id	sid	tid	token	lemma	pos
ejpam-3142	1	1	european	european	PROPN
ejpam-3142	1	2	journal	journal	PROPN
ejpam-3142	1	3	of	of	ADP
ejpam-3142	1	4	pure	pure	ADJ
ejpam-3142	1	5	and	and	CCONJ
ejpam-3142	1	6	applied	apply	VERB
ejpam-3142	1	7	mathematics	mathematic	NOUN
ejpam-3142	1	8	vol	vol	NOUN
ejpam-3142	1	9	.	.	PUNCT
ejpam-3142	2	1	11	11	NUM
ejpam-3142	2	2	,	,	PUNCT
ejpam-3142	2	3	no	no	INTJ
ejpam-3142	2	4	.	.	NOUN
ejpam-3142	2	5	1	1	NUM
ejpam-3142	2	6	,	,	PUNCT
ejpam-3142	2	7	2018	2018	NUM
ejpam-3142	2	8	,	,	PUNCT
ejpam-3142	2	9	79	79	NUM
ejpam-3142	2	10	-	-	SYM
ejpam-3142	2	11	89	89	NUM
ejpam-3142	2	12	issn	issn	PROPN
ejpam-3142	2	13	1307	1307	NUM
ejpam-3142	2	14	-	-	SYM
ejpam-3142	2	15	5543	5543	NUM
ejpam-3142	2	16	–	–	PUNCT
ejpam-3142	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3142	2	18	published	publish	VERB
ejpam-3142	2	19	by	by	ADP
ejpam-3142	2	20	new	new	PROPN
ejpam-3142	2	21	york	york	PROPN
ejpam-3142	2	22	business	business	PROPN
ejpam-3142	2	23	global	global	ADJ
ejpam-3142	2	24	on	on	ADP
ejpam-3142	2	25	ideals	ideal	NOUN
ejpam-3142	2	26	and	and	CCONJ
ejpam-3142	2	27	commutativity	commutativity	NOUN
ejpam-3142	2	28	of	of	ADP
ejpam-3142	2	29	prime	prime	ADJ
ejpam-3142	2	30	rings	ring	NOUN
ejpam-3142	2	31	with	with	ADP
ejpam-3142	2	32	generalized	generalized	ADJ
ejpam-3142	2	33	derivations	derivation	NOUN
ejpam-3142	2	34	m.	m.	NOUN
ejpam-3142	2	35	k.	k.	PROPN
ejpam-3142	2	36	abu	abu	PROPN
ejpam-3142	2	37	nawas1,∗	nawas1,∗	PROPN
ejpam-3142	2	38	,	,	PUNCT
ejpam-3142	2	39	radwan	radwan	VERB
ejpam-3142	2	40	m.	m.	PROPN
ejpam-3142	2	41	al	al	PROPN
ejpam-3142	2	42	-	-	PUNCT
ejpam-3142	2	43	omary2	omary2	PROPN
ejpam-3142	2	44	1	1	NUM
ejpam-3142	2	45	department	department	NOUN
ejpam-3142	2	46	of	of	ADP
ejpam-3142	2	47	mathematics	mathematic	NOUN
ejpam-3142	2	48	,	,	PUNCT
ejpam-3142	2	49	faculty	faculty	NOUN
ejpam-3142	2	50	of	of	ADP
ejpam-3142	2	51	science	science	NOUN
ejpam-3142	2	52	,	,	PUNCT
ejpam-3142	2	53	northern	northern	ADJ
ejpam-3142	2	54	border	border	NOUN
ejpam-3142	2	55	university	university	PROPN
ejpam-3142	2	56	,	,	PUNCT
ejpam-3142	2	57	arar	arar	PROPN
ejpam-3142	2	58	,	,	PUNCT
ejpam-3142	2	59	saudi	saudi	PROPN
ejpam-3142	2	60	arabia	arabia	PROPN
ejpam-3142	2	61	2	2	NUM
ejpam-3142	2	62	department	department	NOUN
ejpam-3142	2	63	of	of	ADP
ejpam-3142	2	64	mathematics	mathematics	PROPN
ejpam-3142	2	65	,	,	PUNCT
ejpam-3142	2	66	ibb	ibb	PROPN
ejpam-3142	2	67	university	university	NOUN
ejpam-3142	2	68	,	,	PUNCT
ejpam-3142	2	69	yemen	yemen	PROPN
ejpam-3142	2	70	abstract	abstract	NOUN
ejpam-3142	2	71	.	.	PUNCT
ejpam-3142	3	1	an	an	DET
ejpam-3142	3	2	additive	additive	ADJ
ejpam-3142	3	3	mapping	mapping	NOUN
ejpam-3142	3	4	f	f	NOUN
ejpam-3142	3	5	:	:	PUNCT
ejpam-3142	3	6	r→	r→	PROPN
ejpam-3142	3	7	r	r	NOUN
ejpam-3142	3	8	is	be	AUX
ejpam-3142	3	9	called	call	VERB
ejpam-3142	3	10	a	a	DET
ejpam-3142	3	11	generalized	generalized	ADJ
ejpam-3142	3	12	derivation	derivation	NOUN
ejpam-3142	3	13	on	on	ADP
ejpam-3142	3	14	r	r	NOUN
ejpam-3142	3	15	if	if	SCONJ
ejpam-3142	3	16	there	there	PRON
ejpam-3142	3	17	exists	exist	VERB
ejpam-3142	3	18	a	a	DET
ejpam-3142	3	19	derivation	derivation	NOUN
ejpam-3142	4	1	d	d	NOUN
ejpam-3142	4	2	:	:	PUNCT
ejpam-3142	4	3	r	r	NOUN
ejpam-3142	4	4	→	→	SYM
ejpam-3142	4	5	r	r	NOUN
ejpam-3142	4	6	such	such	ADJ
ejpam-3142	4	7	that	that	SCONJ
ejpam-3142	4	8	f	f	PROPN
ejpam-3142	4	9	(	(	PUNCT
ejpam-3142	4	10	xy	xy	PROPN
ejpam-3142	4	11	)	)	PUNCT
ejpam-3142	4	12	=	=	SYM
ejpam-3142	5	1	xf	xf	PROPN
ejpam-3142	5	2	(	(	PUNCT
ejpam-3142	5	3	y	y	NOUN
ejpam-3142	5	4	)	)	PUNCT
ejpam-3142	6	1	+	+	CCONJ
ejpam-3142	6	2	d(x)y	d(x)y	PROPN
ejpam-3142	6	3	holds	hold	VERB
ejpam-3142	6	4	for	for	ADP
ejpam-3142	6	5	all	all	DET
ejpam-3142	6	6	x	x	NOUN
ejpam-3142	6	7	,	,	PUNCT
ejpam-3142	6	8	y	y	PROPN
ejpam-3142	6	9	∈	∈	PROPN
ejpam-3142	6	10	r.	r.	PROPN
ejpam-3142	6	11	it	it	PRON
ejpam-3142	6	12	is	be	AUX
ejpam-3142	6	13	called	call	VERB
ejpam-3142	6	14	a	a	DET
ejpam-3142	6	15	generalized	generalized	ADJ
ejpam-3142	6	16	(	(	PUNCT
ejpam-3142	6	17	α	α	NOUN
ejpam-3142	6	18	,	,	PUNCT
ejpam-3142	6	19	β)−derivation	β)−derivation	NOUN
ejpam-3142	6	20	on	on	ADP
ejpam-3142	6	21	r	r	NOUN
ejpam-3142	6	22	if	if	SCONJ
ejpam-3142	6	23	there	there	PRON
ejpam-3142	6	24	exists	exist	VERB
ejpam-3142	6	25	an	an	DET
ejpam-3142	6	26	(	(	PUNCT
ejpam-3142	6	27	α	α	NOUN
ejpam-3142	6	28	,	,	PUNCT
ejpam-3142	6	29	β)−derivation	β)−derivation	NOUN
ejpam-3142	6	30	d	d	NOUN
ejpam-3142	6	31	:	:	PUNCT
ejpam-3142	6	32	r	r	NOUN
ejpam-3142	6	33	→	→	SYM
ejpam-3142	6	34	r	r	NOUN
ejpam-3142	6	35	such	such	ADJ
ejpam-3142	6	36	that	that	SCONJ
ejpam-3142	6	37	the	the	DET
ejpam-3142	6	38	equation	equation	NOUN
ejpam-3142	6	39	f	f	X
ejpam-3142	6	40	(	(	PUNCT
ejpam-3142	6	41	xy	xy	PROPN
ejpam-3142	6	42	)	)	PUNCT
ejpam-3142	6	43	=	=	SYM
ejpam-3142	6	44	f	f	PROPN
ejpam-3142	6	45	(	(	PUNCT
ejpam-3142	6	46	x)α(y	x)α(y	PROPN
ejpam-3142	6	47	)	)	PUNCT
ejpam-3142	6	48	+	+	SYM
ejpam-3142	6	49	β(x)d(y	β(x)d(y	NOUN
ejpam-3142	6	50	)	)	PUNCT
ejpam-3142	6	51	holds	hold	VERB
ejpam-3142	6	52	for	for	ADP
ejpam-3142	6	53	all	all	DET
ejpam-3142	6	54	x	x	NOUN
ejpam-3142	6	55	,	,	PUNCT
ejpam-3142	6	56	y	y	PROPN
ejpam-3142	6	57	∈	∈	PROPN
ejpam-3142	6	58	r.	r.	PROPN
ejpam-3142	6	59	in	in	ADP
ejpam-3142	6	60	the	the	DET
ejpam-3142	6	61	present	present	ADJ
ejpam-3142	6	62	paper	paper	NOUN
ejpam-3142	6	63	,	,	PUNCT
ejpam-3142	6	64	we	we	PRON
ejpam-3142	6	65	investigate	investigate	VERB
ejpam-3142	6	66	commutativity	commutativity	NOUN
ejpam-3142	6	67	of	of	ADP
ejpam-3142	6	68	a	a	DET
ejpam-3142	6	69	prime	prime	ADJ
ejpam-3142	6	70	ring	ring	NOUN
ejpam-3142	6	71	r	r	NOUN
ejpam-3142	6	72	,	,	PUNCT
ejpam-3142	6	73	which	which	PRON
ejpam-3142	6	74	satisfies	satisfy	VERB
ejpam-3142	6	75	certain	certain	ADJ
ejpam-3142	6	76	differential	differential	ADJ
ejpam-3142	6	77	identities	identity	NOUN
ejpam-3142	6	78	on	on	ADP
ejpam-3142	6	79	the	the	DET
ejpam-3142	6	80	left	left	ADJ
ejpam-3142	6	81	ideals	ideal	NOUN
ejpam-3142	6	82	of	of	ADP
ejpam-3142	6	83	r.	r.	PROPN
ejpam-3142	6	84	moreover	moreover	ADV
ejpam-3142	6	85	some	some	DET
ejpam-3142	6	86	results	result	NOUN
ejpam-3142	6	87	on	on	ADP
ejpam-3142	6	88	commutativity	commutativity	NOUN
ejpam-3142	6	89	of	of	ADP
ejpam-3142	6	90	rings	ring	NOUN
ejpam-3142	6	91	with	with	ADP
ejpam-3142	6	92	involutions	involution	NOUN
ejpam-3142	6	93	that	that	PRON
ejpam-3142	6	94	satisfy	satisfy	VERB
ejpam-3142	6	95	certain	certain	ADJ
ejpam-3142	6	96	identities	identity	NOUN
ejpam-3142	6	97	are	be	AUX
ejpam-3142	6	98	proved	prove	VERB
ejpam-3142	6	99	.	.	PUNCT
ejpam-3142	7	1	2010	2010	NUM
ejpam-3142	7	2	mathematics	mathematic	NOUN
ejpam-3142	7	3	subject	subject	NOUN
ejpam-3142	7	4	classifications	classification	NOUN
ejpam-3142	7	5	:	:	PUNCT
ejpam-3142	7	6	16d90	16d90	NUM
ejpam-3142	7	7	,	,	PUNCT
ejpam-3142	7	8	16w25	16w25	NUM
ejpam-3142	7	9	,	,	PUNCT
ejpam-3142	7	10	16n60	16n60	NUM
ejpam-3142	7	11	,	,	PUNCT
ejpam-3142	7	12	16u80	16u80	NUM
ejpam-3142	7	13	key	key	ADJ
ejpam-3142	7	14	words	word	NOUN
ejpam-3142	7	15	and	and	CCONJ
ejpam-3142	7	16	phrases	phrase	NOUN
ejpam-3142	7	17	:	:	PUNCT
ejpam-3142	7	18	left	leave	VERB
ejpam-3142	7	19	ideals	ideal	NOUN
ejpam-3142	7	20	,	,	PUNCT
ejpam-3142	7	21	prime	prime	ADJ
ejpam-3142	7	22	rings	ring	NOUN
ejpam-3142	7	23	,	,	PUNCT
ejpam-3142	7	24	centralizing	centralizing	NOUN
ejpam-3142	7	25	,	,	PUNCT
ejpam-3142	7	26	derivations	derivation	NOUN
ejpam-3142	7	27	,	,	PUNCT
ejpam-3142	7	28	generalized	generalized	ADJ
ejpam-3142	7	29	derivations	derivation	NOUN
ejpam-3142	7	30	,	,	PUNCT
ejpam-3142	7	31	commutativity	commutativity	NOUN
ejpam-3142	7	32	1	1	NUM
ejpam-3142	7	33	.	.	PUNCT
ejpam-3142	8	1	introduction	introduction	NOUN
ejpam-3142	8	2	recently	recently	ADV
ejpam-3142	8	3	,	,	PUNCT
ejpam-3142	8	4	a	a	DET
ejpam-3142	8	5	considerable	considerable	ADJ
ejpam-3142	8	6	number	number	NOUN
ejpam-3142	8	7	of	of	ADP
ejpam-3142	8	8	researchers	researcher	NOUN
ejpam-3142	8	9	have	have	AUX
ejpam-3142	8	10	investigated	investigate	VERB
ejpam-3142	8	11	the	the	DET
ejpam-3142	8	12	ideals	ideal	NOUN
ejpam-3142	8	13	in	in	ADP
ejpam-3142	8	14	prime	prime	ADJ
ejpam-3142	8	15	rings	ring	NOUN
ejpam-3142	8	16	as	as	ADV
ejpam-3142	8	17	well	well	ADV
ejpam-3142	8	18	as	as	ADP
ejpam-3142	8	19	the	the	DET
ejpam-3142	8	20	commutativity	commutativity	NOUN
ejpam-3142	8	21	of	of	ADP
ejpam-3142	8	22	prime	prime	ADJ
ejpam-3142	8	23	rings	ring	NOUN
ejpam-3142	8	24	that	that	PRON
ejpam-3142	8	25	consider	consider	VERB
ejpam-3142	8	26	derivations	derivation	NOUN
ejpam-3142	8	27	and	and	CCONJ
ejpam-3142	8	28	generalized	generalized	ADJ
ejpam-3142	8	29	derivations	derivation	NOUN
ejpam-3142	8	30	,	,	PUNCT
ejpam-3142	8	31	see	see	VERB
ejpam-3142	8	32	for	for	ADP
ejpam-3142	8	33	example	example	NOUN
ejpam-3142	8	34	[	[	X
ejpam-3142	8	35	2	2	NUM
ejpam-3142	8	36	]	]	PUNCT
ejpam-3142	8	37	,	,	PUNCT
ejpam-3142	8	38	[	[	X
ejpam-3142	8	39	3	3	NUM
ejpam-3142	8	40	]	]	PUNCT
ejpam-3142	8	41	,	,	PUNCT
ejpam-3142	8	42	[	[	X
ejpam-3142	8	43	5	5	NUM
ejpam-3142	8	44	]	]	PUNCT
ejpam-3142	8	45	and	and	CCONJ
ejpam-3142	8	46	[	[	X
ejpam-3142	8	47	7	7	NUM
ejpam-3142	8	48	]	]	PUNCT
ejpam-3142	8	49	.	.	PUNCT
ejpam-3142	9	1	in	in	ADP
ejpam-3142	9	2	[	[	X
ejpam-3142	9	3	4	4	NUM
ejpam-3142	9	4	]	]	PUNCT
ejpam-3142	9	5	,	,	PUNCT
ejpam-3142	9	6	ashraf	ashraf	PROPN
ejpam-3142	9	7	and	and	CCONJ
ejpam-3142	9	8	khan	khan	PROPN
ejpam-3142	9	9	showed	show	VERB
ejpam-3142	9	10	that	that	SCONJ
ejpam-3142	9	11	a	a	DET
ejpam-3142	9	12	∗-ideal	∗-ideal	NOUN
ejpam-3142	9	13	u	u	NOUN
ejpam-3142	9	14	is	be	AUX
ejpam-3142	9	15	central	central	ADJ
ejpam-3142	9	16	if	if	SCONJ
ejpam-3142	9	17	the	the	DET
ejpam-3142	9	18	ring	ring	NOUN
ejpam-3142	9	19	r	r	NOUN
ejpam-3142	9	20	admits	admit	VERB
ejpam-3142	9	21	a	a	DET
ejpam-3142	9	22	general	general	ADJ
ejpam-3142	9	23	derivation	derivation	NOUN
ejpam-3142	9	24	f	f	PROPN
ejpam-3142	9	25	associated	associate	VERB
ejpam-3142	9	26	with	with	ADP
ejpam-3142	9	27	a	a	DET
ejpam-3142	9	28	derivation	derivation	NOUN
ejpam-3142	9	29	d	d	ADP
ejpam-3142	9	30	satisfying	satisfy	VERB
ejpam-3142	9	31	specific	specific	ADJ
ejpam-3142	9	32	properties	property	NOUN
ejpam-3142	9	33	.	.	PUNCT
ejpam-3142	10	1	in	in	ADP
ejpam-3142	10	2	[	[	X
ejpam-3142	10	3	10	10	NUM
ejpam-3142	10	4	]	]	PUNCT
ejpam-3142	10	5	,	,	PUNCT
ejpam-3142	10	6	el	el	PROPN
ejpam-3142	10	7	-	-	PUNCT
ejpam-3142	10	8	soufi	soufi	PROPN
ejpam-3142	10	9	and	and	CCONJ
ejpam-3142	10	10	aboubakr	aboubakr	PROPN
ejpam-3142	10	11	proved	prove	VERB
ejpam-3142	10	12	that	that	SCONJ
ejpam-3142	10	13	j	j	PROPN
ejpam-3142	10	14	⊆	⊆	NUM
ejpam-3142	10	15	z(r	z(r	NOUN
ejpam-3142	10	16	)	)	PUNCT
ejpam-3142	10	17	under	under	ADP
ejpam-3142	10	18	specific	specific	ADJ
ejpam-3142	10	19	properties	property	NOUN
ejpam-3142	10	20	,	,	PUNCT
ejpam-3142	10	21	where	where	SCONJ
ejpam-3142	10	22	r	r	NOUN
ejpam-3142	10	23	is	be	AUX
ejpam-3142	10	24	a	a	DET
ejpam-3142	10	25	2	2	NUM
ejpam-3142	10	26	-	-	PUNCT
ejpam-3142	10	27	torsion	torsion	NOUN
ejpam-3142	10	28	free	free	ADJ
ejpam-3142	10	29	prime	prime	ADJ
ejpam-3142	10	30	ring	ring	NOUN
ejpam-3142	10	31	with	with	ADP
ejpam-3142	10	32	center	center	NOUN
ejpam-3142	10	33	z(r	z(r	NOUN
ejpam-3142	10	34	)	)	PUNCT
ejpam-3142	10	35	admitting	admit	VERB
ejpam-3142	10	36	a	a	DET
ejpam-3142	10	37	generalized	generalized	ADJ
ejpam-3142	10	38	derivation	derivation	NOUN
ejpam-3142	10	39	f	f	PROPN
ejpam-3142	10	40	associated	associate	VERB
ejpam-3142	10	41	with	with	ADP
ejpam-3142	10	42	a	a	DET
ejpam-3142	10	43	derivation	derivation	NOUN
ejpam-3142	10	44	d	d	NOUN
ejpam-3142	10	45	,	,	PUNCT
ejpam-3142	10	46	j	j	PROPN
ejpam-3142	10	47	is	be	AUX
ejpam-3142	10	48	a	a	DET
ejpam-3142	10	49	nonzero	nonzero	PROPN
ejpam-3142	10	50	jordan	jordan	PROPN
ejpam-3142	10	51	ideal	ideal	PROPN
ejpam-3142	10	52	.	.	PUNCT
ejpam-3142	11	1	in	in	ADP
ejpam-3142	11	2	addition	addition	NOUN
ejpam-3142	11	3	,	,	PUNCT
ejpam-3142	11	4	ibraheem	ibraheem	VERB
ejpam-3142	11	5	in	in	ADP
ejpam-3142	11	6	[	[	X
ejpam-3142	11	7	11	11	NUM
ejpam-3142	11	8	]	]	PUNCT
ejpam-3142	11	9	showed	show	VERB
ejpam-3142	11	10	that	that	SCONJ
ejpam-3142	11	11	if	if	SCONJ
ejpam-3142	11	12	f	f	PROPN
ejpam-3142	11	13	is	be	AUX
ejpam-3142	11	14	a	a	DET
ejpam-3142	11	15	generalized	generalized	ADJ
ejpam-3142	11	16	reverse	reverse	ADJ
ejpam-3142	11	17	derivation	derivation	NOUN
ejpam-3142	11	18	on	on	ADP
ejpam-3142	11	19	r	r	NOUN
ejpam-3142	11	20	such	such	ADJ
ejpam-3142	11	21	that	that	SCONJ
ejpam-3142	11	22	f	f	PROPN
ejpam-3142	11	23	is	be	AUX
ejpam-3142	11	24	commuting	commute	VERB
ejpam-3142	11	25	and	and	CCONJ
ejpam-3142	11	26	centralizing	centralize	VERB
ejpam-3142	11	27	on	on	ADP
ejpam-3142	11	28	a	a	DET
ejpam-3142	11	29	right	right	ADJ
ejpam-3142	11	30	ideal	ideal	NOUN
ejpam-3142	11	31	i	i	PRON
ejpam-3142	11	32	of	of	ADP
ejpam-3142	11	33	r	r	NOUN
ejpam-3142	11	34	,	,	PUNCT
ejpam-3142	11	35	then	then	ADV
ejpam-3142	11	36	r	r	NOUN
ejpam-3142	11	37	is	be	AUX
ejpam-3142	11	38	a	a	DET
ejpam-3142	11	39	commutative	commutative	ADJ
ejpam-3142	11	40	,	,	PUNCT
ejpam-3142	11	41	where	where	SCONJ
ejpam-3142	11	42	r	r	NOUN
ejpam-3142	11	43	is	be	AUX
ejpam-3142	11	44	a	a	DET
ejpam-3142	11	45	prime	prime	ADJ
ejpam-3142	11	46	ring	ring	NOUN
ejpam-3142	11	47	and	and	CCONJ
ejpam-3142	11	48	d	d	NOUN
ejpam-3142	11	49	is	be	AUX
ejpam-3142	11	50	a	a	DET
ejpam-3142	11	51	reverse	reverse	ADJ
ejpam-3142	11	52	derivation	derivation	NOUN
ejpam-3142	11	53	on	on	ADP
ejpam-3142	11	54	r.	r.	PROPN
ejpam-3142	11	55	moreover	moreover	ADV
ejpam-3142	11	56	,	,	PUNCT
ejpam-3142	11	57	in	in	ADP
ejpam-3142	11	58	[	[	PUNCT
ejpam-3142	11	59	1	1	NUM
ejpam-3142	11	60	]	]	PUNCT
ejpam-3142	11	61	,	,	PUNCT
ejpam-3142	11	62	abu	abu	PROPN
ejpam-3142	11	63	nawas	nawas	INTJ
ejpam-3142	11	64	and	and	CCONJ
ejpam-3142	11	65	al	al	PROPN
