	all	PRON
ejpam-3123	358	39	s	s	PART
ejpam-3123	358	40	∈	∈	PROPN
ejpam-3123	358	41	g	g	NOUN
ejpam-3123	358	42	and	and	CCONJ
ejpam-3123	358	43	u	u	PROPN
ejpam-3123	358	44	∈	∈	PROPN
ejpam-3123	358	45	h	h	NOUN
ejpam-3123	358	46	,	,	PUNCT
ejpam-3123	358	47	we	we	PRON
ejpam-3123	358	48	have	have	VERB
ejpam-3123	358	49	eg	eg	NOUN
ejpam-3123	358	50	/	/	SYM
ejpam-3123	358	51	u	u	NOUN
ejpam-3123	358	52	=	=	NOUN
ejpam-3123	358	53	eg	eg	NOUN
ejpam-3123	358	54	,	,	PUNCT
ejpam-3123	358	55	eg	eg	NOUN
ejpam-3123	358	56	.	.	PUNCT
ejpam-3123	359	1	u	u	NOUN
ejpam-3123	359	2	=	=	SYM
ejpam-3123	359	3	ehue	ehue	PROPN
ejpam-3123	359	4	−1	−1	NOUN
ejpam-3123	359	5	h	h	NOUN
ejpam-3123	359	6	,	,	PUNCT
ejpam-3123	359	7	s	s	PART
ejpam-3123	359	8	.	.	PUNCT
ejpam-3123	360	1	e	e	X
ejpam-3123	360	2	=	=	SYM
ejpam-3123	360	3	e	e	X
ejpam-3123	360	4	,	,	PUNCT
ejpam-3123	360	5	s	s	PART
ejpam-3123	360	6	/	/	SYM
ejpam-3123	360	7	e	e	X
ejpam-3123	360	8	=	=	SYM
ejpam-3123	360	9	s	s	PART
ejpam-3123	360	10	,	,	PUNCT
ejpam-3123	360	11	f(eg	f(eg	NUM
ejpam-3123	360	12	,	,	PUNCT
ejpam-3123	360	13	s	s	X
ejpam-3123	360	14	)	)	PUNCT
ejpam-3123	360	15	=	=	SYM
ejpam-3123	360	16	eh	eh	INTJ
ejpam-3123	360	17	,	,	PUNCT
ejpam-3123	360	18	s	s	PART
ejpam-3123	360	19	.	.	PUNCT
ejpam-3123	361	1	e−1h	e−1h	NOUN
ejpam-3123	361	2	=	=	PUNCT
ejpam-3123	361	3	f(s	f(s	ADV
ejpam-3123	361	4	/	/	SYM
ejpam-3123	361	5	e−1h	e−1h	ADJ
ejpam-3123	361	6	,	,	PUNCT
ejpam-3123	361	7	eg)−1	eg)−1	NOUN
ejpam-3123	361	8	,	,	PUNCT
ejpam-3123	361	9	(	(	PUNCT
ejpam-3123	361	10	s	s	NOUN
ejpam-3123	361	11	/	/	SYM
ejpam-3123	361	12	e−1h	e−1h	ADJ
ejpam-3123	361	13	)	)	PUNCT
ejpam-3123	361	14	∗	∗	NOUN
ejpam-3123	361	15	eg	eg	NOUN
ejpam-3123	361	16	=	=	SYM
ejpam-3123	361	17	s.	s.	PROPN
ejpam-3123	361	18	then	then	ADV
ejpam-3123	361	19	r(e−1	r(e−1	PROPN
ejpam-3123	361	20	h	h	PROPN
ejpam-3123	361	21	,	,	PUNCT
ejpam-3123	361	22	eg	eg	PROPN
ejpam-3123	361	23	)	)	PUNCT
ejpam-3123	361	24	is	be	AUX
ejpam-3123	361	25	the	the	DET
ejpam-3123	361	26	identity	identity	NOUN
ejpam-3123	361	27	component	component	NOUN
ejpam-3123	361	28	for	for	ADP
ejpam-3123	361	29	rh×g	rh×g	NOUN
ejpam-3123	361	30	,	,	PUNCT
ejpam-3123	361	31	where	where	SCONJ
ejpam-3123	361	32	eg	eg	NOUN
ejpam-3123	361	33	is	be	AUX
ejpam-3123	361	34	the	the	DET
ejpam-3123	361	35	left	left	ADJ
ejpam-3123	361	36	identity	identity	NOUN
ejpam-3123	361	37	in	in	ADP
ejpam-3123	361	38	g	g	PROPN
ejpam-3123	361	39	and	and	CCONJ
ejpam-3123	361	40	the	the	DET
ejpam-3123	361	41	functions	function	NOUN
ejpam-3123	361	42	.	.	PUNCT
ejpam-3123	362	1	:	:	PUNCT
ejpam-3123	362	2	g×h	g×h	VERB
ejpam-3123	362	3	→	→	SYM
ejpam-3123	362	4	h	h	NOUN
ejpam-3123	362	5	,	,	PUNCT
ejpam-3123	362	6	/	/	SYM
ejpam-3123	362	7	:	:	PUNCT
ejpam-3123	362	8	g×h	g×h	PROPN
ejpam-3123	362	9	→	→	SYM
ejpam-3123	362	10	g	g	PROPN
ejpam-3123	362	11	and	and	CCONJ
ejpam-3123	362	12	f	f	PROPN
ejpam-3123	362	13	:	:	PUNCT
ejpam-3123	362	14	g×g→	g×g→	PROPN
ejpam-3123	362	15	h	h	NOUN
ejpam-3123	362	16	are	be	AUX
ejpam-3123	362	17	supposed	suppose	VERB
ejpam-3123	362	18	to	to	PART
ejpam-3123	362	19	satisfy	satisfy	VERB
ejpam-3123	362	20	the	the	DET
ejpam-3123	362	21	identities	identity	NOUN
ejpam-3123	362	22	in	in	ADP
ejpam-3123	362	23	proposition	proposition	NOUN
ejpam-3123	362	24	1	1	NUM
ejpam-3123	362	25	.	.	PUNCT
ejpam-3123	363	1	proof	proof	NOUN
ejpam-3123	363	2	.	.	PUNCT
ejpam-3123	364	1	we	we	PRON
ejpam-3123	364	2	start	start	VERB
ejpam-3123	364	3	with	with	ADP
ejpam-3123	364	4	r(u	r(u	PROPN
ejpam-3123	364	5	,	,	PUNCT
ejpam-3123	364	6	s)(e−1	s)(e−1	NOUN
ejpam-3123	364	7	h	h	NOUN
ejpam-3123	364	8	,	,	PUNCT
ejpam-3123	364	9	eg	eg	NOUN
ejpam-3123	364	10	)	)	PUNCT
ejpam-3123	364	11	=	=	SYM
ejpam-3123	365	1	r	r	NOUN
ejpam-3123	365	2	(	(	PUNCT
ejpam-3123	365	3	u(s.e−1	u(s.e−1	NOUN
ejpam-3123	365	4	h	h	NOUN
ejpam-3123	365	5	)	)	PUNCT
ejpam-3123	365	6	f(s	f(s	PROPN
ejpam-3123	365	7	/	/	SYM
ejpam-3123	365	8	e−1	e−1	PROPN
ejpam-3123	365	9	h	h	NOUN
ejpam-3123	365	10	,	,	PUNCT
ejpam-3123	365	11	eg	eg	NOUN
ejpam-3123	365	12	)	)	PUNCT
ejpam-3123	365	13	,	,	PUNCT
ejpam-3123	365	14	(	(	PUNCT
ejpam-3123	365	15	s	s	X
ejpam-3123	365	16	/	/	SYM
ejpam-3123	365	17	e−1	e−1	PROPN
ejpam-3123	365	18	h	h	NOUN
ejpam-3123	365	19	)	)	PUNCT
ejpam-3123	365	20	∗eg	∗eg	PUNCT
ejpam-3123	365	21	)	)	PUNCT
ejpam-3123	366	1	=	=	SYM
ejpam-3123	366	2	r	r	NOUN
ejpam-3123	366	3	(	(	PUNCT
ejpam-3123	366	4	uf(s	uf(s	ADJ
ejpam-3123	366	5	/	/	SYM
ejpam-3123	366	6	e−1	e−1	PROPN
ejpam-3123	366	7	h	h	NOUN
ejpam-3123	366	8	,	,	PUNCT
ejpam-3123	366	9	eg)−1f(s	eg)−1f(s	VERB
ejpam-3123	366	10	/	/	SYM
ejpam-3123	366	11	e−1	e−1	PROPN
ejpam-3123	366	12	h	h	NOUN
ejpam-3123	366	13	,	,	PUNCT
ejpam-3123	366	14	eg	eg	NOUN
ejpam-3123	366	15	)	)	PUNCT
ejpam-3123	366	16	,	,	PUNCT
ejpam-3123	366	17	(	(	PUNCT
ejpam-3123	366	18	s	s	X
ejpam-3123	366	19	/	/	SYM
ejpam-3123	366	20	e−1	e−1	PROPN
ejpam-3123	366	21	h	h	NOUN
ejpam-3123	366	22	)	)	PUNCT
ejpam-3123	366	23	∗eg	∗eg	PUNCT
ejpam-3123	366	24	)	)	PUNCT
ejpam-3123	367	1	=	=	SYM
ejpam-3123	367	2	r(u	r(u	PROPN
ejpam-3123	367	3	,	,	PUNCT
ejpam-3123	367	4	s	s	NOUN
ejpam-3123	367	5	)	)	PUNCT
ejpam-3123	367	6	.	.	PUNCT
ejpam-3123	368	1	(	(	PUNCT
ejpam-3123	368	2	10	10	NUM
ejpam-3123	368	3	)	)	PUNCT
ejpam-3123	368	4	on	on	ADP
ejpam-3123	368	5	the	the	DET
ejpam-3123	368	6	other	other	ADJ
ejpam-3123	368	7	hand	hand	NOUN
ejpam-3123	368	8	,	,	PUNCT
ejpam-3123	368	9	r(e−1	r(e−1	PROPN
ejpam-3123	368	10	h	h	NOUN
ejpam-3123	368	11	,	,	PUNCT
ejpam-3123	368	12	eg)(u	eg)(u	PROPN
ejpam-3123	368	13	,	,	PUNCT
ejpam-3123	368	14	s	s	PART
ejpam-3123	368	15	)	)	PUNCT
ejpam-3123	368	16	=	=	SYM
ejpam-3123	368	17	r	r	X
ejpam-3123	368	18	(	(	PUNCT
ejpam-3123	368	19	e−1	e−1	PROPN
ejpam-3123	368	20	h	h	NOUN
ejpam-3123	368	21	(	(	PUNCT
ejpam-3123	368	22	eg.u	eg.u	ADJ
ejpam-3123	368	23	)	)	PUNCT
ejpam-3123	368	24	f(eg	f(eg	NUM
ejpam-3123	368	25	/	/	SYM
ejpam-3123	368	26	u	u	NOUN
ejpam-3123	368	27	,	,	PUNCT
ejpam-3123	368	28	s),(eg	s),(eg	ADV
ejpam-3123	368	29	/	/	SYM
ejpam-3123	368	30	u)∗s	u)∗s	NOUN
ejpam-3123	368	31	)	)	PUNCT
ejpam-3123	369	1	=	=	SYM
ejpam-3123	369	2	r	r	X
ejpam-3123	369	3	(	(	PUNCT
ejpam-3123	369	4	e−1	e−1	PROPN
ejpam-3123	369	5	h	h	NOUN
ejpam-3123	369	6	(	(	PUNCT
ejpam-3123	369	7	eg.u	eg.u	ADJ
ejpam-3123	369	8	)	)	PUNCT
ejpam-3123	369	9	f(eg	f(eg	NOUN
ejpam-3123	369	10	,	,	PUNCT
ejpam-3123	369	11	s	s	NOUN
ejpam-3123	369	12	)	)	PUNCT
ejpam-3123	369	13	,	,	PUNCT
ejpam-3123	369	14	eg∗s	eg∗	VERB
ejpam-3123	369	15	)	)	PUNCT
ejpam-3123	370	1	=	=	SYM
ejpam-3123	370	2	r	r	X
ejpam-3123	370	3	(	(	PUNCT
ejpam-3123	370	4	e−1	e−1	PROPN
ejpam-3123	370	5	h	h	NOUN
ejpam-3123	370	6	(	(	PUNCT
ejpam-3123	370	7	eg.u)eh	eg.u)eh	NOUN
ejpam-3123	370	8	,	,	PUNCT
ejpam-3123	370	9	s	s	PART
ejpam-3123	370	10	)	)	PUNCT
ejpam-3123	370	11	=	=	SYM
ejpam-3123	371	1	r	r	X
ejpam-3123	371	2	(	(	PUNCT
ejpam-3123	371	3	e−1	e−1	PROPN
ejpam-3123	371	4	h	h	NOUN
ejpam-3123	371	5	(	(	PUNCT
ejpam-3123	371	6	ehue−1	ehue−1	PROPN
ejpam-3123	371	7	h	h	NOUN
ejpam-3123	371	8	)	)	PUNCT
ejpam-3123	371	9	eh	eh	INTJ
ejpam-3123	371	10	,	,	PUNCT
ejpam-3123	371	11	s	s	NOUN
ejpam-3123	371	12	)	)	PUNCT
ejpam-3123	371	13	=	=	SYM
ejpam-3123	372	1	r(u	r(u	PROPN
ejpam-3123	372	2	,	,	PUNCT
ejpam-3123	372	3	s	s	NOUN
ejpam-3123	372	4	)	)	PUNCT
ejpam-3123	372	5	.	.	PUNCT
ejpam-3123	373	1	(	(	PUNCT
ejpam-3123	373	2	11	11	NUM
ejpam-3123	373	3	)	)	PUNCT
ejpam-3123	373	4	thus	thus	ADV
ejpam-3123	373	5	,	,	PUNCT
ejpam-3123	373	6	equations	equation	NOUN
ejpam-3123	373	7	(	(	PUNCT
ejpam-3123	373	8	10	10	NUM
ejpam-3123	373	9	)	)	PUNCT
ejpam-3123	373	10	and	and	CCONJ
ejpam-3123	373	11	(	(	PUNCT
ejpam-3123	373	12	11	11	X
ejpam-3123	373	13	)	)	PUNCT
ejpam-3123	373	14	show	show	VERB
ejpam-3123	373	15	that	that	SCONJ
ejpam-3123	373	16	r(e−1	r(e−1	PROPN
ejpam-3123	373	17	h	h	NOUN
ejpam-3123	373	18	,	,	PUNCT
ejpam-3123	373	19	eg	eg	PROPN
ejpam-3123	373	20	)	)	PUNCT
ejpam-3123	373	21	is	be	AUX
ejpam-3123	373	22	the	the	DET
ejpam-3123	373	23	identity	identity	NOUN
ejpam-3123	373	24	component	component	NOUN
ejpam-3123	373	25	for	for	ADP
ejpam-3123	373	26	rh×g	rh×g	NOUN
ejpam-3123	373	27	.	.	PUNCT
ejpam-3123	374	1	equivalently	equivalently	ADV
ejpam-3123	374	2	,	,	PUNCT
ejpam-3123	374	3	we	we	PRON
ejpam-3123	374	4	can	can	AUX
ejpam-3123	374	5	say	say	VERB
ejpam-3123	374	6	that	that	PRON
ejpam-3123	374	7	(	(	PUNCT
ejpam-3123	374	8	e−1h	e−1h	ADJ
ejpam-3123	374	9	,	,	PUNCT
ejpam-3123	374	10	eg	eg	PROPN