ejpam-3142	11	66	-	-	PUNCT
ejpam-3142	11	67	omary	omary	NOUN
ejpam-3142	11	68	investigated	investigate	VERB
ejpam-3142	11	69	the	the	DET
ejpam-3142	11	70	commutativity	commutativity	NOUN
ejpam-3142	11	71	of	of	ADP
ejpam-3142	11	72	r	r	NOUN
ejpam-3142	11	73	such	such	ADJ
ejpam-3142	11	74	that	that	SCONJ
ejpam-3142	11	75	r	r	NOUN
ejpam-3142	11	76	is	be	AUX
ejpam-3142	11	77	a	a	DET
ejpam-3142	11	78	∗-prime	∗-prime	ADJ
ejpam-3142	11	79	ring	ring	NOUN
ejpam-3142	11	80	admitting	admit	VERB
ejpam-3142	11	81	∗corresponding	∗corresponde	VERB
ejpam-3142	11	82	author	author	NOUN
ejpam-3142	11	83	.	.	PUNCT
ejpam-3142	12	1	email	email	NOUN
ejpam-3142	12	2	addresses	address	NOUN
ejpam-3142	12	3	:	:	PUNCT
ejpam-3142	12	4	m.abunawas.math.nbu@gmail.com	m.abunawas.math.nbu@gmail.com	X
ejpam-3142	12	5	(	(	PUNCT
ejpam-3142	12	6	m.	m.	NOUN
ejpam-3142	12	7	abu	abu	PROPN
ejpam-3142	12	8	nawas	nawas	PROPN
ejpam-3142	12	9	)	)	PUNCT
ejpam-3142	12	10	,	,	PUNCT
ejpam-3142	12	11	radwan959@yahoo.com	radwan959@yahoo.com	X
ejpam-3142	12	12	(	(	PUNCT
ejpam-3142	12	13	radwan	radwan	VERB
ejpam-3142	12	14	al	al	PROPN
ejpam-3142	12	15	-	-	PUNCT
ejpam-3142	12	16	omary	omary	NOUN
ejpam-3142	12	17	)	)	PUNCT
ejpam-3142	12	18	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3142	13	1	79	79	NUM
ejpam-3142	13	2	c	c	X
ejpam-3142	13	3	©	©	PROPN
ejpam-3142	13	4	2018	2018	NUM
ejpam-3142	13	5	ejpam	ejpam	VERB
ejpam-3142	13	6	all	all	DET
ejpam-3142	13	7	rights	right	NOUN
ejpam-3142	13	8	reserved	reserve	VERB
ejpam-3142	13	9	.	.	PUNCT
ejpam-3142	14	1	m.	m.	NOUN
ejpam-3142	14	2	k.	k.	PROPN
ejpam-3142	15	1	abu	abu	PROPN
ejpam-3142	16	1	nawas	nawas	PROPN
ejpam-3142	16	2	,	,	PUNCT
ejpam-3142	16	3	r.	r.	PROPN
ejpam-3142	16	4	m.	m.	PROPN
ejpam-3142	16	5	al	al	PROPN
ejpam-3142	16	6	-	-	PUNCT
ejpam-3142	16	7	omary	omary	ADJ
ejpam-3142	16	8	/	/	SYM
ejpam-3142	16	9	eur	eur	PROPN
ejpam-3142	16	10	.	.	PUNCT
ejpam-3142	17	1	j.	j.	PROPN
ejpam-3142	17	2	pure	pure	PROPN
ejpam-3142	17	3	appl	appl	PROPN
ejpam-3142	17	4	.	.	PROPN
ejpam-3142	17	5	math	math	PROPN
ejpam-3142	17	6	,	,	PUNCT
ejpam-3142	17	7	11	11	NUM
ejpam-3142	17	8	(	(	PUNCT
ejpam-3142	17	9	1	1	NUM
ejpam-3142	17	10	)	)	PUNCT
ejpam-3142	17	11	(	(	PUNCT
ejpam-3142	17	12	2018	2018	NUM
ejpam-3142	17	13	)	)	PUNCT
ejpam-3142	17	14	,	,	PUNCT
ejpam-3142	17	15	79	79	NUM
ejpam-3142	17	16	-	-	SYM
ejpam-3142	17	17	89	89	NUM
ejpam-3142	17	18	80	80	NUM
ejpam-3142	17	19	generalized	generalized	ADJ
ejpam-3142	17	20	(	(	PUNCT
ejpam-3142	17	21	α	α	NOUN
ejpam-3142	17	22	,	,	PUNCT
ejpam-3142	17	23	β)derivations	β)derivation	NOUN
ejpam-3142	17	24	f	f	NOUN
ejpam-3142	17	25	and	and	CCONJ
ejpam-3142	17	26	g	g	PROPN
ejpam-3142	17	27	associated	associate	VERB
ejpam-3142	17	28	with	with	ADP
ejpam-3142	17	29	(	(	PUNCT
ejpam-3142	17	30	α	α	X
ejpam-3142	17	31	,	,	PUNCT
ejpam-3142	17	32	β)−derivations	β)−derivation	NOUN
ejpam-3142	17	33	d	d	NOUN
ejpam-3142	17	34	and	and	CCONJ
ejpam-3142	17	35	g	g	NOUN
ejpam-3142	17	36	,	,	PUNCT
ejpam-3142	17	37	respectively	respectively	ADV
ejpam-3142	17	38	,	,	PUNCT
ejpam-3142	17	39	that	that	SCONJ
ejpam-3142	17	40	satisfying	satisfy	VERB
ejpam-3142	17	41	certain	certain	ADJ
ejpam-3142	17	42	properties	property	NOUN
ejpam-3142	17	43	.	.	PUNCT
ejpam-3142	18	1	let	let	VERB
ejpam-3142	18	2	r	r	PRON
ejpam-3142	18	3	be	be	AUX
ejpam-3142	18	4	an	an	DET
ejpam-3142	18	5	associative	associative	ADJ
ejpam-3142	18	6	ring	ring	NOUN
ejpam-3142	18	7	with	with	ADP
ejpam-3142	18	8	center	center	NOUN
ejpam-3142	18	9	z(r	z(r	NOUN
ejpam-3142	18	10	)	)	PUNCT
ejpam-3142	18	11	.	.	PUNCT
ejpam-3142	19	1	for	for	ADP
ejpam-3142	19	2	x	x	SYM
ejpam-3142	19	3	,	,	PUNCT
ejpam-3142	19	4	y	y	PROPN
ejpam-3142	19	5	∈	∈	PROPN
ejpam-3142	19	6	r	r	NOUN
ejpam-3142	19	7	denote	denote	VERB
ejpam-3142	19	8	the	the	DET
ejpam-3142	19	9	commutator	commutator	NOUN
ejpam-3142	19	10	xy	xy	PROPN
ejpam-3142	20	1	−	−	PROPN
ejpam-3142	21	1	yx	yx	INTJ
ejpam-3142	21	2	by	by	ADP
ejpam-3142	21	3	[	[	X
ejpam-3142	21	4	x	x	X
ejpam-3142	21	5	,	,	PUNCT
ejpam-3142	21	6	y	y	PROPN
ejpam-3142	21	7	]	]	PUNCT
ejpam-3142	21	8	and	and	CCONJ
ejpam-3142	21	9	the	the	DET
ejpam-3142	21	10	anti	anti	NOUN
ejpam-3142	21	11	-	-	NOUN
ejpam-3142	21	12	commutator	commutator	ADJ
ejpam-3142	21	13	xy	xy	PROPN
ejpam-3142	22	1	+	+	CCONJ
ejpam-3142	22	2	yx	yx	AUX
ejpam-3142	22	3	by	by	ADP
ejpam-3142	22	4	x	x	SYM
ejpam-3142	22	5	◦	◦	NOUN
ejpam-3142	22	6	y.	y.	NOUN
ejpam-3142	22	7	recall	recall	VERB
ejpam-3142	22	8	that	that	SCONJ
ejpam-3142	22	9	a	a	DET
ejpam-3142	22	10	ring	ring	NOUN
ejpam-3142	22	11	r	r	NOUN
ejpam-3142	22	12	is	be	AUX
ejpam-3142	22	13	prime	prime	ADJ
ejpam-3142	22	14	if	if	SCONJ
ejpam-3142	22	15	for	for	ADP
ejpam-3142	22	16	any	any	DET
ejpam-3142	22	17	a	a	NOUN
ejpam-3142	22	18	,	,	PUNCT
ejpam-3142	22	19	b	b	X
ejpam-3142	22	20	∈	∈	PROPN
ejpam-3142	22	21	r	r	NOUN
ejpam-3142	22	22	,	,	PUNCT
ejpam-3142	22	23	arb	arb	NOUN
ejpam-3142	22	24	=	=	PUNCT
ejpam-3142	22	25	{	{	PUNCT
ejpam-3142	22	26	0	0	NUM
ejpam-3142	22	27	}	}	PUNCT
ejpam-3142	22	28	implies	imply	VERB
ejpam-3142	22	29	that	that	SCONJ
ejpam-3142	22	30	a	a	DET
ejpam-3142	22	31	=	=	SYM
ejpam-3142	22	32	0	0	NUM
ejpam-3142	22	33	or	or	CCONJ
ejpam-3142	22	34	b	b	NOUN
ejpam-3142	22	35	=	=	SYM
ejpam-3142	22	36	0	0	PROPN
ejpam-3142	22	37	.	.	PUNCT
ejpam-3142	23	1	an	an	DET
ejpam-3142	23	2	additive	additive	ADJ
ejpam-3142	23	3	mapping	mapping	NOUN
ejpam-3142	23	4	d	d	NOUN
ejpam-3142	23	5	:	:	PUNCT
ejpam-3142	23	6	r	r	NOUN
ejpam-3142	23	7	−→	−→	NOUN
ejpam-3142	23	8	r	r	NOUN
ejpam-3142	23	9	is	be	AUX
ejpam-3142	23	10	called	call	VERB
ejpam-3142	23	11	a	a	DET
ejpam-3142	23	12	derivation	derivation	NOUN
ejpam-3142	23	13	if	if	SCONJ
ejpam-3142	23	14	d(xy	d(xy	NUM
ejpam-3142	23	15	)	)	PUNCT
ejpam-3142	23	16	=	=	SYM
ejpam-3142	23	17	d(x)y+	d(x)y+	X
ejpam-3142	23	18	xd(y	xd(y	NUM
ejpam-3142	23	19	)	)	PUNCT
ejpam-3142	23	20	for	for	ADP
ejpam-3142	23	21	all	all	DET
ejpam-3142	23	22	x	x	NOUN
ejpam-3142	23	23	,	,	PUNCT
ejpam-3142	23	24	y	y	PROPN
ejpam-3142	23	25	∈	∈	PROPN
ejpam-3142	23	26	r.	r.	PROPN
ejpam-3142	23	27	in	in	ADP
ejpam-3142	23	28	particular	particular	ADJ
ejpam-3142	23	29	,	,	PUNCT
ejpam-3142	23	30	for	for	ADP
ejpam-3142	23	31	a	a	DET
ejpam-3142	23	32	fixed	fix	VERB
ejpam-3142	23	33	a	a	DET
ejpam-3142	23	34	∈	∈	PROPN
ejpam-3142	23	35	r	r	NOUN
ejpam-3142	23	36	,	,	PUNCT
ejpam-3142	23	37	the	the	DET
ejpam-3142	23	38	mapping	mapping	NOUN
ejpam-3142	23	39	ia	ia	NOUN
ejpam-3142	23	40	:	:	PUNCT
ejpam-3142	24	1	r	r	NOUN
ejpam-3142	24	2	−→	−→	NOUN
ejpam-3142	24	3	r	r	NOUN
ejpam-3142	24	4	given	give	VERB
ejpam-3142	24	5	by	by	ADP
ejpam-3142	24	6	ia(x	ia(x	NOUN
ejpam-3142	24	7	)	)	PUNCT
ejpam-3142	24	8	=	=	PUNCT
ejpam-3142	25	1	[	[	X
ejpam-3142	25	2	x	x	X
ejpam-3142	25	3	,	,	PUNCT
ejpam-3142	25	4	a	a	PRON
ejpam-3142	25	5	]	]	X
ejpam-3142	25	6	is	be	AUX
ejpam-3142	25	7	a	a	DET
ejpam-3142	25	8	derivation	derivation	NOUN
ejpam-3142	25	9	called	call	VERB
ejpam-3142	25	10	an	an	DET
ejpam-3142	25	11	inner	inner	ADJ
ejpam-3142	25	12	derivation	derivation	NOUN
ejpam-3142	25	13	.	.	PUNCT
ejpam-3142	26	1	an	an	DET
ejpam-3142	26	2	additive	additive	ADJ
ejpam-3142	26	3	mapping	mapping	NOUN
ejpam-3142	26	4	x	x	PUNCT
ejpam-3142	26	5	7→	7→	NUM
ejpam-3142	26	6	x∗	x∗	NOUN
ejpam-3142	26	7	on	on	ADP
ejpam-3142	26	8	a	a	DET
ejpam-3142	26	9	ring	ring	NOUN
ejpam-3142	26	10	r	r	NOUN
ejpam-3142	26	11	is	be	AUX
ejpam-3142	26	12	called	call	VERB
ejpam-3142	26	13	an	an	DET
ejpam-3142	26	14	involution	involution	NOUN
ejpam-3142	26	15	if	if	SCONJ
ejpam-3142	26	16	(	(	PUNCT
ejpam-3142	26	17	x∗)∗	x∗)∗	PROPN
ejpam-3142	26	18	=	=	SYM
ejpam-3142	26	19	x	x	PROPN
ejpam-3142	26	20	and	and	CCONJ
ejpam-3142	26	21	(	(	PUNCT
ejpam-3142	26	22	xy)∗	xy)∗	PUNCT
ejpam-3142	26	23	=	=	SYM
ejpam-3142	26	24	y∗x∗	y∗x∗	NOUN
ejpam-3142	26	25	for	for	ADP
ejpam-3142	26	26	all	all	DET
ejpam-3142	26	27	x	x	NOUN
ejpam-3142	26	28	,	,	PUNCT
ejpam-3142	26	29	y	y	PROPN
ejpam-3142	26	30	∈	∈	PROPN
ejpam-3142	26	31	r.	r.	PROPN
ejpam-3142	26	32	a	a	DET
ejpam-3142	26	33	ring	ring	NOUN
ejpam-3142	26	34	r	r	NOUN
ejpam-3142	26	35	equipped	equip	VERB
ejpam-3142	26	36	with	with	ADP
ejpam-3142	26	37	an	an	DET
ejpam-3142	26	38	involution	involution	NOUN
ejpam-3142	26	39	∗	∗	NOUN
ejpam-3142	26	40	is	be	AUX
ejpam-3142	26	41	said	say	VERB
ejpam-3142	26	42	to	to	PART
ejpam-3142	26	43	be	be	AUX
ejpam-3142	26	44	a	a	DET
ejpam-3142	26	45	∗-prime	∗-prime	ADJ
ejpam-3142	26	46	ring	ring	NOUN
ejpam-3142	26	47	if	if	SCONJ
ejpam-3142	26	48	arb	arb	PROPN
ejpam-3142	26	49	=	=	PUNCT
ejpam-3142	26	50	arb∗	arb∗	PROPN
ejpam-3142	26	51	=	=	SYM
ejpam-3142	26	52	{	{	PUNCT
ejpam-3142	26	53	0	0	NUM
ejpam-3142	26	54	}	}	PUNCT
ejpam-3142	26	55	implies	imply	VERB
ejpam-3142	26	56	a	a	DET
ejpam-3142	26	57	=	=	SYM
ejpam-3142	26	58	0	0	NUM
ejpam-3142	26	59	or	or	CCONJ
ejpam-3142	26	60	b	b	NOUN
ejpam-3142	26	61	=	=	SYM
ejpam-3142	26	62	0	0	NUM
ejpam-3142	26	63	for	for	ADP
ejpam-3142	26	64	any	any	DET
ejpam-3142	26	65	a	a	NOUN
ejpam-3142	26	66	,	,	PUNCT
ejpam-3142	26	67	b	b	PROPN
ejpam-3142	26	68	∈	∈	PROPN
ejpam-3142	26	69	r.	r.	NOUN
ejpam-3142	26	70	an	an	DET
ejpam-3142	26	71	additive	additive	ADJ
ejpam-3142	26	72	function	function	NOUN
ejpam-3142	26	73	f	f	NOUN
ejpam-3142	26	74	:	:	PUNCT
ejpam-3142	26	75	r	r	NOUN
ejpam-3142	26	76	−→	−→	NOUN
ejpam-3142	26	77	r	r	NOUN
ejpam-3142	26	78	is	be	AUX
ejpam-3142	26	79	called	call	VERB
ejpam-3142	26	80	a	a	DET
ejpam-3142	26	81	generalized	generalized	ADJ
ejpam-3142	26	82	inner	inner	ADJ
ejpam-3142	26	83	derivation	derivation	NOUN
ejpam-3142	26	84	if	if	SCONJ
ejpam-3142	26	85	f	f	PROPN
ejpam-3142	26	86	(	(	PUNCT
ejpam-3142	26	87	x	x	X
ejpam-3142	26	88	)	)	PUNCT
ejpam-3142	26	89	=	=	SYM
ejpam-3142	26	90	ax+xb	ax+xb	INTJ
ejpam-3142	26	91	for	for	SCONJ
ejpam-3142	26	92	fixed	fix	VERB
ejpam-3142	26	93	a	a	PRON
ejpam-3142	26	94	,	,	PUNCT
ejpam-3142	26	95	b	b	PROPN
ejpam-3142	26	96	∈	∈	PROPN
ejpam-3142	26	97	r.	r.	PROPN
ejpam-3142	26	98	for	for	ADP
ejpam-3142	26	99	such	such	DET
ejpam-3142	26	100	a	a	DET
ejpam-3142	26	101	mapping	mapping	NOUN
ejpam-3142	26	102	f	f	NOUN
ejpam-3142	26	103	,	,	PUNCT
ejpam-3142	26	104	it	it	PRON
ejpam-3142	26	105	is	be	AUX
ejpam-3142	26	106	easy	easy	ADJ
ejpam-3142	26	107	to	to	PART
ejpam-3142	26	108	see	see	VERB
ejpam-3142	26	109	that	that	SCONJ
ejpam-3142	26	110	f	f	PROPN
ejpam-3142	26	111	(	(	PUNCT
ejpam-3142	26	112	xy	xy	PROPN
ejpam-3142	26	113	)	)	PUNCT
ejpam-3142	27	1	=	=	SYM
ejpam-3142	27	2	xf	xf	PROPN
ejpam-3142	27	3	(	(	PUNCT
ejpam-3142	27	4	y	y	NOUN
ejpam-3142	27	5	)	)	PUNCT
ejpam-3142	27	6	+	+	CCONJ
ejpam-3142	28	1	[	[	X
ejpam-3142	28	2	a	a	X
ejpam-3142	28	3	,	,	PUNCT
ejpam-3142	28	4	x]y	x]y	PROPN
ejpam-3142	28	5	=	=	SYM
ejpam-3142	28	6	xf	xf	PROPN
ejpam-3142	28	7	(	(	PUNCT
ejpam-3142	28	8	y	y	NOUN
ejpam-3142	28	9	)	)	PUNCT
ejpam-3142	28	10	+	+	CCONJ
ejpam-3142	28	11	ia(x)y	ia(x)y	PROPN
ejpam-3142	28	12	for	for	ADP
ejpam-3142	28	13	all	all	DET
ejpam-3142	28	14	x	x	NOUN
ejpam-3142	28	15	,	,	PUNCT
ejpam-3142	28	16	y	y	PROPN
ejpam-3142	28	17	∈	∈	PROPN
ejpam-3142	28	18	r.	r.	NOUN
ejpam-3142	28	19	this	this	DET
ejpam-3142	28	20	observation	observation	NOUN
ejpam-3142	28	21	leads	lead	VERB
ejpam-3142	28	22	to	to	ADP
ejpam-3142	28	23	the	the	DET
ejpam-3142	28	24	following	follow	VERB
ejpam-3142	28	25	definition	definition	NOUN
ejpam-3142	28	26	,	,	PUNCT
ejpam-3142	28	27	given	give	VERB
ejpam-3142	28	28	in	in	ADP
ejpam-3142	28	29	[	[	PUNCT
ejpam-3142	28	30	9	9	NUM
ejpam-3142	28	31	]	]	X
ejpam-3142	28	32	:	:	PUNCT
ejpam-3142	28	33	an	an	DET
ejpam-3142	28	34	additive	additive	ADJ
ejpam-3142	28	35	mapping	mapping	NOUN
ejpam-3142	28	36	f	f	NOUN
ejpam-3142	29	1	:	:	PUNCT
ejpam-3142	29	2	r	r	NOUN
ejpam-3142	29	3	−→	−→	NOUN
ejpam-3142	29	4	r	r	NOUN
ejpam-3142	29	5	is	be	AUX
ejpam-3142	29	6	called	call	VERB
ejpam-3142	29	7	a	a	DET
ejpam-3142	29	8	generalized	generalized	ADJ
ejpam-3142	29	9	derivation	derivation	NOUN
ejpam-3142	29	10	with	with	ADP
ejpam-3142	29	11	associated	associated	ADJ
ejpam-3142	29	12	derivation	derivation	NOUN
ejpam-3142	29	13	d	d	NOUN
ejpam-3142	29	14	if	if	SCONJ
ejpam-3142	29	15	f	f	PROPN
ejpam-3142	29	16	(	(	PUNCT
ejpam-3142	29	17	xy	xy	PROPN
ejpam-3142	29	18	)	)	PUNCT
ejpam-3142	30	1	=	=	SYM
ejpam-3142	30	2	xf	xf	PROPN
ejpam-3142	30	3	(	(	PUNCT
ejpam-3142	30	4	y	y	NOUN
ejpam-3142	30	5	)	)	PUNCT
ejpam-3142	30	6	+	+	CCONJ
ejpam-3142	30	7	d(x)y	d(x)y	PROPN
ejpam-3142	30	8	for	for	ADP
ejpam-3142	30	9	all	all	DET
ejpam-3142	30	10	x	x	NOUN
ejpam-3142	30	11	,	,	PUNCT
ejpam-3142	30	12	y	y	PROPN
ejpam-3142	30	13	∈	∈	PROPN
ejpam-3142	30	14	r.	r.	PROPN
ejpam-3142	30	15	familiar	familiar	ADJ
ejpam-3142	30	16	examples	example	NOUN
ejpam-3142	30	17	of	of	ADP
ejpam-3142	30	18	generalized	generalized	ADJ
ejpam-3142	30	19	derivations	derivation	NOUN
ejpam-3142	30	20	are	be	AUX
ejpam-3142	30	21	derivations	derivation	NOUN
ejpam-3142	30	22	and	and	CCONJ
ejpam-3142	30	23	generalized	generalize	VERB
ejpam-3142	30	24	inner	inner	ADJ
ejpam-3142	30	25	derivations	derivation	NOUN
ejpam-3142	30	26	that	that	PRON
ejpam-3142	30	27	include	include	VERB
ejpam-3142	30	28	left	leave	VERB
ejpam-3142	30	29	multipliers	multiplier	NOUN
ejpam-3142	30	30	and	and	CCONJ
ejpam-3142	30	31	right	right	ADJ
ejpam-3142	30	32	multipliers	multiplier	NOUN
ejpam-3142	30	33	.	.	PUNCT
ejpam-3142	31	1	since	since	SCONJ
ejpam-3142	31	2	the	the	DET
ejpam-3142	31	3	sum	sum	NOUN
ejpam-3142	31	4	of	of	ADP
ejpam-3142	31	5	two	two	NUM
ejpam-3142	31	6	generalized	generalized	ADJ
ejpam-3142	31	7	derivations	derivation	NOUN
ejpam-3142	31	8	is	be	AUX
ejpam-3142	31	9	a	a	DET
ejpam-3142	31	10	generalized	generalized	ADJ
ejpam-3142	31	11	derivation	derivation	NOUN
ejpam-3142	31	12	,	,	PUNCT
ejpam-3142	31	13	every	every	DET
ejpam-3142	31	14	map	map	NOUN
ejpam-3142	31	15	of	of	ADP
ejpam-3142	31	16	the	the	DET
ejpam-3142	31	17	form	form	NOUN
ejpam-3142	31	18	f	f	X
ejpam-3142	31	19	(	(	PUNCT
ejpam-3142	31	20	x	x	X
ejpam-3142	31	21	)	)	PUNCT
ejpam-3142	32	1	=	=	SYM
ejpam-3142	32	2	xc	xc	PROPN
ejpam-3142	32	3	+	+	ADJ
ejpam-3142	32	4	d(x	d(x	PROPN
ejpam-3142	32	5	)	)	PUNCT
ejpam-3142	32	6	,	,	PUNCT
ejpam-3142	32	7	where	where	SCONJ
ejpam-3142	32	8	c	c	PROPN
ejpam-3142	32	9	is	be	AUX
ejpam-3142	32	10	a	a	DET
ejpam-3142	32	11	fixed	fix	VERB
ejpam-3142	32	12	element	element	NOUN
ejpam-3142	32	13	of	of	ADP
ejpam-3142	32	14	r	r	NOUN
ejpam-3142	32	15	and	and	CCONJ
ejpam-3142	32	16	d	d	NOUN
ejpam-3142	32	17	is	be	AUX
ejpam-3142	32	18	a	a	DET
ejpam-3142	32	19	derivation	derivation	NOUN
ejpam-3142	32	20	,	,	PUNCT
ejpam-3142	32	21	is	be	AUX
ejpam-3142	32	22	a	a	DET
ejpam-3142	32	23	generalized	generalized	ADJ
ejpam-3142	32	24	derivation	derivation	NOUN
ejpam-3142	32	25	;	;	PUNCT
ejpam-3142	32	26	and	and	CCONJ
ejpam-3142	32	27	if	if	SCONJ
ejpam-3142	32	28	r	r	NOUN
ejpam-3142	32	29	has	have	VERB
ejpam-3142	32	30	1	1	NUM
ejpam-3142	32	31	,	,	PUNCT
ejpam-3142	32	32	all	all	DET
ejpam-3142	32	33	generalized	generalized	ADJ
ejpam-3142	32	34	derivations	derivation	NOUN
ejpam-3142	32	35	have	have	VERB
ejpam-3142	32	36	this	this	DET
ejpam-3142	32	37	form	form	NOUN
ejpam-3142	32	38	.	.	PUNCT
ejpam-3142	33	1	let	let	VERB
ejpam-3142	33	2	α	α	PRON
ejpam-3142	33	3	and	and	CCONJ
ejpam-3142	33	4	β	β	X
ejpam-3142	33	5	be	be	AUX
ejpam-3142	33	6	endomorphisms	endomorphism	NOUN
ejpam-3142	33	7	of	of	ADP
ejpam-3142	33	8	r.	r.	NOUN
ejpam-3142	33	9	we	we	PRON
ejpam-3142	33	10	shall	shall	AUX
ejpam-3142	33	11	write	write	VERB
ejpam-3142	33	12	for	for	ADP
ejpam-3142	33	13	any	any	DET
ejpam-3142	33	14	pair	pair	NOUN
ejpam-3142	33	15	of	of	ADP
ejpam-3142	33	16	x	x	PRON
ejpam-3142	33	17	,	,	PUNCT
ejpam-3142	33	18	y	y	PROPN
ejpam-3142	33	19	∈	∈	PROPN
ejpam-3142	33	20	r	r	NOUN
ejpam-3142	33	21	,	,	PUNCT
ejpam-3142	33	22	[	[	X
ejpam-3142	33	23	x	x	NOUN
ejpam-3142	33	24	,	,	PUNCT
ejpam-3142	33	25	y]α	y]α	NOUN
ejpam-3142	33	26	,	,	PUNCT
ejpam-3142	33	27	β	β	NOUN
ejpam-3142	33	28	=	=	SYM
ejpam-3142	33	29	xα(y	xα(y	NOUN
ejpam-3142	33	30	)	)	PUNCT
ejpam-3142	34	1	−	−	ADP
ejpam-3142	34	2	β(y)x	β(y)x	PROPN
ejpam-3142	34	3	,	,	PUNCT
ejpam-3142	34	4	(	(	PUNCT
ejpam-3142	34	5	x	x	SYM
ejpam-3142	34	6	◦	◦	NOUN
ejpam-3142	34	7	y)α	y)α	NOUN
ejpam-3142	34	8	,	,	PUNCT
ejpam-3142	34	9	β	β	X
ejpam-3142	34	10	=	=	SYM
ejpam-3142	34	11	xα(y	xα(y	NOUN
ejpam-3142	34	12	)	)	PUNCT
ejpam-3142	35	1	+	+	CCONJ
ejpam-3142	35	2	β(y)x	β(y)x	VERB
ejpam-3142	35	3	an	an	DET
ejpam-3142	35	4	additive	additive	ADJ
ejpam-3142	35	5	map	map	NOUN
ejpam-3142	35	6	d	d	NOUN
ejpam-3142	35	7	:	:	PUNCT
ejpam-3142	35	8	r	r	NOUN
ejpam-3142	35	9	−→	−→	NOUN
ejpam-3142	35	10	r	r	NOUN
ejpam-3142	35	11	is	be	AUX
ejpam-3142	35	12	called	call	VERB
ejpam-3142	35	13	an	an	DET
ejpam-3142	35	14	(	(	PUNCT
ejpam-3142	35	15	α	α	NOUN
ejpam-3142	35	16	,	,	PUNCT
ejpam-3142	35	17	β)-derivation	β)-derivation	PUNCT
ejpam-3142	35	18	if	if	SCONJ
ejpam-3142	35	19	d(xy	d(xy	NUM
ejpam-3142	35	20	)	)	PUNCT
ejpam-3142	35	21	=	=	SYM
ejpam-3142	35	22	d(x)α(y	d(x)α(y	NOUN
ejpam-3142	35	23	)	)	PUNCT
ejpam-3142	35	24	+	+	NUM
ejpam-3142	35	25	β(x)d(y	β(x)d(y	NOUN
ejpam-3142	35	26	)	)	PUNCT
ejpam-3142	35	27	for	for	ADP
ejpam-3142	35	28	all	all	DET
ejpam-3142	35	29	x	x	NOUN
ejpam-3142	35	30	,	,	PUNCT
ejpam-3142	35	31	y	y	PROPN
ejpam-3142	35	32	∈	∈	PROPN
ejpam-3142	35	33	r.	r.	AUX
ejpam-3142	35	34	an	an	DET
ejpam-3142	35	35	additive	additive	ADJ
ejpam-3142	35	36	mapping	mapping	NOUN
ejpam-3142	35	37	f	f	NOUN
ejpam-3142	35	38	:	:	PUNCT
ejpam-3142	35	39	r	r	NOUN
ejpam-3142	35	40	−→	−→	NOUN
ejpam-3142	35	41	r	r	NOUN
ejpam-3142	35	42	is	be	AUX
ejpam-3142	35	43	called	call	VERB
ejpam-3142	35	44	a	a	DET
ejpam-3142	35	45	generalized	generalized	ADJ
ejpam-3142	35	46	(	(	PUNCT
ejpam-3142	35	47	α	α	NOUN
ejpam-3142	35	48	,	,	PUNCT
ejpam-3142	35	49	β)-inner	β)-inner	PUNCT
ejpam-3142	35	50	derivation	derivation	NOUN
ejpam-3142	35	51	if	if	SCONJ
ejpam-3142	35	52	f	f	PROPN
ejpam-3142	35	53	(	(	PUNCT
ejpam-3142	35	54	x	x	X
ejpam-3142	35	55	)	)	PUNCT
ejpam-3142	35	56	=	=	PUNCT
ejpam-3142	35	57	aα(x	aα(x	X
ejpam-3142	35	58	)	)	PUNCT
ejpam-3142	36	1	+	+	CCONJ
ejpam-3142	36	2	β(x)b	β(x)b	PROPN
ejpam-3142	36	3	,	,	PUNCT
ejpam-3142	36	4	for	for	ADP
ejpam-3142	36	5	some	some	DET
ejpam-3142	36	6	fixed	fix	VERB
ejpam-3142	36	7	a	a	PRON
ejpam-3142	36	8	,	,	PUNCT
ejpam-3142	36	9	b	b	X
ejpam-3142	36	10	∈	∈	PROPN
ejpam-3142	36	11	r	r	NOUN
ejpam-3142	36	12	and	and	CCONJ
ejpam-3142	36	13	for	for	ADP
ejpam-3142	36	14	all	all	DET
ejpam-3142	36	15	x	x	PROPN
ejpam-3142	36	16	∈	∈	PROPN
ejpam-3142	36	17	r.	r.	NOUN
ejpam-3142	36	18	an	an	DET
ejpam-3142	36	19	additive	additive	ADJ
ejpam-3142	36	20	map	map	NOUN
ejpam-3142	37	1	f	f	NOUN
ejpam-3142	37	2	:	:	PUNCT
ejpam-3142	37	3	r	r	NOUN
ejpam-3142	37	4	−→	−→	NOUN
ejpam-3142	37	5	r	r	NOUN
ejpam-3142	37	6	is	be	AUX
ejpam-3142	37	7	called	call	VERB
ejpam-3142	37	8	a	a	DET
ejpam-3142	37	9	generalized	generalized	ADJ
ejpam-3142	37	10	(	(	PUNCT
ejpam-3142	37	11	α	α	NOUN
ejpam-3142	37	12	,	,	PUNCT
ejpam-3142	37	13	β)-derivation	β)-derivation	PUNCT
ejpam-3142	37	14	associated	associate	VERB
ejpam-3142	37	15	with	with	ADP
ejpam-3142	37	16	an	an	DET
ejpam-3142	37	17	(	(	PUNCT
ejpam-3142	37	18	α	α	NOUN
ejpam-3142	37	19	,	,	PUNCT
ejpam-3142	37	20	β)-derivation	β)-derivation	PUNCT
ejpam-3142	38	1	d	d	NOUN
ejpam-3142	38	2	:	:	PUNCT
ejpam-3142	38	3	r	r	NOUN
ejpam-3142	38	4	−→	−→	NOUN
ejpam-3142	38	5	r	r	NOUN
ejpam-3142	38	6	if	if	SCONJ
ejpam-3142	38	7	f	f	PROPN
ejpam-3142	38	8	(	(	PUNCT
ejpam-3142	38	9	xy	xy	PROPN
ejpam-3142	38	10	)	)	PUNCT
ejpam-3142	38	11	=	=	SYM
ejpam-3142	38	12	f	f	PROPN
ejpam-3142	38	13	(	(	PUNCT
ejpam-3142	38	14	x)α(y	x)α(y	PROPN
ejpam-3142	38	15	)	)	PUNCT
ejpam-3142	38	16	+	+	NUM
ejpam-3142	38	17	β(x)d(y	β(x)d(y	NOUN
ejpam-3142	38	18	)	)	PUNCT
ejpam-3142	38	19	for	for	ADP
ejpam-3142	38	20	all	all	DET
ejpam-3142	38	21	x	x	NOUN
ejpam-3142	38	22	,	,	PUNCT
ejpam-3142	38	23	y	y	PROPN
ejpam-3142	38	24	∈	∈	PROPN
ejpam-3142	38	25	r.	r.	PROPN
ejpam-3142	38	26	over	over	ADP
ejpam-3142	38	27	the	the	DET
ejpam-3142	38	28	last	last	ADJ
ejpam-3142	38	29	four	four	NUM
ejpam-3142	38	30	decade	decade	NOUN
ejpam-3142	38	31	,	,	PUNCT
ejpam-3142	38	32	several	several	ADJ
ejpam-3142	38	33	authors	author	NOUN
ejpam-3142	38	34	have	have	AUX
ejpam-3142	38	35	proved	prove	VERB
ejpam-3142	38	36	results	result	NOUN
ejpam-3142	38	37	on	on	ADP
ejpam-3142	38	38	commutativity	commutativity	NOUN
ejpam-3142	38	39	of	of	ADP
ejpam-3142	38	40	prime	prime	ADJ
ejpam-3142	38	41	rings	ring	NOUN
ejpam-3142	38	42	or	or	CCONJ
ejpam-3142	38	43	semiprime	semiprime	NOUN
ejpam-3142	38	44	rings	ring	NOUN
ejpam-3142	38	45	that	that	SCONJ
ejpam-3142	38	46	admitting	admit	VERB
ejpam-3142	38	47	automorphisms	automorphism	NOUN
ejpam-3142	38	48	,	,	PUNCT
ejpam-3142	38	49	derivations	derivation	NOUN
ejpam-3142	38	50	or	or	CCONJ
ejpam-3142	38	51	generalized	generalized	ADJ
ejpam-3142	38	52	derivations	derivation	NOUN
ejpam-3142	38	53	which	which	PRON
ejpam-3142	38	54	are	be	AUX
ejpam-3142	38	55	centralizing	centralize	VERB
ejpam-3142	38	56	or	or	CCONJ
ejpam-3142	38	57	commuting	commute	VERB
ejpam-3142	38	58	on	on	ADP
ejpam-3142	38	59	appropriate	appropriate	ADJ
ejpam-3142	38	60	subset	subset	NOUN
ejpam-3142	38	61	of	of	ADP
ejpam-3142	38	62	r	r	NOUN
ejpam-3142	38	63	(	(	PUNCT
ejpam-3142	38	64	see	see	VERB
ejpam-3142	38	65	[	[	X
ejpam-3142	38	66	5	5	NUM
ejpam-3142	38	67	]	]	PUNCT
ejpam-3142	38	68	,	,	PUNCT
ejpam-3142	38	69	[	[	X
ejpam-3142	38	70	8	8	NUM
ejpam-3142	38	71	]	]	PUNCT
ejpam-3142	38	72	,	,	PUNCT
ejpam-3142	38	73	[	[	X
ejpam-3142	38	74	12	12	NUM
ejpam-3142	38	75	]	]	PUNCT
ejpam-3142	38	76	,	,	PUNCT
ejpam-3142	39	1	[	[	X
ejpam-3142	39	2	14]-[16	14]-[16	PROPN
ejpam-3142	39	3	]	]	X
ejpam-3142	39	4	)	)	PUNCT
ejpam-3142	39	5	.	.	PUNCT
ejpam-3142	40	1	in	in	ADP
ejpam-3142	40	2	this	this	DET
ejpam-3142	40	3	paper	paper	NOUN
ejpam-3142	40	4	,	,	PUNCT
ejpam-3142	40	5	we	we	PRON
ejpam-3142	40	6	investigate	investigate	VERB
ejpam-3142	40	7	the	the	DET
ejpam-3142	40	8	commutativity	commutativity	NOUN
ejpam-3142	40	9	of	of	ADP
ejpam-3142	40	10	a	a	DET
ejpam-3142	40	11	prime	prime	ADJ
ejpam-3142	40	12	ring	ring	NOUN
ejpam-3142	40	13	r	r	NOUN
ejpam-3142	40	14	admitting	admit	VERB
ejpam-3142	40	15	generalized	generalized	ADJ
ejpam-3142	40	16	derivations	derivation	NOUN
ejpam-3142	40	17	f	f	NOUN
ejpam-3142	40	18	and	and	CCONJ
ejpam-3142	40	19	g	g	PROPN
ejpam-3142	40	20	satisfying	satisfy	VERB
ejpam-3142	40	21	any	any	DET
ejpam-3142	40	22	one	one	NUM
ejpam-3142	40	23	of	of	ADP
ejpam-3142	40	24	the	the	DET
ejpam-3142	40	25	following	follow	VERB
ejpam-3142	40	26	properties	property	NOUN
ejpam-3142	40	27	:	:	PUNCT
ejpam-3142	40	28	(	(	PUNCT
ejpam-3142	40	29	i	i	NOUN
ejpam-3142	40	30	)	)	PUNCT
ejpam-3142	40	31	f	f	PROPN
ejpam-3142	40	32	(	(	PUNCT
ejpam-3142	40	33	x)	x)	PROPN
ejpam-3142	40	34	◦	◦	NOUN
ejpam-3142	40	35	x	x	SYM
ejpam-3142	40	36	∈	∈	PROPN
ejpam-3142	40	37	z(r	z(r	PROPN
ejpam-3142	40	38	)	)	PUNCT
ejpam-3142	40	39	,	,	PUNCT
ejpam-3142	40	40	(	(	PUNCT
ejpam-3142	40	41	ii	ii	NOUN
ejpam-3142	40	42	)	)	PUNCT
ejpam-3142	41	1	[	[	X
ejpam-3142	41	2	f	f	X
ejpam-3142	41	3	(	(	PUNCT
ejpam-3142	41	4	x	x	NOUN
ejpam-3142	41	5	)	)	PUNCT
ejpam-3142	41	6	,	,	PUNCT
ejpam-3142	41	7	f	f	PROPN
ejpam-3142	41	8	(	(	PUNCT
ejpam-3142	41	9	y)]−f	y)]−f	PROPN
ejpam-3142	41	10	[	[	X
ejpam-3142	41	11	x	x	X
ejpam-3142	41	12	,	,	PUNCT
ejpam-3142	41	13	y	y	PROPN
ejpam-3142	41	14	]	]	X
ejpam-3142	41	15	∈	∈	PROPN
ejpam-3142	41	16	z(r	z(r	PROPN
ejpam-3142	41	17	)	)	PUNCT
ejpam-3142	41	18	,	,	PUNCT
ejpam-3142	41	19	(	(	PUNCT
ejpam-3142	41	20	iii	iii	X
ejpam-3142	41	21	)	)	PUNCT
ejpam-3142	41	22	f	f	NOUN
ejpam-3142	41	23	(	(	PUNCT
ejpam-3142	41	24	x)	x)	PROPN
ejpam-3142	41	25	◦	◦	NOUN
ejpam-3142	41	26	f	f	X
ejpam-3142	41	27	(	(	PUNCT
ejpam-3142	41	28	y)−f	y)−f	PROPN
ejpam-3142	41	29	(	(	PUNCT
ejpam-3142	41	30	x	x	PROPN
ejpam-3142	41	31	◦	◦	NOUN
ejpam-3142	41	32	y	y	NOUN
ejpam-3142	41	33	)	)	PUNCT
ejpam-3142	41	34	∈	∈	PROPN
ejpam-3142	41	35	z(r	z(r	PROPN
ejpam-3142	41	36	)	)	PUNCT
ejpam-3142	41	37	,	,	PUNCT
ejpam-3142	41	38	(	(	PUNCT
ejpam-3142	41	39	iv	iv	X
ejpam-3142	41	40	)	)	PUNCT
ejpam-3142	41	41	f	f	NOUN
ejpam-3142	42	1	[	[	X
ejpam-3142	42	2	x	x	X
ejpam-3142	42	3	,	,	PUNCT
ejpam-3142	42	4	y]+[f	y]+[f	PROPN
ejpam-3142	42	5	(	(	PUNCT
ejpam-3142	42	6	x	x	NOUN
ejpam-3142	42	7	)	)	PUNCT
ejpam-3142	42	8	,	,	PUNCT
ejpam-3142	42	9	y]−	y]−	PRON
ejpam-3142	43	1	[	[	X
ejpam-3142	43	2	f	f	X
ejpam-3142	43	3	(	(	PUNCT
ejpam-3142	43	4	x	x	NOUN
ejpam-3142	43	5	)	)	PUNCT
ejpam-3142	43	6	,	,	PUNCT
ejpam-3142	43	7	f	f	PROPN
ejpam-3142	43	8	(	(	PUNCT
ejpam-3142	43	9	y	y	NOUN
ejpam-3142	43	10	)	)	PUNCT
ejpam-3142	43	11	]	]	PUNCT
ejpam-3142	44	1	∈	∈	PROPN
ejpam-3142	44	2	z(r	z(r	PROPN
ejpam-3142	44	3	)	)	PUNCT
ejpam-3142	44	4	,	,	PUNCT
ejpam-3142	44	5	(	(	PUNCT
ejpam-3142	44	6	v	v	NOUN
ejpam-3142	44	7	)	)	PUNCT
ejpam-3142	44	8	f	f	NOUN
ejpam-3142	44	9	(	(	PUNCT
ejpam-3142	44	10	x	x	SYM
ejpam-3142	44	11	◦	◦	VERB
ejpam-3142	44	12	y	y	NOUN
ejpam-3142	44	13	)	)	PUNCT
ejpam-3142	44	14	−	−	PROPN
ejpam-3142	45	1	[	[	X
ejpam-3142	45	2	x	x	X
ejpam-3142	45	3	,	,	PUNCT
ejpam-3142	45	4	y	y	PROPN
ejpam-3142	45	5	]	]	X
ejpam-3142	45	6	∈	∈	PROPN
ejpam-3142	45	7	z(r	z(r	PROPN
ejpam-3142	45	8	)	)	PUNCT
ejpam-3142	45	9	,	,	PUNCT
ejpam-3142	45	10	(	(	PUNCT
ejpam-3142	45	11	vi	vi	NOUN
ejpam-3142	45	12	)	)	PUNCT
ejpam-3142	45	13	[	[	X
ejpam-3142	45	14	f	f	X
ejpam-3142	45	15	(	(	PUNCT
ejpam-3142	45	16	x	x	NOUN
ejpam-3142	45	17	)	)	PUNCT
ejpam-3142	45	18	,	,	PUNCT
ejpam-3142	45	19	f	f	PROPN
ejpam-3142	45	20	(	(	PUNCT
ejpam-3142	45	21	y	y	PROPN
ejpam-3142	45	22	)	)	PUNCT
ejpam-3142	45	23	]	]	PUNCT
ejpam-3142	46	1	−	−	NOUN
ejpam-3142	46	2	x	x	PUNCT
ejpam-3142	46	3	◦	◦	VERB
ejpam-3142	46	4	y	y	PROPN
ejpam-3142	46	5	∈	∈	PROPN
ejpam-3142	46	6	z(r	z(r	PROPN
ejpam-3142	46	7	)	)	PUNCT
ejpam-3142	46	8	,	,	PUNCT
ejpam-3142	46	9	(	(	PUNCT
ejpam-3142	46	10	vii	vii	PROPN
ejpam-3142	46	11	)	)	PUNCT
ejpam-3142	47	1	[	[	X
ejpam-3142	47	2	f	f	X
ejpam-3142	47	3	(	(	PUNCT
ejpam-3142	47	4	x	x	NOUN
ejpam-3142	47	5	)	)	PUNCT
ejpam-3142	47	6	,	,	PUNCT
ejpam-3142	47	7	g(y)]−	g(y)]−	PROPN
ejpam-3142	48	1	[	[	X
ejpam-3142	48	2	x	x	X
ejpam-3142	48	3	,	,	PUNCT
ejpam-3142	48	4	y	y	PROPN
ejpam-3142	48	5	]	]	X
ejpam-3142	48	6	∈	∈	PROPN
ejpam-3142	48	7	z(r	z(r	PROPN
ejpam-3142	48	8	)	)	PUNCT
ejpam-3142	48	9	,	,	PUNCT
ejpam-3142	48	10	(	(	PUNCT
ejpam-3142	48	11	viii	viii	NOUN
ejpam-3142	48	12	)	)	PUNCT
ejpam-3142	49	1	[	[	X
ejpam-3142	49	2	f	f	X
ejpam-3142	49	3	(	(	PUNCT
ejpam-3142	49	4	x	x	NOUN
ejpam-3142	49	5	)	)	PUNCT
ejpam-3142	49	6	,	,	PUNCT
ejpam-3142	49	7	x]−	x]−	PUNCT
ejpam-3142	50	1	[	[	X
ejpam-3142	50	2	x	x	X
ejpam-3142	50	3	,	,	PUNCT
ejpam-3142	50	4	g(x	g(x	NOUN
ejpam-3142	50	5	)	)	PUNCT
ejpam-3142	50	6	]	]	PUNCT
ejpam-3142	50	7	∈	∈	PROPN
ejpam-3142	50	8	z(r	z(r	PROPN
ejpam-3142	50	9	)	)	PUNCT
ejpam-3142	50	10	and	and	CCONJ
ejpam-3142	50	11	f	f	PROPN
ejpam-3142	50	12	(	(	PUNCT
ejpam-3142	50	13	x	x	X
ejpam-3142	50	14	)	)	PUNCT
ejpam-3142	50	15	◦	◦	NOUN
ejpam-3142	50	16	x−	x−	PROPN
ejpam-3142	50	17	x	x	SYM
ejpam-3142	50	18	◦	◦	NOUN
ejpam-3142	50	19	g(x	g(x	NOUN
ejpam-3142	50	20	)	)	PUNCT
ejpam-3142	50	21	∈	∈	PROPN
ejpam-3142	50	22	z(r	z(r	PROPN
ejpam-3142	50	23	)	)	PUNCT
ejpam-3142	50	24	for	for	ADP
ejpam-3142	50	25	all	all	DET
ejpam-3142	50	26	x	x	NOUN
ejpam-3142	50	27	,	,	PUNCT
ejpam-3142	50	28	y	y	PROPN
ejpam-3142	50	29	in	in	ADP
ejpam-3142	50	30	some	some	DET
ejpam-3142	50	31	appropriate	appropriate	ADJ
ejpam-3142	50	32	subset	subset	NOUN
ejpam-3142	50	33	of	of	ADP
ejpam-3142	50	34	r.	r.	PROPN
ejpam-3142	50	35	some	some	DET
ejpam-3142	50	36	results	result	VERB
ejpam-3142	50	37	on	on	ADP
ejpam-3142	50	38	commutativity	commutativity	NOUN
ejpam-3142	50	39	of	of	ADP
ejpam-3142	50	40	rings	ring	NOUN