ejpam-3123	374	11	)	)	PUNCT
ejpam-3123	374	12	is	be	AUX
ejpam-3123	374	13	a	a	DET
ejpam-3123	374	14	2	2	NUM
ejpam-3123	374	15	-	-	PUNCT
ejpam-3123	374	16	sided	sided	ADJ
ejpam-3123	374	17	identity	identity	NOUN
ejpam-3123	374	18	of	of	ADP
ejpam-3123	374	19	h	h	NOUN
ejpam-3123	374	20	×g	×g	NOUN
ejpam-3123	374	21	.	.	PUNCT
ejpam-3123	375	1	it	it	PRON
ejpam-3123	375	2	can	can	AUX
ejpam-3123	375	3	be	be	AUX
ejpam-3123	375	4	noted	note	VERB
ejpam-3123	375	5	that	that	SCONJ
ejpam-3123	375	6	since	since	SCONJ
ejpam-3123	375	7	(	(	PUNCT
ejpam-3123	375	8	g	g	NOUN
ejpam-3123	375	9	,	,	PUNCT
ejpam-3123	375	10	∗	∗	NOUN
ejpam-3123	375	11	)	)	PUNCT
ejpam-3123	375	12	has	have	VERB
ejpam-3123	375	13	the	the	DET
ejpam-3123	375	14	right	right	ADJ
ejpam-3123	375	15	division	division	NOUN
ejpam-3123	375	16	property	property	NOUN
ejpam-3123	375	17	,	,	PUNCT
ejpam-3123	375	18	i.e.	i.e.	X
ejpam-3123	375	19	,	,	PUNCT
ejpam-3123	375	20	for	for	ADP
ejpam-3123	375	21	all	all	DET
ejpam-3123	375	22	s	s	PROPN
ejpam-3123	375	23	,	,	PUNCT
ejpam-3123	375	24	t	t	PROPN
ejpam-3123	375	25	∈	∈	PROPN
ejpam-3123	375	26	g	g	PROPN
ejpam-3123	375	27	there	there	PRON
ejpam-3123	375	28	is	be	VERB
ejpam-3123	375	29	a	a	DET
ejpam-3123	375	30	unique	unique	ADJ
ejpam-3123	375	31	solution	solution	NOUN
ejpam-3123	375	32	p	p	X
ejpam-3123	375	33	∈	∈	PROPN
ejpam-3123	375	34	g	g	NOUN
ejpam-3123	375	35	to	to	ADP
ejpam-3123	375	36	the	the	DET
ejpam-3123	375	37	equation	equation	NOUN
ejpam-3123	375	38	p∗s	p∗s	PUNCT
ejpam-3123	375	39	=	=	SYM
ejpam-3123	375	40	t	t	PROPN
ejpam-3123	375	41	,	,	PUNCT
ejpam-3123	375	42	then	then	ADV
ejpam-3123	375	43	there	there	PRON
ejpam-3123	375	44	is	be	VERB
ejpam-3123	375	45	a	a	DET
ejpam-3123	375	46	unique	unique	ADJ
ejpam-3123	375	47	left	left	ADJ
ejpam-3123	375	48	inverse	inverse	NOUN
ejpam-3123	375	49	sl	sl	NOUN
ejpam-3123	375	50	for	for	ADP
ejpam-3123	375	51	all	all	DET
ejpam-3123	375	52	s	s	PART
ejpam-3123	375	53	∈	∈	ADJ
ejpam-3123	375	54	g	g	NOUN
ejpam-3123	375	55	by	by	ADP
ejpam-3123	375	56	putting	put	VERB
ejpam-3123	375	57	t	t	NOUN
ejpam-3123	375	58	=	=	SYM
ejpam-3123	375	59	eg	eg	NOUN
ejpam-3123	375	60	,	,	PUNCT
ejpam-3123	375	61	the	the	DET
ejpam-3123	375	62	left	left	ADJ
ejpam-3123	375	63	identity	identity	NOUN
ejpam-3123	375	64	in	in	ADP
ejpam-3123	375	65	g.	g.	PROPN
ejpam-3123	375	66	consequently	consequently	ADV
ejpam-3123	375	67	,	,	PUNCT
ejpam-3123	375	68	we	we	PRON
ejpam-3123	375	69	can	can	AUX
ejpam-3123	375	70	define	define	VERB
ejpam-3123	375	71	a	a	DET
ejpam-3123	375	72	left	left	ADJ
ejpam-3123	375	73	inverse	inverse	NOUN
ejpam-3123	375	74	for	for	ADP
ejpam-3123	375	75	all	all	DET
ejpam-3123	375	76	(	(	PUNCT
ejpam-3123	375	77	u	u	NOUN
ejpam-3123	375	78	,	,	PUNCT
ejpam-3123	375	79	s	s	PART
ejpam-3123	375	80	)	)	PUNCT
ejpam-3123	375	81	in	in	ADP
ejpam-3123	375	82	h	h	NOUN
ejpam-3123	375	83	×g	×g	NOUN
ejpam-3123	375	84	as	as	SCONJ
ejpam-3123	375	85	we	we	PRON
ejpam-3123	375	86	see	see	VERB
ejpam-3123	375	87	in	in	ADP
ejpam-3123	375	88	the	the	DET
ejpam-3123	375	89	next	next	ADJ
ejpam-3123	375	90	lemma	lemma	PROPN
ejpam-3123	375	91	.	.	PUNCT
ejpam-3123	376	1	references	reference	NOUN
ejpam-3123	376	2	979	979	NUM
ejpam-3123	376	3	lemma	lemma	PROPN
ejpam-3123	376	4	3	3	X
ejpam-3123	376	5	.	.	PUNCT
ejpam-3123	377	1	let	let	VERB
ejpam-3123	377	2	x	x	PRON
ejpam-3123	377	3	be	be	AUX
ejpam-3123	377	4	a	a	DET
ejpam-3123	377	5	group	group	NOUN
ejpam-3123	377	6	,	,	PUNCT
ejpam-3123	377	7	h	h	PROPN
ejpam-3123	377	8	be	be	VERB
ejpam-3123	377	9	a	a	DET
ejpam-3123	377	10	subgroup	subgroup	NOUN
ejpam-3123	377	11	of	of	ADP
ejpam-3123	377	12	x	x	PROPN
ejpam-3123	377	13	,	,	PUNCT
ejpam-3123	377	14	g	g	PROPN
ejpam-3123	377	15	⊂	⊂	PROPN
ejpam-3123	377	16	x	x	VERB
ejpam-3123	377	17	be	be	AUX
ejpam-3123	377	18	a	a	DET
ejpam-3123	377	19	set	set	NOUN
ejpam-3123	377	20	of	of	ADP
ejpam-3123	377	21	left	left	ADJ
ejpam-3123	377	22	coset	coset	NOUN
ejpam-3123	377	23	representatives	representative	NOUN
ejpam-3123	377	24	and	and	CCONJ
ejpam-3123	377	25	r(u	r(u	PROPN
ejpam-3123	377	26	,	,	PUNCT
ejpam-3123	377	27	s)(v	s)(v	PROPN
ejpam-3123	377	28	,	,	PUNCT
ejpam-3123	377	29	t	t	NOUN
ejpam-3123	377	30	)	)	PUNCT
ejpam-3123	377	31	=	=	SYM