ejpam-3142	50	41	with	with	ADP
ejpam-3142	50	42	involutions	involution	NOUN
ejpam-3142	50	43	that	that	PRON
ejpam-3142	50	44	satisfy	satisfy	VERB
ejpam-3142	50	45	certain	certain	ADJ
ejpam-3142	50	46	identities	identity	NOUN
ejpam-3142	50	47	are	be	AUX
ejpam-3142	50	48	also	also	ADV
ejpam-3142	50	49	proved	prove	VERB
ejpam-3142	50	50	.	.	PUNCT
ejpam-3142	51	1	m.	m.	PROPN
ejpam-3142	52	1	k.	k.	PROPN
ejpam-3142	52	2	abu	abu	PROPN
ejpam-3142	53	1	nawas	nawas	PROPN
ejpam-3142	53	2	,	,	PUNCT
ejpam-3142	53	3	r.	r.	PROPN
ejpam-3142	53	4	m.	m.	PROPN
ejpam-3142	53	5	al	al	PROPN
ejpam-3142	53	6	-	-	PUNCT
ejpam-3142	53	7	omary	omary	ADJ
ejpam-3142	53	8	/	/	SYM
ejpam-3142	53	9	eur	eur	PROPN
ejpam-3142	53	10	.	.	PUNCT
ejpam-3142	54	1	j.	j.	PROPN
ejpam-3142	54	2	pure	pure	PROPN
ejpam-3142	54	3	appl	appl	PROPN
ejpam-3142	54	4	.	.	PROPN
ejpam-3142	54	5	math	math	PROPN
ejpam-3142	54	6	,	,	PUNCT
ejpam-3142	54	7	11	11	NUM
ejpam-3142	54	8	(	(	PUNCT
ejpam-3142	54	9	1	1	NUM
ejpam-3142	54	10	)	)	PUNCT
ejpam-3142	54	11	(	(	PUNCT
ejpam-3142	54	12	2018	2018	NUM
ejpam-3142	54	13	)	)	PUNCT
ejpam-3142	54	14	,	,	PUNCT
ejpam-3142	54	15	79	79	NUM
ejpam-3142	54	16	-	-	SYM
ejpam-3142	54	17	89	89	NUM
ejpam-3142	54	18	81	81	NUM
ejpam-3142	54	19	2	2	NUM
ejpam-3142	54	20	.	.	PUNCT
ejpam-3142	54	21	preliminaries	preliminary	NOUN
ejpam-3142	54	22	we	we	PRON
ejpam-3142	54	23	shall	shall	AUX
ejpam-3142	54	24	use	use	VERB
ejpam-3142	54	25	,	,	PUNCT
ejpam-3142	54	26	without	without	ADP
ejpam-3142	54	27	explicit	explicit	ADJ
ejpam-3142	54	28	mention	mention	NOUN
ejpam-3142	54	29	,	,	PUNCT
ejpam-3142	54	30	the	the	DET
ejpam-3142	54	31	following	follow	VERB
ejpam-3142	54	32	basic	basic	ADJ
ejpam-3142	54	33	identities	identity	NOUN
ejpam-3142	54	34	that	that	PRON
ejpam-3142	54	35	hold	hold	VERB
ejpam-3142	54	36	for	for	ADP
ejpam-3142	54	37	any	any	DET
ejpam-3142	54	38	x	x	NOUN
ejpam-3142	54	39	,	,	PUNCT
ejpam-3142	54	40	y	y	PROPN
ejpam-3142	54	41	,	,	PUNCT
ejpam-3142	54	42	z	z	NOUN
ejpam-3142	54	43	∈	∈	PROPN
ejpam-3142	55	1	r	r	NOUN
ejpam-3142	55	2	:	:	PUNCT
ejpam-3142	55	3	[	[	X
ejpam-3142	55	4	xy	xy	X
ejpam-3142	55	5	,	,	PUNCT
ejpam-3142	55	6	z	z	NOUN
ejpam-3142	55	7	]	]	X
ejpam-3142	55	8	=	=	SYM
ejpam-3142	55	9	x[y	x[y	PROPN
ejpam-3142	55	10	,	,	PUNCT
ejpam-3142	55	11	z	z	X
ejpam-3142	55	12	]	]	X
ejpam-3142	56	1	+	+	CCONJ
ejpam-3142	56	2	[	[	X
ejpam-3142	56	3	x	x	X
ejpam-3142	56	4	,	,	PUNCT
ejpam-3142	56	5	z]y	z]y	PRON
ejpam-3142	56	6	;	;	PUNCT
ejpam-3142	56	7	[	[	X
ejpam-3142	56	8	x	x	X
ejpam-3142	56	9	,	,	PUNCT
ejpam-3142	56	10	yz	yz	PROPN
ejpam-3142	56	11	]	]	X
ejpam-3142	56	12	=	=	SYM
ejpam-3142	56	13	y[x	y[x	NOUN
ejpam-3142	56	14	,	,	PUNCT
ejpam-3142	56	15	z	z	X
ejpam-3142	56	16	]	]	X
ejpam-3142	57	1	+	+	CCONJ
ejpam-3142	57	2	[	[	X
ejpam-3142	57	3	x	x	X
ejpam-3142	57	4	,	,	PUNCT
ejpam-3142	57	5	y]z	y]z	NOUN
ejpam-3142	57	6	;	;	PUNCT
ejpam-3142	57	7	x	x	X
ejpam-3142	57	8	◦	◦	NOUN
ejpam-3142	57	9	(	(	PUNCT
ejpam-3142	57	10	yz	yz	NOUN
ejpam-3142	57	11	)	)	PUNCT
ejpam-3142	57	12	=	=	PRON
ejpam-3142	57	13	(	(	PUNCT
ejpam-3142	57	14	x	x	SYM
ejpam-3142	57	15	◦	◦	VERB
ejpam-3142	57	16	y)z	y)z	X
ejpam-3142	57	17	−	−	NOUN
ejpam-3142	57	18	y[x	y[x	NOUN
ejpam-3142	57	19	,	,	PUNCT
ejpam-3142	57	20	z	z	NOUN
ejpam-3142	57	21	]	]	X
ejpam-3142	57	22	=	=	SYM
ejpam-3142	57	23	y(x	y(x	PROPN
ejpam-3142	57	24	◦	◦	NOUN
ejpam-3142	57	25	z	z	NOUN
ejpam-3142	57	26	)	)	PUNCT
ejpam-3142	58	1	+	+	CCONJ
ejpam-3142	59	1	[	[	X
ejpam-3142	59	2	x	x	X
ejpam-3142	59	3	,	,	PUNCT
ejpam-3142	59	4	y]z	y]z	NOUN
ejpam-3142	59	5	;	;	PUNCT
ejpam-3142	59	6	(	(	PUNCT
ejpam-3142	59	7	xy	xy	NOUN
ejpam-3142	59	8	)	)	PUNCT
ejpam-3142	59	9	◦	◦	NOUN
ejpam-3142	59	10	z	z	NOUN
ejpam-3142	59	11	=	=	SYM
ejpam-3142	60	1	x(y	x(y	PUNCT
ejpam-3142	60	2	◦	◦	NOUN
ejpam-3142	60	3	z)−	z)−	PUNCT
ejpam-3142	61	1	[	[	X
ejpam-3142	61	2	x	x	X
ejpam-3142	61	3	,	,	PUNCT
ejpam-3142	61	4	z]y	z]y	NUM
ejpam-3142	61	5	=	=	SYM
ejpam-3142	61	6	(	(	PUNCT
ejpam-3142	61	7	x	x	PART
ejpam-3142	61	8	◦	◦	NOUN
ejpam-3142	61	9	z)y	z)y	NOUN
ejpam-3142	61	10	+	+	CCONJ
ejpam-3142	61	11	x[y	x[y	PROPN
ejpam-3142	61	12	,	,	PUNCT
ejpam-3142	61	13	z	z	X
ejpam-3142	61	14	]	]	X
ejpam-3142	61	15	;	;	PUNCT
ejpam-3142	61	16	[	[	X
ejpam-3142	61	17	xy	xy	INTJ
ejpam-3142	61	18	,	,	PUNCT
ejpam-3142	61	19	z]α	z]α	PROPN
ejpam-3142	61	20	,	,	PUNCT
ejpam-3142	61	21	β	β	X
ejpam-3142	61	22	=	=	SYM
ejpam-3142	61	23	x[y	x[y	PROPN
ejpam-3142	61	24	,	,	PUNCT
ejpam-3142	61	25	z]α	z]α	NUM
ejpam-3142	61	26	,	,	PUNCT
ejpam-3142	61	27	β	β	X
ejpam-3142	61	28	+	+	X
ejpam-3142	62	1	[	[	X
ejpam-3142	62	2	x	x	X
ejpam-3142	62	3	,	,	PUNCT
ejpam-3142	62	4	β(z)]y	β(z)]y	PUNCT
ejpam-3142	62	5	=	=	SYM
ejpam-3142	62	6	x[y	x[y	PROPN
ejpam-3142	62	7	,	,	PUNCT
ejpam-3142	62	8	α(z	α(z	NOUN
ejpam-3142	62	9	)	)	PUNCT
ejpam-3142	62	10	]	]	PUNCT
ejpam-3142	63	1	+	+	CCONJ
ejpam-3142	63	2	[	[	X
ejpam-3142	63	3	x	x	X
ejpam-3142	63	4	,	,	PUNCT
ejpam-3142	63	5	z]α	z]α	NUM
ejpam-3142	63	6	,	,	PUNCT
ejpam-3142	63	7	βy	βy	ADP
ejpam-3142	63	8	;	;	PUNCT
ejpam-3142	63	9	[	[	X
ejpam-3142	63	10	x	x	X
ejpam-3142	63	11	,	,	PUNCT
ejpam-3142	63	12	yz]α	yz]α	PROPN
ejpam-3142	63	13	,	,	PUNCT
ejpam-3142	63	14	β	β	NOUN
ejpam-3142	63	15	=	=	SYM
ejpam-3142	63	16	β(y)[x	β(y)[x	NOUN
ejpam-3142	63	17	,	,	PUNCT
ejpam-3142	63	18	z]α	z]α	PROPN
ejpam-3142	63	19	,	,	PUNCT
ejpam-3142	63	20	β	β	X
ejpam-3142	63	21	+	+	X
ejpam-3142	64	1	[	[	X
ejpam-3142	64	2	x	x	X
ejpam-3142	64	3	,	,	PUNCT
ejpam-3142	64	4	y]α	y]α	NOUN
ejpam-3142	64	5	,	,	PUNCT
ejpam-3142	64	6	βα(z	βα(z	NUM
ejpam-3142	64	7	)	)	PUNCT
ejpam-3142	64	8	;	;	PUNCT
ejpam-3142	64	9	(	(	PUNCT
ejpam-3142	64	10	x	x	X
ejpam-3142	64	11	◦	◦	NOUN
ejpam-3142	64	12	(	(	PUNCT
ejpam-3142	64	13	yz))α	yz))α	PROPN
ejpam-3142	64	14	,	,	PUNCT
ejpam-3142	64	15	β	β	X
ejpam-3142	64	16	=	=	SYM
ejpam-3142	64	17	(	(	PUNCT
ejpam-3142	64	18	x	x	SYM
ejpam-3142	64	19	◦	◦	NOUN
ejpam-3142	64	20	y)α	y)α	NOUN
ejpam-3142	64	21	,	,	PUNCT
ejpam-3142	64	22	βα(z)−	βα(z)−	PUNCT
ejpam-3142	64	23	β(y)[x	β(y)[x	NOUN
ejpam-3142	64	24	,	,	PUNCT
ejpam-3142	64	25	z]α	z]α	PROPN
ejpam-3142	64	26	,	,	PUNCT
ejpam-3142	64	27	β	β	X
ejpam-3142	64	28	=	=	SYM
ejpam-3142	64	29	β(y)(x	β(y)(x	PUNCT
ejpam-3142	64	30	◦	◦	NOUN
ejpam-3142	64	31	z)α	z)α	NOUN
ejpam-3142	64	32	,	,	PUNCT
ejpam-3142	64	33	β	β	X
ejpam-3142	64	34	+	+	X
ejpam-3142	64	35	[	[	X
ejpam-3142	64	36	x	x	X
ejpam-3142	64	37	,	,	PUNCT
ejpam-3142	64	38	y]α	y]α	NOUN
ejpam-3142	64	39	,	,	PUNCT
ejpam-3142	64	40	βα(z	βα(z	NUM
ejpam-3142	64	41	)	)	PUNCT
ejpam-3142	64	42	;	;	PUNCT
ejpam-3142	64	43	(	(	PUNCT
ejpam-3142	64	44	(	(	PUNCT
ejpam-3142	64	45	xy	xy	NOUN
ejpam-3142	64	46	)	)	PUNCT
ejpam-3142	64	47	◦	◦	NOUN
ejpam-3142	64	48	z)α	z)α	NOUN
ejpam-3142	64	49	,	,	PUNCT
ejpam-3142	64	50	β	β	X
ejpam-3142	64	51	=	=	PUNCT
ejpam-3142	64	52	x(y	x(y	PROPN
ejpam-3142	64	53	◦	◦	NOUN
ejpam-3142	64	54	z)α	z)α	PROPN
ejpam-3142	64	55	,	,	PUNCT
ejpam-3142	64	56	β	β	X
ejpam-3142	64	57	−	−	PROPN
ejpam-3142	65	1	[	[	X
ejpam-3142	65	2	x	x	X
ejpam-3142	65	3	,	,	PUNCT
ejpam-3142	65	4	β(z)]y	β(z)]y	PUNCT
ejpam-3142	65	5	=	=	PUNCT
ejpam-3142	65	6	(	(	PUNCT
ejpam-3142	65	7	x	x	SYM
ejpam-3142	65	8	◦	◦	NOUN
ejpam-3142	65	9	z)α	z)α	NUM
ejpam-3142	65	10	,	,	PUNCT
ejpam-3142	65	11	βy	βy	PRON
ejpam-3142	65	12	+	+	ADJ
ejpam-3142	65	13	x[y	x[y	PROPN
ejpam-3142	65	14	,	,	PUNCT
ejpam-3142	65	15	α(z	α(z	NOUN
ejpam-3142	65	16	)	)	PUNCT
ejpam-3142	65	17	]	]	PUNCT
ejpam-3142	65	18	.	.	PUNCT
ejpam-3142	66	1	the	the	DET
ejpam-3142	66	2	following	follow	VERB
ejpam-3142	66	3	results	result	NOUN
ejpam-3142	66	4	are	be	AUX
ejpam-3142	66	5	also	also	ADV
ejpam-3142	66	6	going	go	VERB
ejpam-3142	66	7	to	to	PART
ejpam-3142	66	8	be	be	AUX
ejpam-3142	66	9	used	use	VERB
ejpam-3142	66	10	:	:	PUNCT
ejpam-3142	66	11	remark	remark	VERB
ejpam-3142	66	12	2.1	2.1	NUM
ejpam-3142	66	13	.	.	PUNCT
ejpam-3142	67	1	in	in	ADP
ejpam-3142	67	2	a	a	DET
ejpam-3142	67	3	prime	prime	ADJ
ejpam-3142	67	4	ring	ring	NOUN
ejpam-3142	67	5	,	,	PUNCT
ejpam-3142	67	6	the	the	DET
ejpam-3142	67	7	centralizer	centralizer	NOUN
ejpam-3142	67	8	of	of	ADP
ejpam-3142	67	9	any	any	DET
ejpam-3142	67	10	nonzero	nonzero	ADJ
ejpam-3142	67	11	one	one	NUM
ejpam-3142	67	12	-	-	PUNCT
ejpam-3142	67	13	sided	sided	ADJ
ejpam-3142	67	14	ideal	ideal	NOUN
ejpam-3142	67	15	is	be	AUX
ejpam-3142	67	16	equal	equal	ADJ
ejpam-3142	67	17	to	to	ADP
ejpam-3142	67	18	the	the	DET
ejpam-3142	67	19	center	center	NOUN
ejpam-3142	67	20	of	of	ADP
ejpam-3142	67	21	r	r	NOUN
ejpam-3142	67	22	;	;	PUNCT
ejpam-3142	67	23	in	in	ADP
ejpam-3142	67	24	particular	particular	ADJ
ejpam-3142	67	25	,	,	PUNCT
ejpam-3142	67	26	if	if	SCONJ
ejpam-3142	67	27	r	r	NOUN
ejpam-3142	67	28	has	have	VERB
ejpam-3142	67	29	nonzero	nonzero	ADJ
ejpam-3142	67	30	central	central	ADJ
ejpam-3142	67	31	ideal	ideal	NOUN
ejpam-3142	67	32	,	,	PUNCT
ejpam-3142	67	33	r	r	NOUN
ejpam-3142	67	34	must	must	AUX
ejpam-3142	67	35	be	be	AUX
ejpam-3142	67	36	commutative	commutative	ADJ
ejpam-3142	67	37	.	.	PUNCT
ejpam-3142	68	1	remark	remark	PROPN
ejpam-3142	68	2	2.2	2.2	NUM
ejpam-3142	68	3	.	.	PUNCT
ejpam-3142	69	1	let	let	VERB
ejpam-3142	69	2	r	r	PRON
ejpam-3142	69	3	be	be	AUX
ejpam-3142	69	4	a	a	DET
ejpam-3142	69	5	prime	prime	ADJ
ejpam-3142	69	6	ring	ring	NOUN
ejpam-3142	69	7	.	.	PUNCT
ejpam-3142	70	1	for	for	ADP
ejpam-3142	70	2	a	a	DET
ejpam-3142	70	3	nonzero	nonzero	NOUN
ejpam-3142	70	4	element	element	NOUN
ejpam-3142	70	5	a	a	DET
ejpam-3142	70	6	∈	∈	PROPN
ejpam-3142	70	7	z(r	z(r	PROPN
ejpam-3142	70	8	)	)	PUNCT
ejpam-3142	70	9	,	,	PUNCT
ejpam-3142	70	10	if	if	SCONJ
ejpam-3142	70	11	ab	ab	PROPN
ejpam-3142	70	12	∈	∈	PROPN
ejpam-3142	70	13	z(r	z(r	PROPN
ejpam-3142	70	14	)	)	PUNCT
ejpam-3142	70	15	,	,	PUNCT
ejpam-3142	70	16	then	then	ADV
ejpam-3142	70	17	b	b	X
ejpam-3142	70	18	∈	∈	PROPN
ejpam-3142	70	19	z(r	z(r	PROPN
ejpam-3142	70	20	)	)	PUNCT
ejpam-3142	70	21	.	.	PUNCT
ejpam-3142	71	1	we	we	PRON
ejpam-3142	71	2	begin	begin	VERB
ejpam-3142	71	3	our	our	PRON
ejpam-3142	71	4	discussion	discussion	NOUN
ejpam-3142	71	5	with	with	ADP
ejpam-3142	71	6	the	the	DET
ejpam-3142	71	7	following	follow	VERB
ejpam-3142	71	8	results	result	NOUN
ejpam-3142	71	9	.	.	PUNCT
ejpam-3142	72	1	lemma	lemma	PROPN
ejpam-3142	72	2	2.1	2.1	NUM
ejpam-3142	72	3	.	.	PUNCT
ejpam-3142	73	1	let	let	VERB
ejpam-3142	73	2	r	r	PRON
ejpam-3142	73	3	be	be	AUX
ejpam-3142	73	4	a	a	DET
ejpam-3142	73	5	prime	prime	ADJ
ejpam-3142	73	6	ring	ring	NOUN
ejpam-3142	73	7	.	.	PUNCT
ejpam-3142	74	1	if	if	SCONJ
ejpam-3142	74	2	d	d	NOUN
ejpam-3142	74	3	:	:	PUNCT
ejpam-3142	74	4	r	r	NOUN
ejpam-3142	74	5	−→	−→	NOUN
ejpam-3142	74	6	r	r	NOUN
ejpam-3142	74	7	is	be	AUX
ejpam-3142	74	8	a	a	DET
ejpam-3142	74	9	derivation	derivation	NOUN
ejpam-3142	74	10	on	on	ADP
ejpam-3142	74	11	r	r	NOUN
ejpam-3142	74	12	,	,	PUNCT
ejpam-3142	74	13	then	then	ADV
ejpam-3142	74	14	for	for	ADP
ejpam-3142	74	15	any	any	DET
ejpam-3142	74	16	0	0	NUM
ejpam-3142	74	17	6=	6=	ADP
ejpam-3142	74	18	z	z	PROPN
ejpam-3142	74	19	∈	∈	PROPN
ejpam-3142	74	20	z(r	z(r	PROPN
ejpam-3142	74	21	)	)	PUNCT
ejpam-3142	74	22	,	,	PUNCT
ejpam-3142	74	23	d(z	d(z	PROPN
ejpam-3142	74	24	)	)	PUNCT
ejpam-3142	74	25	∈	∈	PROPN
ejpam-3142	74	26	z(r	z(r	PROPN
ejpam-3142	74	27	)	)	PUNCT
ejpam-3142	74	28	.	.	PUNCT
ejpam-3142	75	1	proof	proof	NOUN
ejpam-3142	75	2	.	.	PUNCT
ejpam-3142	76	1	we	we	PRON
ejpam-3142	76	2	have	have	VERB
ejpam-3142	76	3	0	0	NUM
ejpam-3142	76	4	6=	6=	NUM
ejpam-3142	76	5	z	z	PROPN
ejpam-3142	76	6	∈	∈	PROPN
ejpam-3142	76	7	z(r	z(r	PROPN
ejpam-3142	76	8	)	)	PUNCT
ejpam-3142	76	9	,	,	PUNCT
ejpam-3142	76	10	that	that	PRON
ejpam-3142	76	11	is	be	AUX
ejpam-3142	76	12	[	[	X
ejpam-3142	76	13	z	z	NOUN
ejpam-3142	76	14	,	,	PUNCT
ejpam-3142	76	15	r	r	X
ejpam-3142	76	16	]	]	X
ejpam-3142	76	17	=	=	SYM
ejpam-3142	76	18	0	0	NUM
ejpam-3142	76	19	for	for	ADP
ejpam-3142	76	20	all	all	DET
ejpam-3142	76	21	r	r	NOUN
ejpam-3142	76	22	∈	∈	NOUN
ejpam-3142	76	23	r	r	NOUN
ejpam-3142	76	24	and	and	CCONJ
ejpam-3142	76	25	hence	hence	ADV
ejpam-3142	76	26	d[z	d[z	NOUN
ejpam-3142	76	27	,	,	PUNCT
ejpam-3142	76	28	r	r	NOUN
ejpam-3142	76	29	]	]	X
ejpam-3142	76	30	=	=	SYM
ejpam-3142	76	31	0	0	NUM
ejpam-3142	76	32	,	,	PUNCT
ejpam-3142	76	33	d(zr−	d(zr−	PROPN
ejpam-3142	76	34	rz	rz	NOUN
ejpam-3142	76	35	)	)	PUNCT
ejpam-3142	76	36	=	=	SYM
ejpam-3142	77	1	0	0	NUM
ejpam-3142	77	2	,	,	PUNCT
ejpam-3142	77	3	i.e	i.e	PROPN
ejpam-3142	77	4	d(z)r+	d(z)r+	X
ejpam-3142	77	5	z(d(r)−	z(d(r)−	PROPN
ejpam-3142	77	6	d(r)z−	d(r)z−	PROPN
ejpam-3142	77	7	rd(z	rd(z	PUNCT
ejpam-3142	77	8	)	)	PUNCT
ejpam-3142	77	9	=	=	SYM
ejpam-3142	77	10	0	0	NUM
ejpam-3142	77	11	,	,	PUNCT
ejpam-3142	77	12	that	that	PRON
ejpam-3142	77	13	is	be	AUX
ejpam-3142	77	14	[	[	X
ejpam-3142	77	15	d(z	d(z	NOUN
ejpam-3142	77	16	)	)	PUNCT
ejpam-3142	77	17	,	,	PUNCT
ejpam-3142	78	1	r	r	X
ejpam-3142	78	2	]	]	X
ejpam-3142	78	3	+	+	CCONJ
ejpam-3142	78	4	[	[	X
ejpam-3142	78	5	z	z	NOUN
ejpam-3142	78	6	,	,	PUNCT
ejpam-3142	78	7	d(r	d(r	PROPN
ejpam-3142	78	8	)	)	PUNCT
ejpam-3142	78	9	]	]	PUNCT
ejpam-3142	79	1	=	=	PUNCT
ejpam-3142	79	2	0	0	NUM
ejpam-3142	79	3	,	,	PUNCT
ejpam-3142	79	4	since	since	SCONJ
ejpam-3142	79	5	z	z	PROPN
ejpam-3142	79	6	∈	∈	PROPN
ejpam-3142	79	7	z(r	z(r	PROPN
ejpam-3142	79	8	)	)	PUNCT
ejpam-3142	79	9	so	so	SCONJ
ejpam-3142	79	10	we	we	PRON
ejpam-3142	79	11	get	get	VERB
ejpam-3142	79	12	[	[	X
ejpam-3142	79	13	d(z	d(z	NOUN
ejpam-3142	79	14	)	)	PUNCT
ejpam-3142	79	15	,	,	PUNCT
ejpam-3142	79	16	r	r	X
ejpam-3142	79	17	]	]	X
ejpam-3142	79	18	=	=	SYM
ejpam-3142	79	19	0	0	NUM
ejpam-3142	79	20	for	for	ADP
ejpam-3142	79	21	all	all	DET
ejpam-3142	79	22	r	r	NOUN
ejpam-3142	79	23	∈	∈	NOUN
ejpam-3142	79	24	r	r	NOUN
ejpam-3142	79	25	which	which	PRON
ejpam-3142	79	26	yields	yield	VERB
ejpam-3142	79	27	that	that	SCONJ
ejpam-3142	79	28	d(z	d(z	NOUN
ejpam-3142	79	29	)	)	PUNCT
ejpam-3142	79	30	∈	∈	PROPN
ejpam-3142	79	31	z(r	z(r	PROPN