ejpam-3123	378	1	r	r	X
ejpam-3123	378	2	(	(	PUNCT
ejpam-3123	378	3	u(s.v)f((s	u(s.v)f((s	ADJ
ejpam-3123	378	4	/	/	SYM
ejpam-3123	378	5	v),t),(s	v),t),(s	ADJ
ejpam-3123	378	6	/	/	SYM
ejpam-3123	378	7	v)∗t	v)∗t	NOUN
ejpam-3123	378	8	)	)	PUNCT
ejpam-3123	378	9	for	for	ADP
ejpam-3123	378	10	all	all	DET
ejpam-3123	378	11	(	(	PUNCT
ejpam-3123	378	12	u	u	NOUN
ejpam-3123	378	13	,	,	PUNCT
ejpam-3123	378	14	s	s	PART
ejpam-3123	378	15	)	)	PUNCT
ejpam-3123	378	16	,	,	PUNCT
ejpam-3123	378	17	(	(	PUNCT
ejpam-3123	378	18	v	v	NOUN
ejpam-3123	378	19	,	,	PUNCT
ejpam-3123	378	20	t	t	PROPN
ejpam-3123	378	21	)	)	PUNCT
ejpam-3123	378	22	in	in	ADP
ejpam-3123	378	23	h	h	NOUN
ejpam-3123	378	24	×g	×g	NOUN
ejpam-3123	378	25	.	.	PUNCT
ejpam-3123	378	26	suppose	suppose	VERB
ejpam-3123	378	27	that	that	SCONJ
ejpam-3123	378	28	the	the	DET
ejpam-3123	378	29	properties	property	NOUN
ejpam-3123	378	30	in	in	ADP
ejpam-3123	378	31	lemmas	lemmas	PROPN
ejpam-3123	378	32	1	1	NUM
ejpam-3123	378	33	and	and	CCONJ
ejpam-3123	378	34	2	2	NUM
ejpam-3123	378	35	are	be	AUX
ejpam-3123	378	36	satisfied	satisfied	ADJ
ejpam-3123	378	37	,	,	PUNCT
ejpam-3123	378	38	then	then	ADV
ejpam-3123	378	39	h	h	PROPN
ejpam-3123	378	40	×g	×g	PROPN
ejpam-3123	378	41	has	have	VERB
ejpam-3123	378	42	a	a	DET
ejpam-3123	378	43	left	left	ADJ
ejpam-3123	378	44	inverse	inverse	NOUN
ejpam-3123	378	45	satisfying	satisfy	VERB
ejpam-3123	378	46	the	the	DET
ejpam-3123	378	47	following	follow	VERB
ejpam-3123	378	48	equality	equality	NOUN
ejpam-3123	378	49	:	:	PUNCT
ejpam-3123	378	50	r(v	r(v	PROPN
ejpam-3123	378	51	,	,	PUNCT
ejpam-3123	378	52	t)l	t)l	NOUN
ejpam-3123	378	53	=	=	SYM
ejpam-3123	378	54	r	r	NOUN
ejpam-3123	378	55	(	(	PUNCT
ejpam-3123	378	56	e−1	e−1	PROPN
ejpam-3123	378	57	h	h	NOUN
ejpam-3123	378	58	f(tl	f(tl	PROPN
ejpam-3123	378	59	,	,	PUNCT
ejpam-3123	378	60	t)−1(tl.v−1	t)−1(tl.v−1	PROPN
ejpam-3123	378	61	)	)	PUNCT
ejpam-3123	378	62	,	,	PUNCT
ejpam-3123	378	63	tl	tl	PROPN
ejpam-3123	378	64	/	/	SYM
ejpam-3123	378	65	v−1	v−1	PROPN
ejpam-3123	378	66	)	)	PUNCT
ejpam-3123	378	67	.	.	PUNCT
ejpam-3123	379	1	proof	proof	NOUN
ejpam-3123	379	2	.	.	PUNCT
ejpam-3123	380	1	to	to	PART
ejpam-3123	380	2	show	show	VERB
ejpam-3123	380	3	that	that	SCONJ
ejpam-3123	380	4	r(v	r(v	PROPN
ejpam-3123	380	5	,	,	PUNCT
ejpam-3123	380	6	t)l(v	t)l(v	PRON
ejpam-3123	380	7	,	,	PUNCT
ejpam-3123	380	8	t	t	NOUN
ejpam-3123	380	9	)	)	PUNCT
ejpam-3123	380	10	=	=	NOUN
ejpam-3123	380	11	r(e−1	r(e−1	NOUN
ejpam-3123	380	12	h	h	NOUN
ejpam-3123	380	13	,	,	PUNCT
ejpam-3123	380	14	eg	eg	PROPN
ejpam-3123	380	15	)	)	PUNCT
ejpam-3123	380	16	,	,	PUNCT
ejpam-3123	380	17	we	we	PRON
ejpam-3123	380	18	start	start	VERB
ejpam-3123	380	19	with	with	ADP
ejpam-3123	380	20	the	the	DET
ejpam-3123	380	21	left	left	ADJ
ejpam-3123	380	22	hand	hand	NOUN
ejpam-3123	380	23	side	side	NOUN
ejpam-3123	380	24	as	as	SCONJ
ejpam-3123	380	25	follows	follow	VERB
ejpam-3123	380	26	:	:	PUNCT
ejpam-3123	380	27	r(v	r(v	PROPN
ejpam-3123	380	28	,	,	PUNCT
ejpam-3123	380	29	t)l(v	t)l(v	PRON
ejpam-3123	380	30	,	,	PUNCT
ejpam-3123	380	31	t	t	NOUN
ejpam-3123	380	32	)	)	PUNCT
ejpam-3123	380	33	=	=	SYM
ejpam-3123	381	1	r	r	X
ejpam-3123	381	2	(	(	PUNCT
ejpam-3123	381	3	e−1	e−1	PROPN
ejpam-3123	381	4	h	h	NOUN
ejpam-3123	381	5	f(tl	f(tl	PROPN
ejpam-3123	381	6	,	,	PUNCT
ejpam-3123	381	7	t)−1(tl.v−1	t)−1(tl.v−1	PROPN
ejpam-3123	381	8	)	)	PUNCT
ejpam-3123	381	9	,	,	PUNCT
ejpam-3123	381	10	tl	tl	PROPN
ejpam-3123	381	11	/	/	SYM
ejpam-3123	381	12	v−1	v−1	PROPN
ejpam-3123	381	13	)	)	PUNCT
ejpam-3123	381	14	(	(	PUNCT
ejpam-3123	381	15	v	v	NOUN
ejpam-3123	381	16	,	,	PUNCT
ejpam-3123	381	17	t	t	PROPN
ejpam-3123	381	18	)	)	PUNCT
ejpam-3123	381	19	=	=	SYM
ejpam-3123	382	1	r	r	X
ejpam-3123	382	2	(	(	PUNCT
ejpam-3123	382	3	e−1	e−1	PROPN
ejpam-3123	382	4	h	h	NOUN
ejpam-3123	382	5	f(tl	f(tl	PROPN
ejpam-3123	382	6	,	,	PUNCT
ejpam-3123	382	7	t)−1(tl.v−1	t)−1(tl.v−1	PROPN
ejpam-3123	382	8	)	)	PUNCT
ejpam-3123	382	9	(	(	PUNCT
ejpam-3123	382	10	(	(	PUNCT
ejpam-3123	382	11	tl	tl	PROPN
ejpam-3123	382	12	/	/	SYM
ejpam-3123	382	13	v−1).v	v−1).v	NOUN
ejpam-3123	382	14	)	)	PUNCT
ejpam-3123	382	15	f	f	NOUN
ejpam-3123	382	16	(	(	PUNCT
ejpam-3123	382	17	(	(	PUNCT
ejpam-3123	382	18	tl	tl	PROPN
ejpam-3123	382	19	/	/	SYM
ejpam-3123	382	20	v−1)/v	v−1)/v	PROPN
ejpam-3123	382	21	,	,	PUNCT
ejpam-3123	382	22	t	t	PROPN
ejpam-3123	382	23	)	)	PUNCT
ejpam-3123	382	24	,	,	PUNCT
ejpam-3123	382	25	(	(	PUNCT
ejpam-3123	382	26	(	(	PUNCT
ejpam-3123	382	27	tl	tl	PROPN
ejpam-3123	382	28	/	/	SYM
ejpam-3123	382	29	v−1)/v	v−1)/v	PROPN
ejpam-3123	382	30	)	)	PUNCT
ejpam-3123	382	31	∗t	∗t	ADJ
ejpam-3123	382	32	)	)	PUNCT
ejpam-3123	382	33	=	=	SYM
ejpam-3123	383	1	r	r	X
ejpam-3123	383	2	(	(	PUNCT
ejpam-3123	383	3	e−1	e−1	PROPN
ejpam-3123	383	4	h	h	NOUN
ejpam-3123	383	5	f(tl	f(tl	PROPN
ejpam-3123	383	6	,	,	PUNCT
ejpam-3123	383	7	t)−1(tl.v−1v)f	t)−1(tl.v−1v)f	PROPN
ejpam-3123	383	8	(	(	PUNCT
ejpam-3123	383	9	tl	tl	PROPN
ejpam-3123	383	10	/	/	SYM
ejpam-3123	383	11	v−1v	v−1v	PROPN
ejpam-3123	383	12	,	,	PUNCT
ejpam-3123	383	13	t	t	NOUN
ejpam-3123	383	14	)	)	PUNCT
ejpam-3123	383	15	,	,	PUNCT
ejpam-3123	383	16	(	(	PUNCT
ejpam-3123	383	17	tl	tl	PROPN
ejpam-3123	383	18	/	/	SYM
ejpam-3123	383	19	v−1v)∗t	v−1v)∗t	NOUN
ejpam-3123	383	20	)	)	PUNCT
ejpam-3123	384	1	=	=	PUNCT
ejpam-3123	384	2	r	r	X
ejpam-3123	384	3	(	(	PUNCT
ejpam-3123	384	4	e−1	e−1	PROPN
ejpam-3123	384	5	h	h	PROPN
ejpam-3123	384	6	f(tl	f(tl	PROPN
ejpam-3123	384	7	,	,	PUNCT
ejpam-3123	384	8	t)−1(tl.e)f	t)−1(tl.e)f	PROPN
ejpam-3123	384	9	(	(	PUNCT
ejpam-3123	384	10	tl	tl	PROPN
ejpam-3123	384	11	/	/	SYM
ejpam-3123	384	12	e	e	PROPN
ejpam-3123	384	13	,	,	PUNCT
ejpam-3123	384	14	t	t	PROPN
ejpam-3123	384	15	)	)	PUNCT
ejpam-3123	384	16	,	,	PUNCT
ejpam-3123	384	17	(	(	PUNCT
ejpam-3123	384	18	tl	tl	PROPN
ejpam-3123	384	19	/	/	SYM
ejpam-3123	384	20	e)∗t	e)∗t	NOUN
ejpam-3123	384	21	)	)	PUNCT
ejpam-3123	384	22	=	=	SYM
ejpam-3123	385	1	r	r	X
ejpam-3123	385	2	(	(	PUNCT
ejpam-3123	385	3	e−1	e−1	PROPN
ejpam-3123	385	4	h	h	PROPN
ejpam-3123	385	5	f(tl	f(tl	PROPN
ejpam-3123	385	6	,	,	PUNCT
ejpam-3123	385	7	t)−1f(tl	t)−1f(tl	PROPN
ejpam-3123	385	8	,	,	PUNCT
ejpam-3123	385	9	t	t	PROPN
ejpam-3123	385	10	)	)	PUNCT
ejpam-3123	385	11	)	)	PUNCT
ejpam-3123	385	12	,	,	PUNCT
ejpam-3123	385	13	tl∗t	tl∗t	NOUN
ejpam-3123	385	14	)	)	PUNCT
ejpam-3123	385	15	=	=	SYM
ejpam-3123	386	1	r	r	X
ejpam-3123	386	2	(	(	PUNCT
ejpam-3123	386	3	e−1	e−1	PROPN
ejpam-3123	386	4	h	h	NOUN
ejpam-3123	386	5	,	,	PUNCT
ejpam-3123	386	6	eg	eg	NOUN
ejpam-3123	386	7	)	)	PUNCT
ejpam-3123	386	8	.	.	PUNCT
ejpam-3123	387	1	as	as	SCONJ
ejpam-3123	387	2	required	require	VERB
ejpam-3123	387	3	.	.	PUNCT
ejpam-3123	388	1	references	reference	NOUN
ejpam-3123	388	2	[	[	X
ejpam-3123	388	3	1	1	NUM
ejpam-3123	388	4	]	]	X
ejpam-3123	388	5	g.	g.	PROPN
ejpam-3123	388	6	abrams	abrams	PROPN
ejpam-3123	388	7	and	and	CCONJ
ejpam-3123	388	8	c.	c.	PROPN
ejpam-3123	388	9	menini	menini	PROPN
ejpam-3123	388	10	.	.	PUNCT
ejpam-3123	389	1	rings	ring	NOUN
ejpam-3123	389	2	of	of	ADP
ejpam-3123	389	3	endomorphisms	endomorphism	NOUN
ejpam-3123	389	4	of	of	ADP
ejpam-3123	389	5	semigroup	semigroup	NOUN
ejpam-3123	389	6	-	-	PUNCT
ejpam-3123	389	7	graded	grade	VERB
ejpam-3123	389	8	modules	module	NOUN
ejpam-3123	389	9	.	.	PUNCT
ejpam-3123	390	1	rocky	rocky	ADJ
ejpam-3123	390	2	mountain	mountain	PROPN
ejpam-3123	390	3	j.	j.	PROPN
ejpam-3123	390	4	math	math	PROPN
ejpam-3123	390	5	.	.	PUNCT
ejpam-3123	390	6	,	,	PUNCT
ejpam-3123	390	7	26(2):375	26(2):375	NUM
ejpam-3123	390	8	-	-	SYM
ejpam-3123	390	9	406	406	NUM
ejpam-3123	390	10	,	,	PUNCT
ejpam-3123	390	11	(	(	PUNCT
ejpam-3123	390	12	1996	1996	NUM
ejpam-3123	390	13	)	)	PUNCT
ejpam-3123	390	14	.	.	PUNCT
ejpam-3123	391	1	[	[	X
ejpam-3123	391	2	2	2	NUM
ejpam-3123	391	3	]	]	PUNCT
ejpam-3123	391	4	m.	m.	NOUN
ejpam-3123	391	5	m.	m.	PROPN
ejpam-3123	391	6	al	al	PROPN
ejpam-3123	391	7	-	-	PUNCT
ejpam-3123	391	8	shomrani	shomrani	PROPN
ejpam-3123	391	9	.	.	PUNCT
ejpam-3123	392	1	a	a	DET
ejpam-3123	392	2	construction	construction	NOUN
ejpam-3123	392	3	of	of	ADP
ejpam-3123	392	4	graded	grade	VERB
ejpam-3123	392	5	rings	ring	NOUN
ejpam-3123	392	6	using	use	VERB
ejpam-3123	392	7	a	a	DET
ejpam-3123	392	8	set	set	NOUN
ejpam-3123	392	9	of	of	ADP
ejpam-3123	392	10	left	left	ADJ
ejpam-3123	392	11	coset	coset	NOUN
ejpam-3123	392	12	representatives	representative	NOUN
ejpam-3123	392	13	.	.	PUNCT