ejpam-3142	79	32	)	)	PUNCT
ejpam-3142	79	33	.	.	PUNCT
ejpam-3142	80	1	lemma	lemma	PROPN
ejpam-3142	80	2	2.2	2.2	NUM
ejpam-3142	80	3	.	.	PUNCT
ejpam-3142	81	1	[	[	X
ejpam-3142	81	2	[	[	X
ejpam-3142	81	3	6	6	NUM
ejpam-3142	81	4	]	]	PUNCT
ejpam-3142	81	5	,	,	PUNCT
ejpam-3142	81	6	theorem	theorem	VERB
ejpam-3142	81	7	2	2	NUM
ejpam-3142	81	8	]	]	PUNCT
ejpam-3142	81	9	let	let	VERB
ejpam-3142	81	10	r	r	PRON
ejpam-3142	81	11	be	be	AUX
ejpam-3142	81	12	a	a	DET
ejpam-3142	81	13	prime	prime	ADJ
ejpam-3142	81	14	ring	ring	NOUN
ejpam-3142	81	15	and	and	CCONJ
ejpam-3142	81	16	i	i	PRON
ejpam-3142	81	17	a	a	DET
ejpam-3142	81	18	nonzero	nonzero	NOUN
ejpam-3142	81	19	left	leave	VERB
ejpam-3142	81	20	ideal	ideal	NOUN
ejpam-3142	81	21	of	of	ADP
ejpam-3142	81	22	r	r	NOUN
ejpam-3142	81	23	such	such	ADJ
ejpam-3142	81	24	that	that	SCONJ
ejpam-3142	81	25	i	i	PRON
ejpam-3142	81	26	∩z(r	∩z(r	PROPN
ejpam-3142	81	27	)	)	PUNCT
ejpam-3142	81	28	6=	6=	ADP
ejpam-3142	81	29	0	0	X
ejpam-3142	81	30	.	.	PUNCT
ejpam-3142	82	1	if	if	SCONJ
ejpam-3142	82	2	r	r	NOUN
ejpam-3142	82	3	admits	admit	VERB
ejpam-3142	82	4	a	a	DET
ejpam-3142	82	5	generalized	generalized	ADJ
ejpam-3142	82	6	derivation	derivation	NOUN
ejpam-3142	82	7	f	f	PROPN
ejpam-3142	82	8	with	with	ADP
ejpam-3142	82	9	associated	associated	ADJ
ejpam-3142	82	10	derivation	derivation	NOUN
ejpam-3142	82	11	d	d	ADP
ejpam-3142	82	12	such	such	ADJ
ejpam-3142	82	13	that	that	SCONJ
ejpam-3142	82	14	f	f	PROPN
ejpam-3142	82	15	is	be	AUX
ejpam-3142	82	16	centralizing	centralize	VERB
ejpam-3142	82	17	on	on	ADP
ejpam-3142	82	18	i	i	PRON
ejpam-3142	82	19	,	,	PUNCT
ejpam-3142	82	20	then	then	ADV
ejpam-3142	82	21	r	r	NOUN
ejpam-3142	82	22	is	be	AUX
ejpam-3142	82	23	commutative	commutative	ADJ
ejpam-3142	82	24	.	.	PUNCT
ejpam-3142	83	1	lemma	lemma	PROPN
ejpam-3142	83	2	2.3	2.3	NUM
ejpam-3142	83	3	.	.	PUNCT
ejpam-3142	84	1	[	[	X
ejpam-3142	84	2	[	[	X
ejpam-3142	84	3	7	7	NUM
ejpam-3142	84	4	]	]	PUNCT
ejpam-3142	84	5	,	,	PUNCT
ejpam-3142	84	6	theorem	theorem	VERB
ejpam-3142	84	7	4	4	NUM
ejpam-3142	84	8	]	]	PUNCT
ejpam-3142	84	9	let	let	VERB
ejpam-3142	84	10	r	r	PRON
ejpam-3142	84	11	be	be	AUX
ejpam-3142	84	12	a	a	DET
ejpam-3142	84	13	prime	prime	ADJ
ejpam-3142	84	14	ring	ring	NOUN
ejpam-3142	84	15	and	and	CCONJ
ejpam-3142	84	16	i	i	PRON
ejpam-3142	84	17	a	a	DET
ejpam-3142	84	18	nonzero	nonzero	NOUN
ejpam-3142	84	19	left	leave	VERB
ejpam-3142	84	20	ideal	ideal	NOUN
ejpam-3142	84	21	.	.	PUNCT
ejpam-3142	85	1	if	if	SCONJ
ejpam-3142	85	2	r	r	NOUN
ejpam-3142	85	3	admits	admit	VERB
ejpam-3142	85	4	a	a	DET
ejpam-3142	85	5	nonzero	nonzero	ADJ
ejpam-3142	85	6	derivation	derivation	NOUN
ejpam-3142	85	7	d	d	ADP
ejpam-3142	85	8	such	such	ADJ
ejpam-3142	85	9	that	that	SCONJ
ejpam-3142	85	10	[	[	X
ejpam-3142	85	11	d(x	d(x	NOUN
ejpam-3142	85	12	)	)	PUNCT
ejpam-3142	85	13	,	,	PUNCT
ejpam-3142	85	14	x	x	X
ejpam-3142	85	15	]	]	X
ejpam-3142	85	16	∈	∈	PROPN
ejpam-3142	85	17	z(r	z(r	PROPN
ejpam-3142	85	18	)	)	PUNCT
ejpam-3142	85	19	for	for	ADP
ejpam-3142	85	20	all	all	DET
ejpam-3142	85	21	x	x	SYM
ejpam-3142	85	22	∈	∈	PROPN
ejpam-3142	85	23	i	i	PRON
ejpam-3142	85	24	,	,	PUNCT
ejpam-3142	85	25	then	then	ADV
ejpam-3142	85	26	r	r	NOUN
ejpam-3142	85	27	is	be	AUX
ejpam-3142	85	28	commutative	commutative	ADJ
ejpam-3142	85	29	.	.	PUNCT
ejpam-3142	86	1	lemma	lemma	PROPN
ejpam-3142	86	2	2.4	2.4	NUM
ejpam-3142	86	3	.	.	PUNCT
ejpam-3142	87	1	[	[	X
ejpam-3142	87	2	[	[	X
ejpam-3142	87	3	13	13	NUM
ejpam-3142	87	4	]	]	PUNCT
ejpam-3142	87	5	,	,	PUNCT
ejpam-3142	87	6	lemma	lemma	PROPN
ejpam-3142	87	7	2.5	2.5	NUM
ejpam-3142	87	8	]	]	PUNCT
ejpam-3142	87	9	if	if	SCONJ
ejpam-3142	87	10	a	a	DET
ejpam-3142	87	11	prime	prime	ADJ
ejpam-3142	87	12	ring	ring	NOUN
ejpam-3142	87	13	r	r	NOUN
ejpam-3142	87	14	contains	contain	VERB
ejpam-3142	87	15	a	a	DET
ejpam-3142	87	16	nonzero	nonzero	PROPN
ejpam-3142	87	17	commutative	commutative	ADJ
ejpam-3142	87	18	right	right	ADJ
ejpam-3142	87	19	ideal	ideal	NOUN
ejpam-3142	87	20	,	,	PUNCT
ejpam-3142	87	21	then	then	ADV
ejpam-3142	87	22	r	r	NOUN
ejpam-3142	87	23	is	be	AUX
ejpam-3142	87	24	commutative	commutative	ADJ
ejpam-3142	87	25	.	.	PUNCT
ejpam-3142	88	1	lemma	lemma	PROPN
ejpam-3142	88	2	2.5	2.5	NUM
ejpam-3142	88	3	.	.	PUNCT
ejpam-3142	89	1	let	let	VERB
ejpam-3142	89	2	r	r	PRON
ejpam-3142	89	3	be	be	AUX
ejpam-3142	89	4	a	a	DET
ejpam-3142	89	5	prime	prime	ADJ
ejpam-3142	89	6	ring	ring	NOUN
ejpam-3142	89	7	and	and	CCONJ
ejpam-3142	89	8	i	i	PRON
ejpam-3142	89	9	be	be	VERB
ejpam-3142	89	10	a	a	DET
ejpam-3142	89	11	nonzero	nonzero	NOUN
ejpam-3142	89	12	left	leave	VERB
ejpam-3142	89	13	ideal	ideal	NOUN
ejpam-3142	89	14	of	of	ADP
ejpam-3142	89	15	r	r	NOUN
ejpam-3142	89	16	such	such	ADJ
ejpam-3142	89	17	that	that	SCONJ
ejpam-3142	89	18	(	(	PUNCT
ejpam-3142	89	19	a	a	NOUN
ejpam-3142	89	20	)	)	PUNCT
ejpam-3142	89	21	[	[	X
ejpam-3142	89	22	x	x	X
ejpam-3142	89	23	,	,	PUNCT
ejpam-3142	89	24	y	y	PROPN
ejpam-3142	89	25	]	]	X
ejpam-3142	89	26	∈	∈	PROPN
ejpam-3142	89	27	z(r	z(r	PROPN
ejpam-3142	89	28	)	)	PUNCT
ejpam-3142	89	29	for	for	ADP
ejpam-3142	89	30	all	all	DET
ejpam-3142	89	31	x	x	NOUN
ejpam-3142	89	32	,	,	PUNCT
ejpam-3142	89	33	y	y	PROPN
ejpam-3142	89	34	∈	∈	PROPN
ejpam-3142	90	1	i	i	PRON
ejpam-3142	90	2	,	,	PUNCT
ejpam-3142	90	3	or	or	CCONJ
ejpam-3142	90	4	(	(	PUNCT
ejpam-3142	90	5	b	b	NOUN
ejpam-3142	90	6	)	)	PUNCT
ejpam-3142	90	7	x	x	VERB
ejpam-3142	90	8	◦	◦	VERB
ejpam-3142	90	9	y	y	PROPN
ejpam-3142	90	10	∈	∈	PROPN
ejpam-3142	90	11	z(r	z(r	PROPN
ejpam-3142	90	12	)	)	PUNCT
ejpam-3142	90	13	for	for	ADP
ejpam-3142	90	14	all	all	DET
ejpam-3142	90	15	x	x	NOUN
ejpam-3142	90	16	,	,	PUNCT
ejpam-3142	90	17	y	y	PROPN
ejpam-3142	90	18	∈	∈	PROPN
ejpam-3142	90	19	i.	i.	PROPN
ejpam-3142	90	20	m.	m.	PROPN
ejpam-3142	90	21	k.	k.	PROPN
ejpam-3142	91	1	abu	abu	PROPN
ejpam-3142	91	2	nawas	nawas	PROPN
ejpam-3142	91	3	,	,	PUNCT
ejpam-3142	91	4	r.	r.	PROPN
ejpam-3142	91	5	m.	m.	PROPN
ejpam-3142	92	1	al	al	PROPN
ejpam-3142	92	2	-	-	PUNCT
ejpam-3142	92	3	omary	omary	ADJ
ejpam-3142	92	4	/	/	SYM
ejpam-3142	92	5	eur	eur	PROPN
ejpam-3142	92	6	.	.	PUNCT
ejpam-3142	93	1	j.	j.	PROPN
ejpam-3142	93	2	pure	pure	PROPN
ejpam-3142	93	3	appl	appl	PROPN
ejpam-3142	93	4	.	.	PROPN
ejpam-3142	93	5	math	math	PROPN
ejpam-3142	93	6	,	,	PUNCT
ejpam-3142	93	7	11	11	NUM
ejpam-3142	93	8	(	(	PUNCT
ejpam-3142	93	9	1	1	NUM
ejpam-3142	93	10	)	)	PUNCT
ejpam-3142	93	11	(	(	PUNCT
ejpam-3142	93	12	2018	2018	NUM
ejpam-3142	93	13	)	)	PUNCT
ejpam-3142	93	14	,	,	PUNCT
ejpam-3142	93	15	79	79	NUM
ejpam-3142	93	16	-	-	SYM
ejpam-3142	93	17	89	89	NUM
ejpam-3142	93	18	82	82	NUM
ejpam-3142	93	19	then	then	ADV
ejpam-3142	93	20	r	r	NOUN
ejpam-3142	93	21	is	be	AUX
ejpam-3142	93	22	commutative	commutative	ADJ
ejpam-3142	93	23	.	.	PUNCT
ejpam-3142	94	1	proof	proof	NOUN
ejpam-3142	94	2	.	.	PUNCT
ejpam-3142	95	1	(	(	PUNCT
ejpam-3142	95	2	a	a	X
ejpam-3142	95	3	)	)	PUNCT
ejpam-3142	95	4	we	we	PRON
ejpam-3142	95	5	have	have	VERB
ejpam-3142	95	6	[	[	X
ejpam-3142	95	7	x	x	X
ejpam-3142	95	8	,	,	PUNCT
ejpam-3142	95	9	y	y	PROPN
ejpam-3142	95	10	]	]	X
ejpam-3142	95	11	∈	∈	PROPN
ejpam-3142	95	12	z(r	z(r	PROPN
ejpam-3142	95	13	)	)	PUNCT
ejpam-3142	95	14	for	for	ADP
ejpam-3142	95	15	all	all	DET
ejpam-3142	95	16	x	x	NOUN
ejpam-3142	95	17	,	,	PUNCT
ejpam-3142	95	18	y	y	PROPN
ejpam-3142	95	19	∈	∈	PROPN
ejpam-3142	95	20	i.	i.	NOUN
ejpam-3142	95	21	this	this	PRON
ejpam-3142	95	22	implies	imply	VERB
ejpam-3142	95	23	that	that	SCONJ
ejpam-3142	95	24	[	[	X
ejpam-3142	95	25	r	r	X
ejpam-3142	95	26	,	,	PUNCT
ejpam-3142	95	27	[	[	X
ejpam-3142	95	28	x	x	X
ejpam-3142	95	29	,	,	PUNCT
ejpam-3142	95	30	y	y	PROPN
ejpam-3142	95	31	]	]	X
ejpam-3142	95	32	]	]	X
ejpam-3142	95	33	=	=	SYM
ejpam-3142	95	34	0	0	NUM
ejpam-3142	95	35	for	for	ADP
ejpam-3142	95	36	all	all	DET
ejpam-3142	95	37	r	r	PROPN
ejpam-3142	95	38	∈	∈	PROPN
ejpam-3142	95	39	r.	r.	NOUN
ejpam-3142	95	40	replace	replace	NOUN
ejpam-3142	95	41	y	y	PROPN
ejpam-3142	95	42	by	by	ADP
ejpam-3142	95	43	yx	yx	PROPN
ejpam-3142	95	44	in	in	ADP
ejpam-3142	95	45	the	the	DET
ejpam-3142	95	46	above	above	ADJ
ejpam-3142	95	47	relation	relation	NOUN
ejpam-3142	95	48	,	,	PUNCT
ejpam-3142	95	49	to	to	PART
ejpam-3142	95	50	get	get	VERB
ejpam-3142	95	51	[	[	X
ejpam-3142	95	52	r	r	X
ejpam-3142	95	53	,	,	PUNCT
ejpam-3142	95	54	[	[	X
ejpam-3142	95	55	x	x	X
ejpam-3142	95	56	,	,	PUNCT
ejpam-3142	95	57	yx	yx	X
ejpam-3142	95	58	]	]	X
ejpam-3142	95	59	]	]	X
ejpam-3142	95	60	=	=	PUNCT
ejpam-3142	96	1	[	[	X
ejpam-3142	96	2	r	r	X
ejpam-3142	96	3	,	,	PUNCT
ejpam-3142	96	4	[	[	X
ejpam-3142	96	5	x	x	X
ejpam-3142	96	6	,	,	PUNCT
ejpam-3142	96	7	y]x	y]x	NOUN
ejpam-3142	96	8	]	]	X
ejpam-3142	96	9	=	=	PUNCT
ejpam-3142	97	1	[	[	X
ejpam-3142	97	2	x	x	X
ejpam-3142	97	3	,	,	PUNCT
ejpam-3142	97	4	y][r	y][r	PROPN
ejpam-3142	97	5	,	,	PUNCT
ejpam-3142	97	6	x	x	X
ejpam-3142	97	7	]	]	X
ejpam-3142	98	1	+	+	CCONJ
ejpam-3142	98	2	[	[	X
ejpam-3142	98	3	r	r	X
ejpam-3142	98	4	,	,	PUNCT
ejpam-3142	98	5	[	[	X
ejpam-3142	98	6	x	x	X
ejpam-3142	98	7	,	,	PUNCT
ejpam-3142	98	8	y]]x	y]]x	PROPN
ejpam-3142	98	9	=	=	SYM
ejpam-3142	98	10	0	0	NUM
ejpam-3142	98	11	,	,	PUNCT
ejpam-3142	98	12	now	now	ADV
ejpam-3142	98	13	use	use	VERB
ejpam-3142	98	14	the	the	DET
ejpam-3142	98	15	relation	relation	NOUN
ejpam-3142	98	16	[	[	X
ejpam-3142	98	17	r	r	X
ejpam-3142	98	18	,	,	PUNCT
ejpam-3142	98	19	[	[	X
ejpam-3142	98	20	x	x	X
ejpam-3142	98	21	,	,	PUNCT
ejpam-3142	98	22	y	y	PROPN
ejpam-3142	98	23	]	]	X
ejpam-3142	98	24	]	]	X
ejpam-3142	98	25	=	=	SYM
ejpam-3142	98	26	0	0	NUM
ejpam-3142	98	27	,	,	PUNCT
ejpam-3142	98	28	to	to	PART
ejpam-3142	98	29	get	get	VERB
ejpam-3142	98	30	[	[	X
ejpam-3142	98	31	x	x	NOUN
ejpam-3142	98	32	,	,	PUNCT
ejpam-3142	98	33	y][r	y][r	PROPN
ejpam-3142	98	34	,	,	PUNCT
ejpam-3142	98	35	x	x	X
ejpam-3142	98	36	]	]	X
ejpam-3142	98	37	=	=	SYM
ejpam-3142	98	38	0	0	NUM
ejpam-3142	98	39	for	for	SCONJ
ejpam-3142	98	40	all	all	DET
ejpam-3142	98	41	x	x	NOUN
ejpam-3142	98	42	,	,	PUNCT
ejpam-3142	98	43	y	y	PROPN
ejpam-3142	98	44	∈	∈	PROPN
ejpam-3142	98	45	i	i	PRON
ejpam-3142	98	46	,	,	PUNCT
ejpam-3142	98	47	r	r	PROPN
ejpam-3142	98	48	∈	∈	PROPN
ejpam-3142	98	49	r.	r.	NOUN
ejpam-3142	98	50	again	again	ADV
ejpam-3142	98	51	,	,	PUNCT
ejpam-3142	98	52	replace	replace	VERB
ejpam-3142	98	53	r	r	NOUN
ejpam-3142	98	54	by	by	ADP
ejpam-3142	98	55	ry	ry	NOUN
ejpam-3142	98	56	to	to	PART
ejpam-3142	98	57	get	get	VERB
ejpam-3142	98	58	[	[	X
ejpam-3142	98	59	x	x	NOUN
ejpam-3142	98	60	,	,	PUNCT
ejpam-3142	98	61	y]r(−[x	y]r(−[x	PROPN
ejpam-3142	98	62	,	,	PUNCT
ejpam-3142	98	63	y	y	NOUN
ejpam-3142	98	64	]	]	X
ejpam-3142	98	65	)	)	PUNCT
ejpam-3142	98	66	=	=	SYM
ejpam-3142	98	67	{	{	PUNCT
ejpam-3142	98	68	0	0	NUM
ejpam-3142	98	69	}	}	PUNCT
ejpam-3142	98	70	for	for	ADP
ejpam-3142	98	71	all	all	DET
ejpam-3142	98	72	x	x	NOUN
ejpam-3142	98	73	,	,	PUNCT
ejpam-3142	98	74	y	y	PROPN
ejpam-3142	98	75	∈	∈	PROPN
ejpam-3142	98	76	i	i	PRON
ejpam-3142	98	77	and	and	CCONJ
ejpam-3142	98	78	primeness	primeness	NOUN
ejpam-3142	98	79	of	of	ADP
ejpam-3142	98	80	r	r	NOUN
ejpam-3142	98	81	yields	yield	NOUN
ejpam-3142	98	82	that	that	SCONJ
ejpam-3142	98	83	[	[	X
ejpam-3142	98	84	x	x	X
ejpam-3142	98	85	,	,	PUNCT
ejpam-3142	98	86	y	y	PROPN
ejpam-3142	98	87	]	]	X
ejpam-3142	98	88	=	=	SYM
ejpam-3142	98	89	0	0	NUM
ejpam-3142	98	90	for	for	ADP
ejpam-3142	98	91	all	all	DET
ejpam-3142	98	92	x	x	NOUN
ejpam-3142	98	93	,	,	PUNCT
ejpam-3142	98	94	y	y	PROPN
ejpam-3142	98	95	∈	∈	PROPN
ejpam-3142	98	96	i	i	PRON
ejpam-3142	98	97	and	and	CCONJ
ejpam-3142	98	98	hence	hence	ADV
ejpam-3142	98	99	by	by	ADP
ejpam-3142	98	100	lemma	lemma	PROPN
ejpam-3142	98	101	2.4	2.4	NUM
ejpam-3142	98	102	,	,	PUNCT
ejpam-3142	98	103	r	r	NOUN
ejpam-3142	98	104	is	be	AUX
ejpam-3142	98	105	commutative	commutative	ADJ
ejpam-3142	98	106	.	.	PUNCT
ejpam-3142	99	1	(	(	PUNCT
ejpam-3142	99	2	b	b	X
ejpam-3142	99	3	)	)	PUNCT
ejpam-3142	99	4	if	if	SCONJ
ejpam-3142	99	5	x	x	NOUN
ejpam-3142	99	6	◦	◦	VERB
ejpam-3142	99	7	y	y	NOUN
ejpam-3142	99	8	∈	∈	PROPN
ejpam-3142	99	9	z(r	z(r	PROPN
ejpam-3142	99	10	)	)	PUNCT
ejpam-3142	99	11	for	for	ADP
ejpam-3142	99	12	all	all	DET
ejpam-3142	99	13	x	x	NOUN
ejpam-3142	99	14	,	,	PUNCT
ejpam-3142	99	15	y	y	PROPN
ejpam-3142	99	16	∈	∈	PROPN
ejpam-3142	100	1	i	i	PRON
ejpam-3142	100	2	,	,	PUNCT
ejpam-3142	100	3	then	then	ADV
ejpam-3142	100	4	[	[	X
ejpam-3142	100	5	x	x	X
ejpam-3142	100	6	◦	◦	NOUN
ejpam-3142	100	7	y	y	PROPN
ejpam-3142	100	8	,	,	PUNCT
ejpam-3142	100	9	r	r	X
ejpam-3142	100	10	]	]	X
ejpam-3142	100	11	=	=	SYM
ejpam-3142	100	12	0	0	NUM
ejpam-3142	100	13	for	for	ADP
ejpam-3142	100	14	all	all	DET
ejpam-3142	100	15	r	r	PROPN
ejpam-3142	100	16	∈	∈	PROPN
ejpam-3142	100	17	r.	r.	NOUN
ejpam-3142	100	18	replacing	replace	VERB
ejpam-3142	100	19	y	y	PRON
ejpam-3142	100	20	by	by	ADP
ejpam-3142	100	21	yx	yx	NOUN
ejpam-3142	100	22	we	we	PRON
ejpam-3142	100	23	find	find	VERB
ejpam-3142	100	24	that	that	SCONJ
ejpam-3142	100	25	(	(	PUNCT
ejpam-3142	100	26	x	x	X
ejpam-3142	100	27	◦	◦	NOUN
ejpam-3142	100	28	y)[x	y)[x	NOUN
ejpam-3142	100	29	,	,	PUNCT
ejpam-3142	100	30	r	r	NOUN
ejpam-3142	100	31	]	]	X
ejpam-3142	100	32	=	=	SYM
ejpam-3142	100	33	0	0	X
ejpam-3142	100	34	.	.	PUNCT
ejpam-3142	101	1	for	for	ADP
ejpam-3142	101	2	any	any	DET
ejpam-3142	101	3	s	s	X
ejpam-3142	101	4	∈	∈	PROPN
ejpam-3142	101	5	r	r	NOUN
ejpam-3142	101	6	,	,	PUNCT
ejpam-3142	101	7	replace	replace	VERB
ejpam-3142	101	8	r	r	NOUN
ejpam-3142	101	9	by	by	ADP
ejpam-3142	101	10	sr	sr	PROPN
ejpam-3142	101	11	to	to	PART
ejpam-3142	101	12	get	get	VERB
ejpam-3142	101	13	(	(	PUNCT
ejpam-3142	101	14	x	x	NOUN
ejpam-3142	101	15	◦	◦	NOUN
ejpam-3142	101	16	y)r[x	y)r[x	NOUN
ejpam-3142	101	17	,	,	PUNCT
ejpam-3142	101	18	r	r	X
ejpam-3142	101	19	]	]	X
ejpam-3142	101	20	=	=	PUNCT
ejpam-3142	101	21	{	{	PUNCT
ejpam-3142	101	22	0	0	NUM
ejpam-3142	101	23	}	}	PUNCT
ejpam-3142	101	24	.	.	PUNCT
ejpam-3142	102	1	thus	thus	ADV