ejpam-3123	393	1	jp	jp	PROPN
ejpam-3123	393	2	journal	journal	PROPN
ejpam-3123	393	3	of	of	ADP
ejpam-3123	393	4	algebra	algebra	PROPN
ejpam-3123	393	5	,	,	PUNCT
ejpam-3123	393	6	number	number	NOUN
ejpam-3123	393	7	theory	theory	NOUN
ejpam-3123	393	8	and	and	CCONJ
ejpam-3123	393	9	applications	application	NOUN
ejpam-3123	393	10	,	,	PUNCT
ejpam-3123	393	11	25(2):133	25(2):133	NUM
ejpam-3123	393	12	-	-	SYM
ejpam-3123	393	13	144	144	NUM
ejpam-3123	393	14	,	,	PUNCT
ejpam-3123	393	15	(	(	PUNCT
ejpam-3123	393	16	2012	2012	NUM
ejpam-3123	393	17	)	)	PUNCT
ejpam-3123	393	18	.	.	PUNCT
ejpam-3123	394	1	[	[	X
ejpam-3123	394	2	3	3	X
ejpam-3123	394	3	]	]	X
ejpam-3123	394	4	m.	m.	NOUN
ejpam-3123	394	5	m.	m.	PROPN
ejpam-3123	394	6	al	al	PROPN
ejpam-3123	394	7	-	-	PUNCT
ejpam-3123	394	8	shomrani	shomrani	PROPN
ejpam-3123	394	9	and	and	CCONJ
ejpam-3123	394	10	e.	e.	PROPN
ejpam-3123	394	11	j.	j.	PROPN
ejpam-3123	394	12	beggs	beggs	PROPN
ejpam-3123	394	13	.	.	PUNCT
ejpam-3123	395	1	making	make	VERB
ejpam-3123	395	2	nontrivially	nontrivially	ADV
ejpam-3123	395	3	associated	associate	VERB
ejpam-3123	395	4	modular	modular	ADJ
ejpam-3123	395	5	categories	category	NOUN
ejpam-3123	395	6	from	from	ADP
ejpam-3123	395	7	finite	finite	ADJ
ejpam-3123	395	8	groups	group	NOUN
ejpam-3123	395	9	.	.	PUNCT
ejpam-3123	396	1	int	int	NOUN
ejpam-3123	396	2	.	.	PUNCT
ejpam-3123	397	1	j.	j.	PROPN
ejpam-3123	397	2	math	math	PROPN
ejpam-3123	397	3	.	.	PUNCT
ejpam-3123	398	1	math	math	NOUN
ejpam-3123	398	2	.	.	PUNCT
ejpam-3123	399	1	sci	sci	PROPN
ejpam-3123	399	2	.	.	PROPN
ejpam-3123	399	3	,	,	PUNCT
ejpam-3123	399	4	2004(42):2231	2004(42):2231	NUM
ejpam-3123	399	5	-	-	SYM
ejpam-3123	399	6	2264	2264	NUM
ejpam-3123	399	7	,	,	PUNCT
ejpam-3123	399	8	(	(	PUNCT
ejpam-3123	399	9	2004	2004	NUM
ejpam-3123	399	10	)	)	PUNCT
ejpam-3123	399	11	.	.	PUNCT
ejpam-3123	400	1	[	[	X
ejpam-3123	400	2	4	4	X
ejpam-3123	400	3	]	]	PUNCT
ejpam-3123	400	4	e.	e.	PROPN
ejpam-3123	400	5	j.	j.	PROPN
ejpam-3123	400	6	beggs	beggs	PROPN
ejpam-3123	400	7	.	.	PUNCT
ejpam-3123	401	1	making	make	VERB
ejpam-3123	401	2	non	non	ADJ
ejpam-3123	401	3	-	-	ADJ
ejpam-3123	401	4	trivially	trivially	ADV
ejpam-3123	401	5	associated	associated	ADJ
ejpam-3123	401	6	tensor	tensor	NOUN
ejpam-3123	401	7	categories	category	NOUN
ejpam-3123	401	8	from	from	ADP
ejpam-3123	401	9	left	left	ADJ
ejpam-3123	401	10	coset	coset	NOUN
ejpam-3123	401	11	representatives	representative	NOUN
ejpam-3123	401	12	.	.	PUNCT
ejpam-3123	402	1	j.	j.	PROPN
ejpam-3123	402	2	pure	pure	PROPN
ejpam-3123	402	3	appl	appl	PROPN
ejpam-3123	402	4	.	.	PUNCT
ejpam-3123	403	1	algebra	algebra	NOUN
ejpam-3123	403	2	,	,	PUNCT
ejpam-3123	403	3	177(1):5	177(1):5	PROPN
ejpam-3123	403	4	-	-	PUNCT
ejpam-3123	403	5	41	41	NUM
ejpam-3123	403	6	,	,	PUNCT
ejpam-3123	403	7	(	(	PUNCT
ejpam-3123	403	8	2003	2003	NUM
ejpam-3123	403	9	)	)	PUNCT
ejpam-3123	403	10	.	.	PUNCT
ejpam-3123	404	1	[	[	X
ejpam-3123	404	2	5	5	X
ejpam-3123	404	3	]	]	PUNCT
ejpam-3123	404	4	m.	m.	NOUN
ejpam-3123	404	5	cohen	cohen	PROPN
ejpam-3123	404	6	and	and	CCONJ
ejpam-3123	404	7	s.	s.	PROPN
ejpam-3123	404	8	montgomery	montgomery	PROPN
ejpam-3123	404	9	.	.	PUNCT
ejpam-3123	405	1	group	group	NOUN
ejpam-3123	405	2	-	-	PUNCT
ejpam-3123	405	3	graded	grade	VERB
ejpam-3123	405	4	rings	ring	NOUN
ejpam-3123	405	5	,	,	PUNCT
ejpam-3123	405	6	smash	smash	VERB
ejpam-3123	405	7	product	product	NOUN
ejpam-3123	405	8	and	and	CCONJ
ejpam-3123	405	9	group	group	NOUN
ejpam-3123	405	10	actions	action	NOUN
ejpam-3123	405	11	.	.	PUNCT
ejpam-3123	406	1	trans	trans	PROPN
ejpam-3123	406	2	.	.	PUNCT
ejpam-3123	407	1	amer	amer	PROPN
ejpam-3123	407	2	.	.	PUNCT
ejpam-3123	407	3	math	math	PROPN
ejpam-3123	407	4	.	.	PUNCT
ejpam-3123	408	1	soc	soc	PROPN
ejpam-3123	408	2	.	.	PUNCT
ejpam-3123	408	3	,	,	PUNCT
ejpam-3123	408	4	282(1):237	282(1):237	NUM
ejpam-3123	408	5	-	-	SYM
ejpam-3123	408	6	258	258	NUM
ejpam-3123	408	7	,	,	PUNCT
ejpam-3123	408	8	(	(	PUNCT
ejpam-3123	408	9	1984	1984	NUM
ejpam-3123	408	10	)	)	PUNCT
ejpam-3123	408	11	.	.	PUNCT
ejpam-3123	409	1	[	[	X
ejpam-3123	409	2	6	6	NUM
ejpam-3123	409	3	]	]	PUNCT
ejpam-3123	409	4	e.	e.	PROPN
ejpam-3123	409	5	c.	c.	PROPN
ejpam-3123	409	6	dade	dade	PROPN
ejpam-3123	409	7	.	.	PUNCT
ejpam-3123	409	8	group	group	PROPN
ejpam-3123	409	9	graded	grade	VERB
ejpam-3123	409	10	rings	ring	NOUN
ejpam-3123	409	11	and	and	CCONJ
ejpam-3123	409	12	modules	module	NOUN
ejpam-3123	409	13	.	.	PUNCT
ejpam-3123	410	1	math	math	NOUN
ejpam-3123	410	2	.	.	PUNCT
ejpam-3123	411	1	z.	z.	PROPN
ejpam-3123	411	2	,	,	PUNCT
ejpam-3123	411	3	174:241	174:241	PROPN
ejpam-3123	411	4	-	-	SYM
ejpam-3123	411	5	262	262	NUM
ejpam-3123	411	6	,	,	PUNCT
ejpam-3123	411	7	(	(	PUNCT
ejpam-3123	411	8	1980	1980	NUM
ejpam-3123	411	9	)	)	PUNCT
ejpam-3123	411	10	.	.	PUNCT
ejpam-3123	412	1	[	[	X
ejpam-3123	412	2	7	7	X
ejpam-3123	412	3	]	]	PUNCT
ejpam-3123	412	4	s.	s.	PROPN
ejpam-3123	412	5	dascalescu	dascalescu	PROPN
ejpam-3123	412	6	,	,	PUNCT
ejpam-3123	412	7	a.	a.	PROPN
ejpam-3123	412	8	v.	v.	PROPN
ejpam-3123	412	9	kelarev	kelarev	PROPN
ejpam-3123	412	10	and	and	CCONJ
ejpam-3123	412	11	l.	l.	PROPN
ejpam-3123	412	12	van	van	PROPN
ejpam-3123	412	13	wyk	wyk	PROPN
ejpam-3123	412	14	.	.	PUNCT
ejpam-3123	413	1	semigroup	semigroup	PROPN
ejpam-3123	413	2	gradings	grading	NOUN
ejpam-3123	413	3	of	of	ADP
ejpam-3123	413	4	full	full	ADJ
ejpam-3123	413	5	matrix	matrix	NOUN
ejpam-3123	413	6	rings	ring	NOUN
ejpam-3123	413	7	.	.	PUNCT
ejpam-3123	414	1	comm	comm	NOUN
ejpam-3123	414	2	.	.	PUNCT
ejpam-3123	415	1	algebra	algebra	NOUN
ejpam-3123	415	2	,	,	PUNCT
ejpam-3123	415	3	29(11):5023	29(11):5023	NUM
ejpam-3123	415	4	-	-	SYM
ejpam-3123	415	5	5031	5031	NUM
ejpam-3123	415	6	,	,	PUNCT
ejpam-3123	415	7	(	(	PUNCT
ejpam-3123	415	8	2001	2001	NUM
ejpam-3123	415	9	)	)	PUNCT
ejpam-3123	415	10	.	.	PUNCT
ejpam-3123	416	1	references	reference	NOUN
ejpam-3123	416	2	980	980	NUM
ejpam-3123	417	1	[	[	SYM
ejpam-3123	417	2	8	8	NUM
ejpam-3123	417	3	]	]	X
ejpam-3123	417	4	r.	r.	PROPN
ejpam-3123	417	5	farnsteiner	farnsteiner	PROPN
ejpam-3123	417	6	.	.	PUNCT
ejpam-3123	418	1	group	group	NOUN
ejpam-3123	418	2	-	-	PUNCT
ejpam-3123	418	3	graded	grade	VERB
ejpam-3123	418	4	algebras	algebra	NOUN
ejpam-3123	418	5	,	,	PUNCT
ejpam-3123	418	6	extensions	extension	NOUN
ejpam-3123	418	7	of	of	ADP
ejpam-3123	418	8	infinitesimal	infinitesimal	ADJ
ejpam-3123	418	9	groups	group	NOUN
ejpam-3123	418	10	,	,	PUNCT
ejpam-3123	418	11	and	and	CCONJ
ejpam-3123	418	12	applications	application	NOUN
ejpam-3123	418	13	.	.	PUNCT
ejpam-3123	419	1	transform	transform	VERB
ejpam-3123	419	2	.	.	PUNCT
ejpam-3123	420	1	groups	group	NOUN
ejpam-3123	420	2	,	,	PUNCT
ejpam-3123	420	3	14(1):127	14(1):127	NUM
ejpam-3123	420	4	-	-	SYM
ejpam-3123	420	5	162	162	NUM
ejpam-3123	420	6	,	,	PUNCT
ejpam-3123	420	7	(	(	PUNCT
ejpam-3123	420	8	2009	2009	NUM
ejpam-3123	420	9	)	)	PUNCT
ejpam-3123	420	10	.	.	PUNCT
ejpam-3123	421	1	[	[	X
ejpam-3123	421	2	9	9	X
ejpam-3123	421	3	]	]	PUNCT
ejpam-3123	421	4	j.	j.	PROPN
ejpam-3123	421	5	l.	l.	PROPN
ejpam-3123	421	6	gómez	gómez	PROPN
ejpam-3123	421	7	pardo	pardo	PROPN
ejpam-3123	421	8	and	and	CCONJ
ejpam-3123	421	9	c.	c.	PROPN
ejpam-3123	421	10	nǎstǎsescu	nǎstǎsescu	PROPN
ejpam-3123	421	11	.	.	PUNCT
ejpam-3123	422	1	relative	relative	ADJ
ejpam-3123	422	2	projectivity	projectivity	NOUN
ejpam-3123	422	3	,	,	PUNCT
ejpam-3123	422	4	graded	grade	VERB
ejpam-3123	422	5	cliffored	cliffore	VERB
ejpam-3123	422	6	theory	theory	NOUN
ejpam-3123	422	7	and	and	CCONJ
ejpam-3123	422	8	applications	application	NOUN
ejpam-3123	422	9	.	.	PUNCT
ejpam-3123	423	1	j.	j.	PROPN
ejpam-3123	423	2	algebra	algebra	PROPN
ejpam-3123	423	3	,	,	PUNCT
ejpam-3123	423	4	141(2):484	141(2):484	NOUN
ejpam-3123	423	5	-	-	SYM
ejpam-3123	423	6	504	504	NUM
ejpam-3123	423	7	,	,	PUNCT
ejpam-3123	423	8	(	(	PUNCT
ejpam-3123	423	9	1991	1991	NUM
ejpam-3123	423	10	)	)	PUNCT
ejpam-3123	423	11	.	.	PUNCT
ejpam-3123	424	1	[	[	X
ejpam-3123	424	2	10	10	NUM
ejpam-3123	424	3	]	]	X
ejpam-3123	424	4	e.	e.	PROPN
ejpam-3123	424	5	jespers	jespers	PROPN
ejpam-3123	424	6	.	.	PUNCT
ejpam-3123	425	1	simple	simple	ADJ
ejpam-3123	425	2	graded	grade	VERB
ejpam-3123	425	3	rings	ring	NOUN
ejpam-3123	425	4	.	.	PUNCT
ejpam-3123	426	1	comm	comm	NOUN
ejpam-3123	426	2	.	.	PUNCT
ejpam-3123	427	1	algebra	algebra	NOUN
ejpam-3123	427	2	,	,	PUNCT
ejpam-3123	427	3	21(7):2437	21(7):2437	NUM
ejpam-3123	427	4	-	-	SYM
ejpam-3123	427	5	2444	2444	NUM