ejpam-3142	102	2	,	,	PUNCT
ejpam-3142	102	3	for	for	SCONJ
ejpam-3142	102	4	each	each	DET
ejpam-3142	102	5	x	x	SYM
ejpam-3142	102	6	∈	∈	PROPN
ejpam-3142	102	7	i	i	PRON
ejpam-3142	102	8	either	either	CCONJ
ejpam-3142	102	9	x	x	VERB
ejpam-3142	102	10	◦	◦	NOUN
ejpam-3142	102	11	y	y	NOUN
ejpam-3142	102	12	=	=	SYM
ejpam-3142	102	13	0	0	NUM
ejpam-3142	102	14	or	or	CCONJ
ejpam-3142	102	15	[	[	X
ejpam-3142	102	16	x	x	X
ejpam-3142	102	17	,	,	PUNCT
ejpam-3142	102	18	r	r	X
ejpam-3142	102	19	]	]	X
ejpam-3142	102	20	=	=	SYM
ejpam-3142	102	21	0	0	X
ejpam-3142	102	22	.	.	PUNCT
ejpam-3142	103	1	let	let	VERB
ejpam-3142	103	2	a	a	DET
ejpam-3142	103	3	=	=	SYM
ejpam-3142	103	4	{	{	PUNCT
ejpam-3142	103	5	x	x	SYM
ejpam-3142	103	6	∈	∈	PROPN
ejpam-3142	104	1	i	i	PRON
ejpam-3142	104	2	|	|	ADV
ejpam-3142	104	3	x	x	VERB
ejpam-3142	104	4	◦	◦	NOUN
ejpam-3142	104	5	y	y	NOUN
ejpam-3142	104	6	=	=	NOUN
ejpam-3142	104	7	0	0	NUM
ejpam-3142	104	8	for	for	ADP
ejpam-3142	104	9	all	all	DET
ejpam-3142	104	10	y	y	PROPN
ejpam-3142	104	11	∈	∈	PROPN
ejpam-3142	104	12	i	i	X
ejpam-3142	104	13	}	}	PUNCT
ejpam-3142	104	14	,	,	PUNCT
ejpam-3142	104	15	b	b	X
ejpam-3142	104	16	=	=	PRON
ejpam-3142	104	17	{	{	PUNCT
ejpam-3142	104	18	x	x	SYM
ejpam-3142	104	19	∈	∈	PROPN
ejpam-3142	105	1	i	i	PRON
ejpam-3142	105	2	|	|	ADV
ejpam-3142	106	1	[	[	X
ejpam-3142	106	2	x	x	X
ejpam-3142	106	3	,	,	PUNCT
ejpam-3142	106	4	r	r	X
ejpam-3142	106	5	]	]	X
ejpam-3142	106	6	=	=	SYM
ejpam-3142	106	7	0	0	NUM
ejpam-3142	106	8	for	for	ADP
ejpam-3142	106	9	all	all	DET
ejpam-3142	106	10	r	r	NOUN
ejpam-3142	106	11	∈	∈	NOUN
ejpam-3142	106	12	r	r	NOUN
ejpam-3142	106	13	}	}	PUNCT
ejpam-3142	106	14	.	.	PUNCT
ejpam-3142	107	1	then	then	ADV
ejpam-3142	107	2	a	a	PRON
ejpam-3142	107	3	and	and	CCONJ
ejpam-3142	107	4	b	b	NOUN
ejpam-3142	107	5	are	be	AUX
ejpam-3142	107	6	additive	additive	ADJ
ejpam-3142	107	7	subgroups	subgroup	NOUN
ejpam-3142	107	8	of	of	ADP
ejpam-3142	107	9	i	i	PRON
ejpam-3142	107	10	whose	whose	DET
ejpam-3142	107	11	union	union	NOUN
ejpam-3142	107	12	is	be	AUX
ejpam-3142	107	13	i.	i.	PROPN
ejpam-3142	107	14	but	but	CCONJ
ejpam-3142	107	15	a	a	DET
ejpam-3142	107	16	group	group	NOUN
ejpam-3142	107	17	can	can	AUX
ejpam-3142	107	18	not	not	PART
ejpam-3142	107	19	be	be	AUX
ejpam-3142	107	20	the	the	DET
ejpam-3142	107	21	union	union	NOUN
ejpam-3142	107	22	of	of	ADP
ejpam-3142	107	23	two	two	NUM
ejpam-3142	107	24	proper	proper	ADJ
ejpam-3142	107	25	subgroups	subgroup	NOUN
ejpam-3142	107	26	and	and	CCONJ
ejpam-3142	108	1	hence	hence	ADV
ejpam-3142	108	2	either	either	CCONJ
ejpam-3142	108	3	x	x	PUNCT
ejpam-3142	108	4	◦	◦	NOUN
ejpam-3142	108	5	y	y	NOUN
ejpam-3142	108	6	=	=	NOUN
ejpam-3142	108	7	0	0	NUM
ejpam-3142	108	8	for	for	ADP
ejpam-3142	108	9	all	all	DET
ejpam-3142	108	10	x	x	NOUN
ejpam-3142	108	11	,	,	PUNCT
ejpam-3142	108	12	y	y	PROPN
ejpam-3142	108	13	∈	∈	PROPN
ejpam-3142	108	14	i	i	PRON
ejpam-3142	108	15	or	or	CCONJ
ejpam-3142	108	16	[	[	X
ejpam-3142	108	17	x	x	X
ejpam-3142	108	18	,	,	PUNCT
ejpam-3142	108	19	r	r	X
ejpam-3142	108	20	]	]	X
ejpam-3142	108	21	=	=	SYM
ejpam-3142	108	22	0	0	NUM
ejpam-3142	108	23	for	for	ADP
ejpam-3142	108	24	all	all	PRON
ejpam-3142	108	25	x	x	SYM
ejpam-3142	108	26	∈	∈	PROPN
ejpam-3142	109	1	i	i	PRON
ejpam-3142	109	2	and	and	CCONJ
ejpam-3142	109	3	r	r	PROPN
ejpam-3142	109	4	∈	∈	PROPN
ejpam-3142	109	5	r.	r.	NOUN
ejpam-3142	109	6	if	if	SCONJ
ejpam-3142	109	7	x	x	SYM
ejpam-3142	109	8	◦	◦	VERB
ejpam-3142	109	9	y	y	NOUN
ejpam-3142	109	10	=	=	SYM
ejpam-3142	109	11	0	0	PROPN
ejpam-3142	109	12	,	,	PUNCT
ejpam-3142	109	13	then	then	ADV
ejpam-3142	109	14	replace	replace	VERB
ejpam-3142	109	15	y	y	PROPN
ejpam-3142	109	16	by	by	ADP
ejpam-3142	109	17	ry	ry	INTJ
ejpam-3142	109	18	we	we	PRON
ejpam-3142	109	19	obtain	obtain	VERB
ejpam-3142	109	20	[	[	X
ejpam-3142	109	21	x	x	NOUN
ejpam-3142	109	22	,	,	PUNCT
ejpam-3142	109	23	r]y	r]y	ADJ
ejpam-3142	109	24	=	=	NOUN
ejpam-3142	109	25	0	0	NUM
ejpam-3142	109	26	for	for	ADP
ejpam-3142	109	27	all	all	DET
ejpam-3142	109	28	x	x	NOUN
ejpam-3142	109	29	,	,	PUNCT
ejpam-3142	109	30	y	y	PROPN
ejpam-3142	109	31	∈	∈	PROPN
ejpam-3142	110	1	i	i	PRON
ejpam-3142	110	2	and	and	CCONJ
ejpam-3142	110	3	r	r	NOUN
ejpam-3142	110	4	∈	∈	PROPN
ejpam-3142	110	5	r	r	NOUN
ejpam-3142	110	6	,	,	PUNCT
ejpam-3142	110	7	that	that	PRON
ejpam-3142	110	8	is	be	AUX
ejpam-3142	110	9	[	[	X
ejpam-3142	110	10	x	x	NOUN
ejpam-3142	110	11	,	,	PUNCT
ejpam-3142	110	12	r]i	r]i	NOUN
ejpam-3142	110	13	=	=	PUNCT
ejpam-3142	110	14	{	{	PUNCT
ejpam-3142	110	15	0	0	NUM
ejpam-3142	110	16	}	}	PUNCT
ejpam-3142	110	17	.	.	PUNCT
ejpam-3142	111	1	since	since	SCONJ
ejpam-3142	111	2	i	i	PRON
ejpam-3142	111	3	6=	6=	PROPN
ejpam-3142	111	4	0	0	NUM
ejpam-3142	111	5	,	,	PUNCT
ejpam-3142	111	6	we	we	PRON
ejpam-3142	111	7	get	get	VERB
ejpam-3142	111	8	[	[	X
ejpam-3142	111	9	x	x	NOUN
ejpam-3142	111	10	,	,	PUNCT
ejpam-3142	111	11	r	r	X
ejpam-3142	111	12	]	]	X
ejpam-3142	111	13	=	=	SYM
ejpam-3142	111	14	0	0	NUM
ejpam-3142	111	15	for	for	ADP
ejpam-3142	111	16	all	all	PRON
ejpam-3142	111	17	x	x	SYM
ejpam-3142	111	18	∈	∈	PROPN
ejpam-3142	111	19	i	i	PRON
ejpam-3142	111	20	and	and	CCONJ
ejpam-3142	111	21	r	r	NOUN
ejpam-3142	111	22	∈	∈	NOUN
ejpam-3142	111	23	r	r	NOUN
ejpam-3142	111	24	and	and	CCONJ
ejpam-3142	111	25	both	both	DET
ejpam-3142	111	26	the	the	DET
ejpam-3142	111	27	cases	case	NOUN
ejpam-3142	111	28	we	we	PRON
ejpam-3142	111	29	find	find	VERB
ejpam-3142	111	30	that	that	SCONJ
ejpam-3142	111	31	i	i	PRON
ejpam-3142	111	32	is	be	AUX
ejpam-3142	111	33	central	central	ADJ
ejpam-3142	111	34	and	and	CCONJ
ejpam-3142	111	35	hence	hence	ADV
ejpam-3142	111	36	by	by	ADP
ejpam-3142	111	37	remark	remark	NOUN
ejpam-3142	111	38	2.1	2.1	NUM
ejpam-3142	111	39	,	,	PUNCT
ejpam-3142	111	40	r	r	NOUN
ejpam-3142	111	41	is	be	AUX
ejpam-3142	111	42	commutative	commutative	ADJ
ejpam-3142	111	43	.	.	PUNCT
ejpam-3142	112	1	3	3	X
ejpam-3142	112	2	.	.	X
ejpam-3142	112	3	main	main	ADJ
ejpam-3142	112	4	results	result	NOUN
ejpam-3142	112	5	theorem	theorem	VERB
ejpam-3142	112	6	3.1	3.1	NUM
ejpam-3142	112	7	.	.	PUNCT
ejpam-3142	113	1	let	let	AUX
ejpam-3142	113	2	r	r	PRON
ejpam-3142	113	3	be	be	AUX
ejpam-3142	113	4	a	a	DET
ejpam-3142	113	5	prime	prime	ADJ
ejpam-3142	113	6	ring	ring	NOUN
ejpam-3142	113	7	and	and	CCONJ
ejpam-3142	113	8	i	i	PRON
ejpam-3142	113	9	a	a	DET
ejpam-3142	113	10	nonzero	nonzero	NOUN
ejpam-3142	113	11	left	leave	VERB
ejpam-3142	113	12	ideal	ideal	NOUN
ejpam-3142	113	13	of	of	ADP
ejpam-3142	113	14	r.	r.	PROPN
ejpam-3142	113	15	suppose	suppose	VERB
ejpam-3142	113	16	that	that	SCONJ
ejpam-3142	113	17	r	r	NOUN
ejpam-3142	113	18	admits	admit	VERB
ejpam-3142	113	19	a	a	DET
ejpam-3142	113	20	generalized	generalized	ADJ
ejpam-3142	113	21	derivation	derivation	NOUN
ejpam-3142	113	22	f	f	PROPN
ejpam-3142	113	23	with	with	ADP
ejpam-3142	113	24	associated	associated	ADJ
ejpam-3142	113	25	derivation	derivation	NOUN
ejpam-3142	113	26	d	d	NOUN
ejpam-3142	113	27	of	of	ADP
ejpam-3142	113	28	r	r	NOUN
ejpam-3142	113	29	such	such	ADJ
ejpam-3142	113	30	that	that	DET
ejpam-3142	113	31	d(z(r	d(z(r	PROPN
ejpam-3142	113	32	)	)	PUNCT
ejpam-3142	113	33	)	)	PUNCT
ejpam-3142	114	1	6=	6=	ADP
ejpam-3142	114	2	0	0	X
ejpam-3142	114	3	.	.	PUNCT
ejpam-3142	115	1	further	far	ADV
ejpam-3142	115	2	,	,	PUNCT
ejpam-3142	115	3	if	if	SCONJ
ejpam-3142	115	4	r	r	NOUN
ejpam-3142	115	5	satisfies	satisfy	VERB
ejpam-3142	115	6	the	the	DET
ejpam-3142	115	7	condition	condition	NOUN
ejpam-3142	115	8	f	f	X
ejpam-3142	115	9	(	(	PUNCT
ejpam-3142	115	10	x)	x)	PROPN
ejpam-3142	115	11	◦	◦	NOUN
ejpam-3142	115	12	x	x	SYM
ejpam-3142	115	13	∈	∈	NOUN
ejpam-3142	115	14	z(r	z(r	PROPN
ejpam-3142	115	15	)	)	PUNCT
ejpam-3142	115	16	for	for	ADP
ejpam-3142	115	17	all	all	DET
ejpam-3142	115	18	x	x	SYM
ejpam-3142	115	19	∈	∈	PROPN
ejpam-3142	115	20	i	i	PRON
ejpam-3142	115	21	,	,	PUNCT
ejpam-3142	115	22	then	then	ADV
ejpam-3142	115	23	r	r	NOUN
ejpam-3142	115	24	is	be	AUX
ejpam-3142	115	25	commutative	commutative	ADJ
ejpam-3142	115	26	.	.	PUNCT
ejpam-3142	116	1	proof	proof	NOUN
ejpam-3142	116	2	.	.	PUNCT
ejpam-3142	117	1	by	by	ADP
ejpam-3142	117	2	hypothesis	hypothesis	NOUN
ejpam-3142	117	3	we	we	PRON
ejpam-3142	117	4	have	have	VERB
ejpam-3142	117	5	f	f	PROPN
ejpam-3142	117	6	(	(	PUNCT
ejpam-3142	117	7	x	x	NOUN
ejpam-3142	117	8	)	)	PUNCT
ejpam-3142	117	9	◦	◦	NOUN
ejpam-3142	117	10	x	x	SYM
ejpam-3142	117	11	∈	∈	PROPN
ejpam-3142	117	12	z(r	z(r	PROPN
ejpam-3142	117	13	)	)	PUNCT
ejpam-3142	117	14	for	for	ADP
ejpam-3142	117	15	all	all	DET
ejpam-3142	117	16	x	x	SYM
ejpam-3142	117	17	∈	∈	PROPN
ejpam-3142	117	18	i.	i.	NOUN
ejpam-3142	117	19	replace	replace	NOUN
ejpam-3142	117	20	x	x	PUNCT
ejpam-3142	117	21	by	by	ADP
ejpam-3142	117	22	x	x	PROPN
ejpam-3142	117	23	+	+	NUM
ejpam-3142	117	24	y	y	NOUN
ejpam-3142	117	25	,	,	PUNCT
ejpam-3142	117	26	to	to	PART
ejpam-3142	117	27	get	get	VERB
ejpam-3142	117	28	f	f	PROPN
ejpam-3142	117	29	(	(	PUNCT
ejpam-3142	117	30	x	x	NOUN
ejpam-3142	117	31	)	)	PUNCT
ejpam-3142	117	32	◦	◦	NOUN
ejpam-3142	117	33	y	y	PROPN
ejpam-3142	118	1	+	+	NUM
ejpam-3142	118	2	f	f	X
ejpam-3142	118	3	(	(	PUNCT
ejpam-3142	118	4	y	y	NOUN
ejpam-3142	118	5	)	)	PUNCT
ejpam-3142	118	6	◦	◦	NOUN
ejpam-3142	118	7	x	x	SYM
ejpam-3142	118	8	∈	∈	PROPN
ejpam-3142	118	9	z(r	z(r	PROPN
ejpam-3142	118	10	)	)	PUNCT
ejpam-3142	118	11	for	for	ADP
ejpam-3142	118	12	all	all	DET
ejpam-3142	118	13	x	x	NOUN
ejpam-3142	118	14	,	,	PUNCT
ejpam-3142	118	15	y	y	PROPN
ejpam-3142	118	16	∈	∈	PROPN
ejpam-3142	118	17	i.	i.	NOUN
ejpam-3142	118	18	(	(	PUNCT
ejpam-3142	118	19	1	1	NUM
ejpam-3142	118	20	)	)	PUNCT
ejpam-3142	118	21	since	since	SCONJ
ejpam-3142	118	22	d(z(r	d(z(r	PROPN
ejpam-3142	118	23	)	)	PUNCT
ejpam-3142	118	24	)	)	PUNCT
ejpam-3142	118	25	6=	6=	ADP
ejpam-3142	118	26	0	0	NUM
ejpam-3142	118	27	,	,	PUNCT
ejpam-3142	118	28	then	then	ADV
ejpam-3142	118	29	there	there	PRON
ejpam-3142	118	30	exists	exist	VERB
ejpam-3142	118	31	z	z	PROPN
ejpam-3142	118	32	∈	∈	PROPN
ejpam-3142	118	33	z(r	z(r	PROPN
ejpam-3142	118	34	)	)	PUNCT
ejpam-3142	119	1	such	such	ADJ
ejpam-3142	119	2	that	that	SCONJ
ejpam-3142	119	3	d(z	d(z	NOUN
ejpam-3142	119	4	)	)	PUNCT
ejpam-3142	119	5	6=	6=	ADP
ejpam-3142	119	6	0	0	X
ejpam-3142	119	7	.	.	PUNCT
ejpam-3142	119	8	replace	replace	VERB
ejpam-3142	119	9	y	y	PROPN
ejpam-3142	119	10	by	by	ADP
ejpam-3142	119	11	zy	zy	PROPN
ejpam-3142	119	12	in	in	ADP
ejpam-3142	119	13	(	(	PUNCT
ejpam-3142	119	14	1	1	NUM
ejpam-3142	119	15	)	)	PUNCT
ejpam-3142	119	16	and	and	CCONJ
ejpam-3142	119	17	using	use	VERB
ejpam-3142	119	18	(	(	PUNCT
ejpam-3142	119	19	1	1	NUM
ejpam-3142	119	20	)	)	PUNCT
ejpam-3142	119	21	,	,	PUNCT
ejpam-3142	119	22	we	we	PRON
ejpam-3142	119	23	get	get	VERB
ejpam-3142	119	24	[	[	X
ejpam-3142	119	25	f	f	X
ejpam-3142	119	26	(	(	PUNCT
ejpam-3142	119	27	x	x	NOUN
ejpam-3142	119	28	)	)	PUNCT
ejpam-3142	119	29	,	,	PUNCT
ejpam-3142	119	30	z]y	z]y	NOUN
ejpam-3142	119	31	−	−	PUNCT
ejpam-3142	120	1	[	[	X
ejpam-3142	120	2	z	z	NOUN
ejpam-3142	120	3	,	,	PUNCT
ejpam-3142	120	4	x]f	x]f	PROPN
ejpam-3142	120	5	(	(	PUNCT
ejpam-3142	120	6	y	y	X
ejpam-3142	120	7	)	)	PUNCT
ejpam-3142	120	8	+	+	CCONJ
ejpam-3142	121	1	d(z)(y	d(z)(y	PUNCT
ejpam-3142	121	2	◦	◦	NOUN
ejpam-3142	121	3	x)−	x)−	PROPN
ejpam-3142	122	1	[	[	X
ejpam-3142	122	2	d(z	d(z	NOUN
ejpam-3142	122	3	)	)	PUNCT
ejpam-3142	122	4	,	,	PUNCT
ejpam-3142	122	5	x]y	x]y	PROPN
ejpam-3142	122	6	∈	∈	PROPN
ejpam-3142	122	7	z(r	z(r	PROPN
ejpam-3142	122	8	)	)	PUNCT
ejpam-3142	122	9	.	.	PUNCT
ejpam-3142	123	1	now	now	ADV
ejpam-3142	123	2	by	by	ADP
ejpam-3142	123	3	lemma	lemma	PROPN
ejpam-3142	123	4	2.1	2.1	NUM
ejpam-3142	123	5	,	,	PUNCT
ejpam-3142	123	6	d(z	d(z	PROPN
ejpam-3142	123	7	)	)	PUNCT
ejpam-3142	123	8	∈	∈	PROPN
ejpam-3142	123	9	z(r	z(r	PROPN
ejpam-3142	123	10	)	)	PUNCT
ejpam-3142	124	1	and	and	CCONJ
ejpam-3142	124	2	therefore	therefore	ADV
ejpam-3142	124	3	we	we	PRON
ejpam-3142	124	4	find	find	VERB
ejpam-3142	124	5	that	that	SCONJ
ejpam-3142	124	6	d(z)(y	d(z)(y	PUNCT
ejpam-3142	124	7	◦	◦	NOUN
ejpam-3142	124	8	x	x	SYM
ejpam-3142	124	9	)	)	PUNCT
ejpam-3142	124	10	∈	∈	PROPN
ejpam-3142	124	11	z(r	z(r	PROPN
ejpam-3142	124	12	)	)	PUNCT
ejpam-3142	124	13	.	.	PUNCT
ejpam-3142	125	1	since	since	SCONJ
ejpam-3142	125	2	r	r	NOUN
ejpam-3142	125	3	is	be	AUX
ejpam-3142	125	4	prime	prime	ADJ
ejpam-3142	125	5	and	and	CCONJ
ejpam-3142	125	6	d(z	d(z	NOUN
ejpam-3142	125	7	)	)	PUNCT
ejpam-3142	125	8	6=	6=	ADP
ejpam-3142	125	9	0	0	NUM
ejpam-3142	125	10	,	,	PUNCT
ejpam-3142	125	11	it	it	PRON
ejpam-3142	125	12	follows	follow	VERB
ejpam-3142	125	13	from	from	ADP
ejpam-3142	125	14	remark	remark	NOUN
ejpam-3142	125	15	2.2	2.2	NUM
ejpam-3142	125	16	that	that	PRON
ejpam-3142	125	17	y	y	NUM
ejpam-3142	125	18	◦	◦	NOUN
ejpam-3142	125	19	x	x	PUNCT
ejpam-3142	125	20	∈	∈	PROPN
ejpam-3142	125	21	z(r	z(r	PROPN
ejpam-3142	125	22	)	)	PUNCT
ejpam-3142	125	23	for	for	ADP
ejpam-3142	125	24	all	all	DET
ejpam-3142	125	25	x	x	NOUN
ejpam-3142	125	26	,	,	PUNCT
ejpam-3142	125	27	y	y	PROPN
ejpam-3142	125	28	∈	∈	PROPN
ejpam-3142	125	29	i	i	PRON
ejpam-3142	125	30	and	and	CCONJ
ejpam-3142	125	31	hence	hence	ADV
ejpam-3142	125	32	by	by	ADP
ejpam-3142	125	33	lemma	lemma	PROPN
ejpam-3142	125	34	2.5(b	2.5(b	NUM
ejpam-3142	125	35	)	)	PUNCT
ejpam-3142	125	36	,	,	PUNCT
ejpam-3142	125	37	r	r	NOUN
ejpam-3142	125	38	is	be	AUX
ejpam-3142	125	39	a	a	DET
ejpam-3142	125	40	commutative	commutative	ADJ
ejpam-3142	125	41	.	.	PUNCT
ejpam-3142	126	1	theorem	theorem	NOUN
ejpam-3142	126	2	3.2	3.2	NUM
ejpam-3142	126	3	.	.	PUNCT
ejpam-3142	127	1	let	let	VERB
ejpam-3142	127	2	r	r	PRON
ejpam-3142	127	3	be	be	AUX
ejpam-3142	127	4	a	a	DET
ejpam-3142	127	5	prime	prime	ADJ
ejpam-3142	127	6	ring	ring	NOUN
ejpam-3142	127	7	and	and	CCONJ
ejpam-3142	127	8	i	i	PRON
ejpam-3142	127	9	a	a	DET
ejpam-3142	127	10	nonzero	nonzero	NOUN
ejpam-3142	127	11	left	leave	VERB
ejpam-3142	127	12	ideal	ideal	NOUN