ejpam-3123	427	6	,	,	PUNCT
ejpam-3123	427	7	(	(	PUNCT
ejpam-3123	427	8	1993	1993	NUM
ejpam-3123	427	9	)	)	PUNCT
ejpam-3123	427	10	.	.	PUNCT
ejpam-3123	428	1	[	[	X
ejpam-3123	428	2	11	11	NUM
ejpam-3123	428	3	]	]	X
ejpam-3123	428	4	g.	g.	PROPN
ejpam-3123	428	5	karpilovsky	karpilovsky	PROPN
ejpam-3123	428	6	.	.	PUNCT
ejpam-3123	429	1	the	the	DET
ejpam-3123	429	2	jacobson	jacobson	PROPN
ejpam-3123	429	3	radical	radical	PROPN
ejpam-3123	429	4	of	of	ADP
ejpam-3123	429	5	monoid	monoid	NOUN
ejpam-3123	429	6	-	-	PUNCT
ejpam-3123	429	7	graded	grade	VERB
ejpam-3123	429	8	algebras	algebra	NOUN
ejpam-3123	429	9	.	.	PUNCT
ejpam-3123	430	1	tsukuba	tsukuba	PROPN
ejpam-3123	430	2	j.	j.	PROPN
ejpam-3123	430	3	math	math	PROPN
ejpam-3123	430	4	,	,	PUNCT
ejpam-3123	430	5	16(1):19	16(1):19	NUM
ejpam-3123	430	6	-	-	SYM
ejpam-3123	430	7	52	52	NUM
ejpam-3123	430	8	,	,	PUNCT
ejpam-3123	430	9	(	(	PUNCT
ejpam-3123	430	10	1992	1992	NUM
ejpam-3123	430	11	)	)	PUNCT
ejpam-3123	430	12	.	.	PUNCT
ejpam-3123	431	1	[	[	X
ejpam-3123	431	2	12	12	NUM
ejpam-3123	431	3	]	]	PUNCT
ejpam-3123	431	4	a.	a.	NOUN
ejpam-3123	431	5	v.	v.	PROPN
ejpam-3123	431	6	kelarev	kelarev	PROPN
ejpam-3123	431	7	.	.	PUNCT
ejpam-3123	432	1	applications	application	NOUN
ejpam-3123	432	2	of	of	ADP
ejpam-3123	432	3	epigroups	epigroup	NOUN
ejpam-3123	432	4	to	to	PART
ejpam-3123	432	5	graded	grade	VERB
ejpam-3123	432	6	ring	ring	NOUN
ejpam-3123	432	7	theory	theory	NOUN
ejpam-3123	432	8	.	.	PUNCT
ejpam-3123	433	1	semigroup	semigroup	PROPN
ejpam-3123	433	2	forum	forum	PROPN
ejpam-3123	433	3	,	,	PUNCT
ejpam-3123	433	4	50(3):327	50(3):327	PROPN
ejpam-3123	433	5	-	-	SYM
ejpam-3123	433	6	350	350	NUM
ejpam-3123	433	7	,	,	PUNCT
ejpam-3123	433	8	(	(	PUNCT
ejpam-3123	433	9	1995	1995	NUM
ejpam-3123	433	10	)	)	PUNCT
ejpam-3123	433	11	.	.	PUNCT
ejpam-3123	434	1	[	[	X
ejpam-3123	434	2	13	13	NUM
ejpam-3123	434	3	]	]	PUNCT
ejpam-3123	434	4	a.	a.	NOUN
ejpam-3123	434	5	v.	v.	PROPN
ejpam-3123	434	6	kelarev	kelarev	PROPN
ejpam-3123	434	7	.	.	PUNCT
ejpam-3123	435	1	semisimple	semisimple	PROPN
ejpam-3123	435	2	rings	ring	NOUN
ejpam-3123	435	3	graded	grade	VERB
ejpam-3123	435	4	by	by	ADP
ejpam-3123	435	5	inverse	inverse	NOUN
ejpam-3123	435	6	semigroups	semigroup	NOUN
ejpam-3123	435	7	.	.	PUNCT
ejpam-3123	436	1	j.	j.	PROPN
ejpam-3123	436	2	algebra	algebra	PROPN
ejpam-3123	436	3	,	,	PUNCT
ejpam-3123	436	4	205:451459	205:451459	NUM
ejpam-3123	436	5	,	,	PUNCT
ejpam-3123	436	6	(	(	PUNCT
ejpam-3123	436	7	1998	1998	NUM
ejpam-3123	436	8	)	)	PUNCT
ejpam-3123	436	9	.	.	PUNCT
ejpam-3123	437	1	[	[	X
ejpam-3123	437	2	14	14	NUM
ejpam-3123	437	3	]	]	X
ejpam-3123	437	4	c.	c.	PROPN
ejpam-3123	437	5	nǎstǎsescu	nǎstǎsescu	PROPN
ejpam-3123	437	6	and	and	CCONJ
ejpam-3123	437	7	f.	f.	PROPN
ejpam-3123	437	8	v.	v.	PROPN
ejpam-3123	437	9	oystaeyen	oystaeyen	PROPN
ejpam-3123	437	10	.	.	PUNCT
ejpam-3123	438	1	methods	method	NOUN
ejpam-3123	438	2	of	of	ADP
ejpam-3123	438	3	graded	grade	VERB
ejpam-3123	438	4	rings	ring	NOUN
ejpam-3123	438	5	.	.	PUNCT
ejpam-3123	439	1	springer	springer	NOUN
ejpam-3123	439	2	-	-	PUNCT
ejpam-3123	439	3	verlag	verlag	PROPN
ejpam-3123	439	4	berlin	berlin	PROPN
ejpam-3123	439	5	heidelberg	heidelberg	PROPN
ejpam-3123	439	6	,	,	PUNCT
ejpam-3123	439	7	new	new	PROPN
ejpam-3123	439	8	york	york	PROPN
ejpam-3123	439	9	,	,	PUNCT
ejpam-3123	439	10	(	(	PUNCT
ejpam-3123	439	11	2004	2004	NUM
ejpam-3123	439	12	)	)	PUNCT
ejpam-3123	439	13	.	.	PUNCT
ejpam-3123	440	1	[	[	X
ejpam-3123	440	2	15	15	NUM
ejpam-3123	440	3	]	]	X
ejpam-3123	440	4	p.	p.	NOUN
ejpam-3123	440	5	nystedt	nystedt	NOUN
ejpam-3123	440	6	and	and	CCONJ
ejpam-3123	440	7	j.	j.	PROPN
ejpam-3123	440	8	oinert	oinert	PROPN
ejpam-3123	440	9	.	.	PUNCT
ejpam-3123	441	1	simple	simple	ADJ
ejpam-3123	441	2	semigroup	semigroup	PROPN
ejpam-3123	441	3	graded	grade	VERB
ejpam-3123	441	4	rings	ring	NOUN
ejpam-3123	441	5	.	.	PUNCT
ejpam-3123	442	1	j.	j.	PROPN
ejpam-3123	442	2	algebra	algebra	PROPN
ejpam-3123	442	3	appl	appl	PROPN
ejpam-3123	442	4	.	.	PROPN
ejpam-3123	442	5	,	,	PUNCT
ejpam-3123	442	6	14(7):110	14(7):110	PROPN
ejpam-3123	442	7	,	,	PUNCT
ejpam-3123	442	8	(	(	PUNCT
ejpam-3123	442	9	2015	2015	NUM
ejpam-3123	442	10	)	)	PUNCT
ejpam-3123	442	11	.	.	PUNCT