ejpam-3142	127	13	of	of	ADP
ejpam-3142	127	14	r	r	NOUN
ejpam-3142	127	15	such	such	ADJ
ejpam-3142	127	16	that	that	SCONJ
ejpam-3142	127	17	i∩z(r	i∩z(r	PRON
ejpam-3142	127	18	)	)	PUNCT
ejpam-3142	127	19	6=	6=	ADP
ejpam-3142	127	20	0	0	X
ejpam-3142	127	21	.	.	PUNCT
ejpam-3142	127	22	suppose	suppose	VERB
ejpam-3142	127	23	that	that	SCONJ
ejpam-3142	127	24	r	r	NOUN
ejpam-3142	127	25	admits	admit	VERB
ejpam-3142	127	26	a	a	DET
ejpam-3142	127	27	generalized	generalized	ADJ
ejpam-3142	127	28	derivation	derivation	NOUN
ejpam-3142	127	29	f	f	PROPN
ejpam-3142	127	30	with	with	ADP
ejpam-3142	127	31	associated	associated	ADJ
ejpam-3142	127	32	derivation	derivation	NOUN
ejpam-3142	127	33	d	d	ADP
ejpam-3142	127	34	such	such	ADJ
ejpam-3142	127	35	that	that	DET
ejpam-3142	127	36	d(z(r	d(z(r	PROPN
ejpam-3142	127	37	)	)	PUNCT
ejpam-3142	127	38	)	)	PUNCT
ejpam-3142	128	1	6=	6=	ADP
ejpam-3142	128	2	0	0	X
ejpam-3142	128	3	.	.	PUNCT
ejpam-3142	129	1	further	far	ADV
ejpam-3142	129	2	,	,	PUNCT
ejpam-3142	129	3	if	if	SCONJ
ejpam-3142	129	4	r	r	NOUN
ejpam-3142	129	5	satisfies	satisfy	VERB
ejpam-3142	129	6	any	any	DET
ejpam-3142	129	7	one	one	NUM
ejpam-3142	129	8	of	of	ADP
ejpam-3142	129	9	the	the	DET
ejpam-3142	129	10	following	following	ADJ
ejpam-3142	129	11	conditions	condition	NOUN
ejpam-3142	129	12	:	:	PUNCT
ejpam-3142	129	13	(	(	PUNCT
ejpam-3142	129	14	i	i	NOUN
ejpam-3142	129	15	)	)	PUNCT
ejpam-3142	130	1	[	[	X
ejpam-3142	130	2	f	f	X
ejpam-3142	130	3	(	(	PUNCT
ejpam-3142	130	4	x	x	NOUN
ejpam-3142	130	5	)	)	PUNCT
ejpam-3142	130	6	,	,	PUNCT
ejpam-3142	130	7	f	f	PROPN
ejpam-3142	130	8	(	(	PUNCT
ejpam-3142	130	9	y)]−	y)]−	NOUN
ejpam-3142	130	10	f	f	PROPN
ejpam-3142	131	1	[	[	X
ejpam-3142	131	2	x	x	X
ejpam-3142	131	3	,	,	PUNCT
ejpam-3142	131	4	y	y	PROPN
ejpam-3142	131	5	]	]	X
ejpam-3142	131	6	∈	∈	PROPN
ejpam-3142	131	7	z(r	z(r	PROPN
ejpam-3142	131	8	)	)	PUNCT
ejpam-3142	131	9	for	for	ADP
ejpam-3142	131	10	all	all	DET
ejpam-3142	131	11	x	x	NOUN
ejpam-3142	131	12	,	,	PUNCT
ejpam-3142	131	13	y	y	PROPN
ejpam-3142	131	14	∈	∈	PROPN
ejpam-3142	131	15	i	i	PRON
ejpam-3142	131	16	,	,	PUNCT
ejpam-3142	131	17	or	or	CCONJ
ejpam-3142	132	1	m.	m.	NOUN
ejpam-3142	132	2	k.	k.	PROPN
ejpam-3142	132	3	abu	abu	PROPN
ejpam-3142	133	1	nawas	nawas	PROPN
ejpam-3142	133	2	,	,	PUNCT
ejpam-3142	133	3	r.	r.	PROPN
ejpam-3142	133	4	m.	m.	PROPN
ejpam-3142	133	5	al	al	PROPN
ejpam-3142	133	6	-	-	PUNCT
ejpam-3142	133	7	omary	omary	ADJ
ejpam-3142	133	8	/	/	SYM
ejpam-3142	133	9	eur	eur	PROPN
ejpam-3142	133	10	.	.	PUNCT
ejpam-3142	134	1	j.	j.	PROPN
ejpam-3142	134	2	pure	pure	PROPN
ejpam-3142	134	3	appl	appl	PROPN
ejpam-3142	134	4	.	.	PROPN
ejpam-3142	134	5	math	math	PROPN
ejpam-3142	134	6	,	,	PUNCT
ejpam-3142	134	7	11	11	NUM
ejpam-3142	134	8	(	(	PUNCT
ejpam-3142	134	9	1	1	NUM
ejpam-3142	134	10	)	)	PUNCT
ejpam-3142	134	11	(	(	PUNCT
ejpam-3142	134	12	2018	2018	NUM
ejpam-3142	134	13	)	)	PUNCT
ejpam-3142	134	14	,	,	PUNCT
ejpam-3142	134	15	79	79	NUM
ejpam-3142	134	16	-	-	SYM
ejpam-3142	134	17	89	89	NUM
ejpam-3142	134	18	83	83	NUM
ejpam-3142	134	19	(	(	PUNCT
ejpam-3142	134	20	ii	ii	NOUN
ejpam-3142	134	21	)	)	PUNCT
ejpam-3142	134	22	f	f	PROPN
ejpam-3142	134	23	(	(	PUNCT
ejpam-3142	134	24	x	x	X
ejpam-3142	134	25	)	)	PUNCT
ejpam-3142	134	26	◦	◦	NOUN
ejpam-3142	134	27	f	f	X
ejpam-3142	135	1	(	(	PUNCT
ejpam-3142	135	2	y)−	y)−	PROPN
ejpam-3142	135	3	f	f	X
ejpam-3142	135	4	(	(	PUNCT
ejpam-3142	135	5	x	x	SYM
ejpam-3142	135	6	◦	◦	VERB
ejpam-3142	135	7	y	y	NOUN
ejpam-3142	135	8	)	)	PUNCT
ejpam-3142	135	9	∈	∈	PROPN
ejpam-3142	135	10	z(r	z(r	PROPN
ejpam-3142	135	11	)	)	PUNCT
ejpam-3142	135	12	for	for	ADP
ejpam-3142	135	13	all	all	DET
ejpam-3142	135	14	x	x	NOUN
ejpam-3142	135	15	,	,	PUNCT
ejpam-3142	135	16	y	y	PROPN
ejpam-3142	135	17	∈	∈	PROPN
ejpam-3142	136	1	i	i	PRON
ejpam-3142	136	2	,	,	PUNCT
ejpam-3142	136	3	then	then	ADV
ejpam-3142	136	4	r	r	NOUN
ejpam-3142	136	5	is	be	AUX
ejpam-3142	136	6	commutative	commutative	ADJ
ejpam-3142	136	7	.	.	PUNCT
ejpam-3142	137	1	proof	proof	NOUN
ejpam-3142	137	2	.	.	PUNCT
ejpam-3142	138	1	(	(	PUNCT
ejpam-3142	138	2	i	i	NOUN
ejpam-3142	138	3	)	)	PUNCT
ejpam-3142	138	4	for	for	ADP
ejpam-3142	138	5	all	all	DET
ejpam-3142	138	6	x	x	NOUN
ejpam-3142	138	7	,	,	PUNCT
ejpam-3142	138	8	y	y	PROPN
ejpam-3142	138	9	∈	∈	PROPN
ejpam-3142	139	1	i	i	PRON
ejpam-3142	139	2	,	,	PUNCT
ejpam-3142	139	3	we	we	PRON
ejpam-3142	139	4	have	have	VERB
ejpam-3142	139	5	[	[	X
ejpam-3142	139	6	f	f	X
ejpam-3142	139	7	(	(	PUNCT
ejpam-3142	139	8	x	x	NOUN
ejpam-3142	139	9	)	)	PUNCT
ejpam-3142	139	10	,	,	PUNCT
ejpam-3142	139	11	f	f	PROPN
ejpam-3142	139	12	(	(	PUNCT
ejpam-3142	139	13	y)]−	y)]−	NOUN
ejpam-3142	139	14	f	f	PROPN
ejpam-3142	140	1	[	[	X
ejpam-3142	140	2	x	x	X
ejpam-3142	140	3	,	,	PUNCT
ejpam-3142	140	4	y	y	PROPN
ejpam-3142	140	5	]	]	X
ejpam-3142	140	6	∈	∈	PROPN
ejpam-3142	140	7	z(r	z(r	PROPN
ejpam-3142	140	8	)	)	PUNCT
ejpam-3142	140	9	.	.	PUNCT
ejpam-3142	141	1	(	(	PUNCT
ejpam-3142	141	2	2	2	X
ejpam-3142	141	3	)	)	PUNCT
ejpam-3142	141	4	since	since	SCONJ
ejpam-3142	141	5	d(z(r	d(z(r	PROPN
ejpam-3142	141	6	)	)	PUNCT
ejpam-3142	141	7	)	)	PUNCT
ejpam-3142	141	8	6=	6=	ADP
ejpam-3142	141	9	0	0	NUM
ejpam-3142	141	10	,	,	PUNCT
ejpam-3142	141	11	then	then	ADV
ejpam-3142	141	12	there	there	PRON
ejpam-3142	141	13	exists	exist	VERB
ejpam-3142	141	14	z	z	PROPN
ejpam-3142	141	15	∈	∈	PROPN
ejpam-3142	141	16	z(r	z(r	PROPN
ejpam-3142	141	17	)	)	PUNCT
ejpam-3142	141	18	such	such	ADJ
ejpam-3142	141	19	that	that	SCONJ
ejpam-3142	141	20	d(z	d(z	NOUN
ejpam-3142	141	21	)	)	PUNCT
ejpam-3142	141	22	6=	6=	ADP
ejpam-3142	141	23	0	0	X
ejpam-3142	141	24	.	.	X
ejpam-3142	142	1	replacing	replace	VERB
ejpam-3142	142	2	y	y	PRON
ejpam-3142	142	3	by	by	ADP
ejpam-3142	142	4	zy	zy	PROPN
ejpam-3142	142	5	in	in	ADP
ejpam-3142	142	6	(	(	PUNCT
ejpam-3142	142	7	2	2	NUM
ejpam-3142	142	8	)	)	PUNCT
ejpam-3142	142	9	and	and	CCONJ
ejpam-3142	142	10	using	use	VERB
ejpam-3142	142	11	(	(	PUNCT
ejpam-3142	142	12	2	2	NUM
ejpam-3142	142	13	)	)	PUNCT
ejpam-3142	142	14	,	,	PUNCT
ejpam-3142	142	15	we	we	PRON
ejpam-3142	142	16	get	get	VERB
ejpam-3142	142	17	[	[	X
ejpam-3142	142	18	f	f	X
ejpam-3142	142	19	(	(	PUNCT
ejpam-3142	142	20	x	x	NOUN
ejpam-3142	142	21	)	)	PUNCT
ejpam-3142	142	22	,	,	PUNCT
ejpam-3142	142	23	z]f	z]f	INTJ
ejpam-3142	143	1	(	(	PUNCT
ejpam-3142	143	2	y	y	NOUN
ejpam-3142	143	3	)	)	PUNCT
ejpam-3142	143	4	+	+	CCONJ
ejpam-3142	144	1	[	[	X
ejpam-3142	144	2	f	f	X
ejpam-3142	144	3	(	(	PUNCT
ejpam-3142	144	4	x	x	NOUN
ejpam-3142	144	5	)	)	PUNCT
ejpam-3142	144	6	,	,	PUNCT
ejpam-3142	144	7	d(z)]y+	d(z)]y+	PROPN
ejpam-3142	144	8	d(z)([f	d(z)([f	PROPN
ejpam-3142	144	9	(	(	PUNCT
ejpam-3142	144	10	x	x	NOUN
ejpam-3142	144	11	)	)	PUNCT
ejpam-3142	144	12	,	,	PUNCT
ejpam-3142	144	13	y]−	y]−	PRON
ejpam-3142	144	14	[	[	X
ejpam-3142	144	15	x	x	X
ejpam-3142	144	16	,	,	PUNCT
ejpam-3142	144	17	y	y	NOUN
ejpam-3142	144	18	]	]	X
ejpam-3142	144	19	)	)	PUNCT
ejpam-3142	144	20	∈	∈	PROPN
ejpam-3142	144	21	z(r	z(r	PROPN
ejpam-3142	144	22	)	)	PUNCT
ejpam-3142	144	23	for	for	ADP
ejpam-3142	144	24	all	all	DET
ejpam-3142	144	25	x	x	NOUN
ejpam-3142	144	26	,	,	PUNCT
ejpam-3142	144	27	y	y	PROPN
ejpam-3142	144	28	∈	∈	PROPN
ejpam-3142	144	29	i.	i.	NOUN
ejpam-3142	144	30	since	since	SCONJ
ejpam-3142	144	31	d(z	d(z	PROPN
ejpam-3142	144	32	)	)	PUNCT
ejpam-3142	144	33	∈	∈	PROPN
ejpam-3142	144	34	z(r	z(r	PROPN
ejpam-3142	144	35	)	)	PUNCT
ejpam-3142	144	36	by	by	ADP
ejpam-3142	144	37	lemma	lemma	PROPN
ejpam-3142	144	38	2.1	2.1	NUM
ejpam-3142	144	39	,	,	PUNCT
ejpam-3142	144	40	and	and	CCONJ
ejpam-3142	144	41	therefore	therefore	ADV
ejpam-3142	144	42	d(z)([f	d(z)([f	NOUN
ejpam-3142	144	43	(	(	PUNCT
ejpam-3142	144	44	x	x	NOUN
ejpam-3142	144	45	)	)	PUNCT
ejpam-3142	144	46	,	,	PUNCT
ejpam-3142	144	47	y]−[x	y]−[x	PROPN
ejpam-3142	144	48	,	,	PUNCT
ejpam-3142	144	49	y	y	PROPN
ejpam-3142	144	50	]	]	X
ejpam-3142	144	51	)	)	PUNCT
ejpam-3142	144	52	∈	∈	PROPN
ejpam-3142	144	53	z(r	z(r	PROPN
ejpam-3142	144	54	)	)	PUNCT
ejpam-3142	144	55	.	.	PUNCT
ejpam-3142	145	1	since	since	SCONJ
ejpam-3142	145	2	d(z	d(z	NOUN
ejpam-3142	145	3	)	)	PUNCT
ejpam-3142	145	4	6=	6=	ADP
ejpam-3142	145	5	0	0	NUM
ejpam-3142	146	1	and	and	CCONJ
ejpam-3142	146	2	r	r	NOUN
ejpam-3142	146	3	is	be	AUX
ejpam-3142	146	4	prime	prime	ADJ
ejpam-3142	146	5	,	,	PUNCT
ejpam-3142	146	6	it	it	PRON
ejpam-3142	146	7	follows	follow	VERB
ejpam-3142	146	8	from	from	ADP
ejpam-3142	146	9	remark	remark	NOUN
ejpam-3142	146	10	2.2	2.2	NUM
ejpam-3142	146	11	that	that	PRON
ejpam-3142	146	12	[	[	X
ejpam-3142	146	13	f	f	X
ejpam-3142	146	14	(	(	PUNCT
ejpam-3142	146	15	x	x	NOUN
ejpam-3142	146	16	)	)	PUNCT
ejpam-3142	146	17	,	,	PUNCT
ejpam-3142	146	18	y	y	PROPN
ejpam-3142	146	19	]	]	X
ejpam-3142	146	20	−	−	PROPN
ejpam-3142	147	1	[	[	X
ejpam-3142	147	2	x	x	X
ejpam-3142	147	3	,	,	PUNCT
ejpam-3142	147	4	y	y	PROPN
ejpam-3142	147	5	]	]	X
ejpam-3142	147	6	∈	∈	PROPN
ejpam-3142	147	7	z(r	z(r	PROPN
ejpam-3142	147	8	)	)	PUNCT
ejpam-3142	147	9	for	for	ADP
ejpam-3142	147	10	all	all	DET
ejpam-3142	147	11	x	x	NOUN
ejpam-3142	147	12	,	,	PUNCT
ejpam-3142	147	13	y	y	PROPN
ejpam-3142	147	14	∈	∈	PROPN
ejpam-3142	147	15	i.	i.	NOUN
ejpam-3142	147	16	now	now	ADV
ejpam-3142	147	17	,	,	PUNCT
ejpam-3142	147	18	replace	replace	VERB
ejpam-3142	147	19	y	y	NOUN
ejpam-3142	147	20	by	by	ADP
ejpam-3142	147	21	d(z)x	d(z)x	PROPN
ejpam-3142	147	22	in	in	ADP
ejpam-3142	147	23	the	the	DET
ejpam-3142	147	24	above	above	ADJ
ejpam-3142	147	25	relation	relation	NOUN
ejpam-3142	147	26	and	and	CCONJ
ejpam-3142	147	27	use	use	VERB
ejpam-3142	147	28	it	it	PRON
ejpam-3142	147	29	,	,	PUNCT
ejpam-3142	147	30	to	to	PART
ejpam-3142	147	31	get	get	VERB
ejpam-3142	147	32	d(z)[f	d(z)[f	NOUN
ejpam-3142	147	33	(	(	PUNCT
ejpam-3142	147	34	x	x	NOUN
ejpam-3142	147	35	)	)	PUNCT
ejpam-3142	147	36	,	,	PUNCT
ejpam-3142	148	1	x	x	X
ejpam-3142	148	2	]	]	X
ejpam-3142	148	3	∈	∈	PROPN
ejpam-3142	148	4	z(r	z(r	PROPN
ejpam-3142	148	5	)	)	PUNCT
ejpam-3142	148	6	.	.	PUNCT
ejpam-3142	149	1	again	again	ADV
ejpam-3142	149	2	using	use	VERB
ejpam-3142	149	3	the	the	DET
ejpam-3142	149	4	same	same	ADJ
ejpam-3142	149	5	arguments	argument	NOUN
ejpam-3142	149	6	as	as	SCONJ
ejpam-3142	149	7	used	use	VERB
ejpam-3142	149	8	above	above	ADV
ejpam-3142	149	9	we	we	PRON
ejpam-3142	149	10	find	find	VERB
ejpam-3142	149	11	that	that	SCONJ
ejpam-3142	149	12	[	[	X
ejpam-3142	149	13	f	f	X
ejpam-3142	149	14	(	(	PUNCT
ejpam-3142	149	15	x	x	NOUN
ejpam-3142	149	16	)	)	PUNCT
ejpam-3142	149	17	,	,	PUNCT
ejpam-3142	149	18	x	x	X
ejpam-3142	149	19	]	]	X
ejpam-3142	149	20	∈	∈	PROPN
ejpam-3142	149	21	z(r	z(r	PROPN
ejpam-3142	149	22	)	)	PUNCT
ejpam-3142	149	23	for	for	ADP
ejpam-3142	149	24	all	all	DET
ejpam-3142	149	25	x	x	SYM
ejpam-3142	149	26	∈	∈	PROPN
ejpam-3142	149	27	i.	i.	NOUN
ejpam-3142	149	28	thus	thus	ADV
ejpam-3142	149	29	,	,	PUNCT
ejpam-3142	149	30	by	by	ADP
ejpam-3142	149	31	lemma	lemma	PROPN
ejpam-3142	149	32	2.2	2.2	NUM
ejpam-3142	149	33	we	we	PRON
ejpam-3142	149	34	get	get	VERB
ejpam-3142	149	35	r	r	NOUN
ejpam-3142	149	36	is	be	AUX
ejpam-3142	149	37	commutative	commutative	ADJ
ejpam-3142	149	38	.	.	PUNCT
ejpam-3142	150	1	(	(	PUNCT
ejpam-3142	150	2	ii	ii	NOUN
ejpam-3142	150	3	)	)	PUNCT
ejpam-3142	150	4	for	for	ADP
ejpam-3142	150	5	all	all	DET
ejpam-3142	150	6	x	x	NOUN
ejpam-3142	150	7	,	,	PUNCT
ejpam-3142	150	8	y	y	PROPN
ejpam-3142	150	9	∈	∈	PROPN
ejpam-3142	151	1	i	i	PRON
ejpam-3142	151	2	,	,	PUNCT
ejpam-3142	151	3	we	we	PRON
ejpam-3142	151	4	have	have	VERB
ejpam-3142	151	5	f	f	PROPN
ejpam-3142	151	6	(	(	PUNCT
ejpam-3142	151	7	x	x	NOUN
ejpam-3142	151	8	)	)	PUNCT
ejpam-3142	151	9	◦	◦	NOUN
ejpam-3142	151	10	f	f	X
ejpam-3142	152	1	(	(	PUNCT
ejpam-3142	152	2	y)−	y)−	PROPN
ejpam-3142	152	3	f	f	X
ejpam-3142	152	4	(	(	PUNCT
ejpam-3142	152	5	x	x	SYM
ejpam-3142	152	6	◦	◦	VERB
ejpam-3142	152	7	y	y	NOUN
ejpam-3142	152	8	)	)	PUNCT
ejpam-3142	152	9	∈	∈	PROPN
ejpam-3142	152	10	z(r	z(r	PROPN
ejpam-3142	152	11	)	)	PUNCT
ejpam-3142	152	12	.	.	PUNCT
ejpam-3142	153	1	(	(	PUNCT
ejpam-3142	153	2	3	3	X
ejpam-3142	153	3	)	)	PUNCT
ejpam-3142	153	4	since	since	SCONJ
ejpam-3142	153	5	d(z(r	d(z(r	PROPN
ejpam-3142	153	6	)	)	PUNCT
ejpam-3142	153	7	)	)	PUNCT
ejpam-3142	154	1	6=	6=	ADP
ejpam-3142	154	2	0	0	NUM
ejpam-3142	154	3	,	,	PUNCT
ejpam-3142	154	4	then	then	ADV
ejpam-3142	154	5	there	there	PRON
ejpam-3142	154	6	exists	exist	VERB
ejpam-3142	154	7	z	z	PROPN
ejpam-3142	154	8	∈	∈	PROPN
ejpam-3142	154	9	z(r	z(r	PROPN
ejpam-3142	154	10	)	)	PUNCT
ejpam-3142	154	11	such	such	ADJ
ejpam-3142	154	12	that	that	SCONJ
ejpam-3142	154	13	d(z	d(z	NOUN
ejpam-3142	154	14	)	)	PUNCT
ejpam-3142	154	15	6=	6=	ADP
ejpam-3142	154	16	0	0	X
ejpam-3142	154	17	.	.	X
ejpam-3142	155	1	replacing	replace	VERB
ejpam-3142	155	2	y	y	PRON
ejpam-3142	155	3	by	by	ADP
ejpam-3142	155	4	zy	zy	PROPN
ejpam-3142	155	5	in	in	ADP
ejpam-3142	155	6	(	(	PUNCT
ejpam-3142	155	7	3	3	NUM
ejpam-3142	155	8	)	)	PUNCT
ejpam-3142	155	9	and	and	CCONJ
ejpam-3142	155	10	using	use	VERB
ejpam-3142	155	11	(	(	PUNCT
ejpam-3142	155	12	3	3	NUM
ejpam-3142	155	13	)	)	PUNCT
ejpam-3142	155	14	,	,	PUNCT
ejpam-3142	155	15	we	we	PRON
ejpam-3142	155	16	get	get	VERB
ejpam-3142	155	17	[	[	X
ejpam-3142	155	18	f	f	X
ejpam-3142	155	19	(	(	PUNCT
ejpam-3142	155	20	x	x	NOUN
ejpam-3142	155	21	)	)	PUNCT
ejpam-3142	155	22	,	,	PUNCT
ejpam-3142	155	23	z]f	z]f	INTJ
ejpam-3142	156	1	(	(	PUNCT
ejpam-3142	156	2	y)+d(z)(f	y)+d(z)(f	PROPN
ejpam-3142	156	3	(	(	PUNCT
ejpam-3142	156	4	x)	x)	PROPN
ejpam-3142	156	5	◦	◦	NOUN
ejpam-3142	156	6	y−x	y−x	NOUN
ejpam-3142	156	7	◦	◦	NOUN
ejpam-3142	156	8	y)+	y)+	NOUN
ejpam-3142	157	1	[	[	X
ejpam-3142	157	2	f	f	X
ejpam-3142	157	3	(	(	PUNCT
ejpam-3142	157	4	x	x	NOUN
ejpam-3142	157	5	)	)	PUNCT
ejpam-3142	157	6	,	,	PUNCT
ejpam-3142	157	7	d(z)]y	d(z)]y	PROPN
ejpam-3142	157	8	∈	∈	PROPN
ejpam-3142	157	9	z(r	z(r	PROPN
ejpam-3142	157	10	)	)	PUNCT
ejpam-3142	157	11	.	.	PUNCT
ejpam-3142	158	1	now	now	ADV
ejpam-3142	158	2	by	by	ADP
ejpam-3142	158	3	lemma	lemma	PROPN
ejpam-3142	158	4	2.1	2.1	NUM
ejpam-3142	158	5	d(z	d(z	PROPN
ejpam-3142	158	6	)	)	PUNCT
ejpam-3142	158	7	∈	∈	PROPN
ejpam-3142	158	8	z(r	z(r	PROPN
ejpam-3142	158	9	)	)	PUNCT
ejpam-3142	158	10	and	and	CCONJ
ejpam-3142	158	11	therefore	therefore	ADV
ejpam-3142	158	12	d(z)(f	d(z)(f	NUM
ejpam-3142	158	13	(	(	PUNCT
ejpam-3142	158	14	x)	x)	NUM
ejpam-3142	158	15	◦	◦	NOUN
ejpam-3142	158	16	y−x	y−x	NOUN
ejpam-3142	158	17	◦	◦	NOUN
ejpam-3142	158	18	y	y	NOUN
ejpam-3142	158	19	)	)	PUNCT
ejpam-3142	158	20	∈	∈	PROPN
ejpam-3142	158	21	z(r	z(r	PROPN
ejpam-3142	158	22	)	)	PUNCT
ejpam-3142	158	23	.	.	PUNCT
ejpam-3142	159	1	since	since	SCONJ
ejpam-3142	159	2	d(z	d(z	NOUN
ejpam-3142	159	3	)	)	PUNCT
ejpam-3142	159	4	6=	6=	ADP
ejpam-3142	159	5	0	0	NUM
ejpam-3142	160	1	and	and	CCONJ
ejpam-3142	160	2	r	r	NOUN
ejpam-3142	160	3	is	be	AUX
ejpam-3142	160	4	prim	prim	ADJ
ejpam-3142	160	5	,	,	PUNCT
ejpam-3142	160	6	hence	hence	ADV
ejpam-3142	160	7	from	from	ADP
ejpam-3142	160	8	remark	remark	NOUN
ejpam-3142	160	9	2.2	2.2	NUM
ejpam-3142	160	10	we	we	PRON
ejpam-3142	160	11	find	find	VERB
ejpam-3142	160	12	that	that	SCONJ
ejpam-3142	160	13	f	f	PROPN
ejpam-3142	160	14	(	(	PUNCT
ejpam-3142	160	15	x)	x)	PROPN
ejpam-3142	160	16	◦	◦	NOUN
ejpam-3142	160	17	y−x	y−x	NOUN
ejpam-3142	160	18	◦	◦	NOUN
ejpam-3142	160	19	y	y	PROPN
ejpam-3142	160	20	∈	∈	PROPN
ejpam-3142	160	21	z(r	z(r	PROPN
ejpam-3142	160	22	)	)	PUNCT
ejpam-3142	160	23	for	for	ADP
ejpam-3142	160	24	all	all	DET
ejpam-3142	160	25	x	x	NOUN
ejpam-3142	160	26	,	,	PUNCT
ejpam-3142	160	27	y	y	PROPN
ejpam-3142	160	28	∈	∈	PROPN
ejpam-3142	160	29	i.	i.	NOUN
ejpam-3142	160	30	again	again	ADV
ejpam-3142	160	31	replace	replace	VERB
ejpam-3142	160	32	x	x	PUNCT
ejpam-3142	160	33	by	by	ADP
ejpam-3142	160	34	zx	zx	PROPN
ejpam-3142	160	35	in	in	ADP
ejpam-3142	160	36	the	the	DET
ejpam-3142	160	37	last	last	ADJ
ejpam-3142	160	38	expression	expression	NOUN
ejpam-3142	160	39	and	and	CCONJ
ejpam-3142	160	40	use	use	VERB
ejpam-3142	160	41	it	it	PRON
ejpam-3142	160	42	,	,	PUNCT
ejpam-3142	160	43	to	to	PART
ejpam-3142	160	44	get	get	VERB
ejpam-3142	160	45	d(z)(x	d(z)(x	PRON
ejpam-3142	160	46	◦	◦	NOUN
ejpam-3142	160	47	y	y	NOUN
ejpam-3142	160	48	)	)	PUNCT
ejpam-3142	160	49	−	−	PROPN
ejpam-3142	161	1	[	[	X
ejpam-3142	161	2	d(z	d(z	NOUN
ejpam-3142	161	3	)	)	PUNCT
ejpam-3142	161	4	,	,	PUNCT
ejpam-3142	161	5	y]x	y]x	PROPN
ejpam-3142	161	6	∈	∈	PROPN
ejpam-3142	161	7	z(r	z(r	PROPN
ejpam-3142	161	8	)	)	PUNCT
ejpam-3142	161	9	.	.	PUNCT
ejpam-3142	162	1	now	now	ADV
ejpam-3142	162	2	by	by	ADP
ejpam-3142	162	3	lemma	lemma	PROPN
ejpam-3142	162	4	2.1	2.1	NUM
ejpam-3142	162	5	d(z	d(z	PROPN
ejpam-3142	162	6	)	)	PUNCT
ejpam-3142	162	7	∈	∈	PROPN
ejpam-3142	162	8	z(r	z(r	PROPN
ejpam-3142	162	9	)	)	PUNCT
ejpam-3142	162	10	and	and	CCONJ
ejpam-3142	162	11	therefore	therefore	ADV
ejpam-3142	162	12	d(z)(x	d(z)(x	VERB
ejpam-3142	162	13	◦	◦	PROPN
ejpam-3142	162	14	y	y	NOUN
ejpam-3142	162	15	)	)	PUNCT
ejpam-3142	162	16	∈	∈	PROPN
ejpam-3142	162	17	z(r	z(r	PROPN
ejpam-3142	162	18	)	)	PUNCT
ejpam-3142	162	19	and	and	CCONJ
ejpam-3142	162	20	hence	hence	ADV
ejpam-3142	162	21	by	by	ADP
ejpam-3142	162	22	remark	remark	NOUN
ejpam-3142	162	23	2.2	2.2	NUM
ejpam-3142	162	24	,	,	PUNCT
ejpam-3142	162	25	we	we	PRON
ejpam-3142	162	26	obtain	obtain	VERB
ejpam-3142	162	27	x	x	VERB
ejpam-3142	162	28	◦	◦	VERB
ejpam-3142	162	29	y	y	PROPN
ejpam-3142	162	30	∈	∈	PROPN
ejpam-3142	162	31	z(r	z(r	PROPN
ejpam-3142	162	32	)	)	PUNCT
ejpam-3142	162	33	for	for	ADP
ejpam-3142	162	34	all	all	DET
ejpam-3142	162	35	x	x	NOUN
ejpam-3142	162	36	,	,	PUNCT
ejpam-3142	162	37	y	y	PROPN
ejpam-3142	162	38	∈	∈	PROPN
ejpam-3142	162	39	i.	i.	NOUN
ejpam-3142	162	40	thus	thus	ADV
ejpam-3142	162	41	,	,	PUNCT
ejpam-3142	162	42	by	by	ADP
ejpam-3142	162	43	lemma	lemma	PROPN
ejpam-3142	162	44	2.5	2.5	NUM
ejpam-3142	162	45	(	(	PUNCT
ejpam-3142	162	46	b	b	NOUN
ejpam-3142	162	47	)	)	PUNCT
ejpam-3142	162	48	,	,	PUNCT
ejpam-3142	162	49	we	we	PRON
ejpam-3142	162	50	conclude	conclude	VERB
ejpam-3142	162	51	that	that	SCONJ
ejpam-3142	162	52	r	r	NOUN
ejpam-3142	162	53	is	be	AUX
ejpam-3142	162	54	commutative	commutative	ADJ
ejpam-3142	162	55	.	.	PUNCT
ejpam-3142	163	1	theorem	theorem	VERB
ejpam-3142	163	2	3.3	3.3	NUM
ejpam-3142	163	3	.	.	PUNCT
ejpam-3142	164	1	let	let	VERB
ejpam-3142	164	2	r	r	PRON
ejpam-3142	164	3	be	be	AUX
ejpam-3142	164	4	a	a	DET
ejpam-3142	164	5	prime	prime	ADJ
ejpam-3142	164	6	ring	ring	NOUN
ejpam-3142	164	7	and	and	CCONJ
ejpam-3142	164	8	i	i	PRON
ejpam-3142	164	9	a	a	DET
ejpam-3142	164	10	nonzero	nonzero	NOUN
ejpam-3142	164	11	left	leave	VERB
ejpam-3142	164	12	ideal	ideal	NOUN
ejpam-3142	164	13	of	of	ADP
ejpam-3142	164	14	r	r	NOUN
ejpam-3142	164	15	such	such	ADJ
ejpam-3142	164	16	that	that	SCONJ
ejpam-3142	164	17	i∩z(r	i∩z(r	PRON
ejpam-3142	164	18	)	)	PUNCT
ejpam-3142	164	19	6=	6=	ADP
ejpam-3142	164	20	0	0	X
ejpam-3142	164	21	.	.	PUNCT
ejpam-3142	164	22	suppose	suppose	VERB
ejpam-3142	164	23	that	that	SCONJ
ejpam-3142	164	24	r	r	NOUN
ejpam-3142	164	25	admits	admit	VERB
ejpam-3142	164	26	a	a	DET
ejpam-3142	164	27	generalized	generalized	ADJ
ejpam-3142	164	28	derivation	derivation	NOUN
ejpam-3142	164	29	f	f	PROPN
ejpam-3142	164	30	with	with	ADP
ejpam-3142	164	31	associated	associated	ADJ
ejpam-3142	164	32	derivation	derivation	NOUN
ejpam-3142	164	33	d	d	ADP
ejpam-3142	164	34	such	such	ADJ
ejpam-3142	164	35	that	that	DET
ejpam-3142	164	36	d(z(r	d(z(r	PROPN
ejpam-3142	164	37	)	)	PUNCT
ejpam-3142	164	38	)	)	PUNCT
ejpam-3142	165	1	6=	6=	ADP
ejpam-3142	165	2	0	0	X
ejpam-3142	165	3	.	.	PUNCT
ejpam-3142	166	1	further	far	ADV
ejpam-3142	166	2	,	,	PUNCT
ejpam-3142	166	3	if	if	SCONJ
ejpam-3142	166	4	r	r	NOUN
ejpam-3142	166	5	satisfies	satisfy	VERB
ejpam-3142	166	6	the	the	DET
ejpam-3142	166	7	condition	condition	NOUN
ejpam-3142	166	8	:	:	PUNCT
ejpam-3142	166	9	f	f	X
ejpam-3142	167	1	[	[	X
ejpam-3142	167	2	x	x	X
ejpam-3142	167	3	,	,	PUNCT
ejpam-3142	167	4	y	y	PROPN
ejpam-3142	167	5	]	]	PUNCT
ejpam-3142	168	1	+	+	CCONJ
ejpam-3142	169	1	[	[	X
ejpam-3142	169	2	f	f	X
ejpam-3142	169	3	(	(	PUNCT
ejpam-3142	169	4	x	x	NOUN
ejpam-3142	169	5	)	)	PUNCT
ejpam-3142	169	6	,	,	PUNCT
ejpam-3142	169	7	y]−	y]−	PRON
ejpam-3142	170	1	[	[	X
ejpam-3142	170	2	f	f	X
ejpam-3142	170	3	(	(	PUNCT
ejpam-3142	170	4	x	x	NOUN
ejpam-3142	170	5	)	)	PUNCT
ejpam-3142	170	6	,	,	PUNCT
ejpam-3142	170	7	f	f	PROPN
ejpam-3142	170	8	(	(	PUNCT
ejpam-3142	170	9	y	y	NOUN
ejpam-3142	170	10	)	)	PUNCT
ejpam-3142	170	11	]	]	PUNCT
ejpam-3142	171	1	∈	∈	PROPN
ejpam-3142	171	2	z(r	z(r	PROPN
ejpam-3142	171	3	)	)	PUNCT
ejpam-3142	171	4	for	for	ADP
ejpam-3142	171	5	all	all	DET
ejpam-3142	171	6	x	x	NOUN
ejpam-3142	171	7	,	,	PUNCT
ejpam-3142	171	8	y	y	PROPN
ejpam-3142	171	9	∈	∈	PROPN
ejpam-3142	172	1	i	i	PRON
ejpam-3142	172	2	,	,	PUNCT
ejpam-3142	172	3	then	then	ADV
ejpam-3142	172	4	r	r	NOUN
ejpam-3142	172	5	is	be	AUX
ejpam-3142	172	6	commutative	commutative	ADJ
ejpam-3142	172	7	.	.	PUNCT
ejpam-3142	173	1	proof	proof	NOUN
ejpam-3142	173	2	.	.	PUNCT
ejpam-3142	174	1	for	for	ADP
ejpam-3142	174	2	all	all	DET
ejpam-3142	174	3	x	x	NOUN
ejpam-3142	174	4	,	,	PUNCT
ejpam-3142	174	5	y	y	PROPN
ejpam-3142	174	6	∈	∈	PROPN
ejpam-3142	175	1	i	i	PRON
ejpam-3142	175	2	,	,	PUNCT
ejpam-3142	175	3	we	we	PRON
ejpam-3142	175	4	have	have	VERB
ejpam-3142	175	5	f	f	PROPN
ejpam-3142	176	1	[	[	X
ejpam-3142	176	2	x	x	X
ejpam-3142	176	3	,	,	PUNCT
ejpam-3142	176	4	y	y	PROPN
ejpam-3142	176	5	]	]	PUNCT
ejpam-3142	177	1	+	+	CCONJ
ejpam-3142	178	1	[	[	X
ejpam-3142	178	2	f	f	X
ejpam-3142	178	3	(	(	PUNCT
ejpam-3142	178	4	x	x	NOUN
ejpam-3142	178	5	)	)	PUNCT
ejpam-3142	178	6	,	,	PUNCT
ejpam-3142	178	7	y]−	y]−	PRON
ejpam-3142	179	1	[	[	X
ejpam-3142	179	2	f	f	X
ejpam-3142	179	3	(	(	PUNCT
ejpam-3142	179	4	x	x	NOUN
ejpam-3142	179	5	)	)	PUNCT
ejpam-3142	179	6	,	,	PUNCT
ejpam-3142	179	7	f	f	PROPN
ejpam-3142	179	8	(	(	PUNCT
ejpam-3142	179	9	y	y	NOUN
ejpam-3142	179	10	)	)	PUNCT
ejpam-3142	179	11	]	]	PUNCT
ejpam-3142	180	1	∈	∈	PROPN
ejpam-3142	180	2	z(r	z(r	PROPN
ejpam-3142	180	3	)	)	PUNCT
ejpam-3142	180	4	.	.	PUNCT
ejpam-3142	181	1	(	(	PUNCT
ejpam-3142	181	2	4	4	X
ejpam-3142	181	3	)	)	PUNCT
ejpam-3142	181	4	since	since	SCONJ
ejpam-3142	181	5	d(z(r	d(z(r	PROPN
ejpam-3142	181	6	)	)	PUNCT
ejpam-3142	181	7	)	)	PUNCT
ejpam-3142	182	1	6=	6=	ADP
ejpam-3142	182	2	0	0	NUM
ejpam-3142	182	3	,	,	PUNCT
ejpam-3142	182	4	then	then	ADV
ejpam-3142	182	5	there	there	PRON
ejpam-3142	182	6	exists	exist	VERB
ejpam-3142	182	7	z	z	PROPN
ejpam-3142	182	8	∈	∈	PROPN
ejpam-3142	182	9	z(r	z(r	PROPN
ejpam-3142	182	10	)	)	PUNCT
ejpam-3142	182	11	such	such	ADJ
ejpam-3142	182	12	that	that	SCONJ
ejpam-3142	182	13	d(z	d(z	NOUN
ejpam-3142	182	14	)	)	PUNCT
ejpam-3142	182	15	6=	6=	ADP
ejpam-3142	182	16	0	0	X
ejpam-3142	182	17	.	.	X
ejpam-3142	183	1	replacing	replace	VERB
ejpam-3142	183	2	y	y	PRON
ejpam-3142	183	3	by	by	ADP
ejpam-3142	183	4	zy	zy	PROPN
ejpam-3142	183	5	in	in	ADP
ejpam-3142	183	6	(	(	PUNCT
ejpam-3142	183	7	4	4	NUM
ejpam-3142	183	8	)	)	PUNCT
ejpam-3142	183	9	and	and	CCONJ
ejpam-3142	183	10	using	use	VERB
ejpam-3142	183	11	(	(	PUNCT
ejpam-3142	183	12	4	4	NUM
ejpam-3142	183	13	)	)	PUNCT
ejpam-3142	183	14	,	,	PUNCT
ejpam-3142	183	15	we	we	PRON
ejpam-3142	183	16	get	get	VERB
ejpam-3142	183	17	d(z)([x	d(z)([x	NOUN
ejpam-3142	183	18	,	,	PUNCT
ejpam-3142	183	19	y]−	y]−	PRON
ejpam-3142	184	1	[	[	X
ejpam-3142	184	2	f	f	X
ejpam-3142	184	3	(	(	PUNCT
ejpam-3142	184	4	x	x	NOUN
ejpam-3142	184	5	)	)	PUNCT
ejpam-3142	184	6	,	,	PUNCT
ejpam-3142	184	7	y])−	y])−	PROPN
ejpam-3142	185	1	[	[	X
ejpam-3142	185	2	f	f	X
ejpam-3142	185	3	(	(	PUNCT
ejpam-3142	185	4	x	x	NOUN
ejpam-3142	185	5	)	)	PUNCT
ejpam-3142	185	6	,	,	PUNCT
ejpam-3142	185	7	d(z)]y	d(z)]y	PROPN
ejpam-3142	185	8	∈	∈	PROPN
ejpam-3142	185	9	z(r	z(r	PROPN
ejpam-3142	185	10	)	)	PUNCT
ejpam-3142	185	11	.	.	PUNCT
ejpam-3142	186	1	since	since	SCONJ
ejpam-3142	186	2	by	by	ADP
ejpam-3142	186	3	lemma	lemma	PROPN
ejpam-3142	186	4	2.1	2.1	NUM
ejpam-3142	186	5	d(z	d(z	PROPN
ejpam-3142	186	6	)	)	PUNCT
ejpam-3142	186	7	∈	∈	PROPN
ejpam-3142	186	8	z(r	z(r	PROPN
ejpam-3142	186	9	)	)	PUNCT
ejpam-3142	186	10	and	and	CCONJ
ejpam-3142	186	11	hence	hence	ADV
ejpam-3142	186	12	by	by	ADP
ejpam-3142	186	13	remark	remark	NOUN
ejpam-3142	186	14	2.2	2.2	NUM
ejpam-3142	186	15	we	we	PRON
ejpam-3142	186	16	obtain	obtain	VERB
ejpam-3142	186	17	,	,	PUNCT
ejpam-3142	187	1	[	[	X
ejpam-3142	187	2	f	f	X
ejpam-3142	187	3	(	(	PUNCT
ejpam-3142	187	4	x	x	NOUN
ejpam-3142	187	5	)	)	PUNCT
ejpam-3142	187	6	,	,	PUNCT
ejpam-3142	187	7	y	y	PROPN
ejpam-3142	187	8	]	]	PUNCT
ejpam-3142	188	1	+	+	CCONJ
ejpam-3142	188	2	[	[	X
ejpam-3142	188	3	x	x	X
ejpam-3142	188	4	,	,	PUNCT
ejpam-3142	188	5	y	y	PROPN
ejpam-3142	188	6	]	]	X
ejpam-3142	188	7	∈	∈	PROPN
ejpam-3142	188	8	z(r	z(r	PROPN
ejpam-3142	188	9	)	)	PUNCT
ejpam-3142	188	10	for	for	ADP
ejpam-3142	188	11	all	all	DET
ejpam-3142	188	12	x	x	NOUN
ejpam-3142	188	13	,	,	PUNCT
ejpam-3142	188	14	y	y	PROPN
ejpam-3142	188	15	∈	∈	PROPN
ejpam-3142	188	16	i.	i.	NOUN
ejpam-3142	188	17	again	again	ADV
ejpam-3142	188	18	replace	replace	VERB
ejpam-3142	188	19	y	y	NOUN
ejpam-3142	188	20	by	by	ADP
ejpam-3142	188	21	d(z)x	d(z)x	PROPN
ejpam-3142	188	22	in	in	ADP
ejpam-3142	188	23	the	the	DET
ejpam-3142	188	24	last	last	ADJ
ejpam-3142	188	25	relation	relation	NOUN
ejpam-3142	188	26	and	and	CCONJ
ejpam-3142	188	27	use	use	VERB
ejpam-3142	188	28	it	it	PRON
ejpam-3142	188	29	,	,	PUNCT
ejpam-3142	188	30	to	to	PART
ejpam-3142	188	31	get	get	VERB
ejpam-3142	188	32	d(z)[f	d(z)[f	NOUN
ejpam-3142	188	33	(	(	PUNCT
ejpam-3142	188	34	x	x	NOUN
ejpam-3142	188	35	)	)	PUNCT
ejpam-3142	188	36	,	,	PUNCT
ejpam-3142	189	1	x	x	X
ejpam-3142	189	2	]	]	X
ejpam-3142	189	3	∈	∈	PROPN
ejpam-3142	189	4	z(r	z(r	PROPN
ejpam-3142	189	5	)	)	PUNCT
ejpam-3142	189	6	for	for	ADP
ejpam-3142	189	7	all	all	DET
ejpam-3142	189	8	x	x	SYM
ejpam-3142	189	9	∈	∈	PROPN
ejpam-3142	189	10	i	i	PRON
ejpam-3142	189	11	,	,	PUNCT
ejpam-3142	189	12	again	again	ADV
ejpam-3142	189	13	using	use	VERB
ejpam-3142	189	14	the	the	DET
ejpam-3142	189	15	same	same	ADJ
ejpam-3142	189	16	arguments	argument	NOUN
ejpam-3142	189	17	as	as	ADP
ejpam-3142	189	18	above	above	ADV
ejpam-3142	189	19	we	we	PRON
ejpam-3142	189	20	find	find	VERB
ejpam-3142	189	21	that	that	SCONJ
ejpam-3142	189	22	[	[	X
ejpam-3142	189	23	f	f	X
ejpam-3142	189	24	(	(	PUNCT
ejpam-3142	189	25	x	x	NOUN
ejpam-3142	189	26	)	)	PUNCT
ejpam-3142	189	27	,	,	PUNCT
ejpam-3142	189	28	x	x	X
ejpam-3142	189	29	]	]	X
ejpam-3142	189	30	∈	∈	PROPN
ejpam-3142	189	31	z(r	z(r	PROPN
ejpam-3142	189	32	)	)	PUNCT
ejpam-3142	189	33	for	for	ADP
ejpam-3142	189	34	all	all	DET
ejpam-3142	189	35	x	x	SYM
ejpam-3142	189	36	∈	∈	PROPN
ejpam-3142	189	37	i	i	PRON
ejpam-3142	189	38	and	and	CCONJ
ejpam-3142	189	39	hence	hence	ADV
ejpam-3142	189	40	by	by	ADP
ejpam-3142	189	41	lemma	lemma	PROPN
ejpam-3142	189	42	2.2	2.2	NUM
ejpam-3142	189	43	,	,	PUNCT
ejpam-3142	189	44	r	r	NOUN
ejpam-3142	189	45	is	be	AUX
ejpam-3142	189	46	commutative	commutative	ADJ
ejpam-3142	189	47	.	.	PUNCT
ejpam-3142	190	1	m.	m.	NOUN
ejpam-3142	191	1	k.	k.	PROPN
ejpam-3142	192	1	abu	abu	PROPN
ejpam-3142	193	1	nawas	nawas	PROPN
ejpam-3142	193	2	,	,	PUNCT
ejpam-3142	193	3	r.	r.	PROPN
ejpam-3142	193	4	m.	m.	PROPN
ejpam-3142	193	5	al	al	PROPN
ejpam-3142	193	6	-	-	PUNCT
ejpam-3142	193	7	omary	omary	ADJ
ejpam-3142	193	8	/	/	SYM
ejpam-3142	193	9	eur	eur	PROPN
ejpam-3142	193	10	.	.	PUNCT
ejpam-3142	194	1	j.	j.	PROPN
ejpam-3142	194	2	pure	pure	PROPN
ejpam-3142	194	3	appl	appl	PROPN
ejpam-3142	194	4	.	.	PROPN
ejpam-3142	194	5	math	math	PROPN
ejpam-3142	194	6	,	,	PUNCT
ejpam-3142	194	7	11	11	NUM
ejpam-3142	194	8	(	(	PUNCT
ejpam-3142	194	9	1	1	NUM
ejpam-3142	194	10	)	)	PUNCT
ejpam-3142	194	11	(	(	PUNCT
ejpam-3142	194	12	2018	2018	NUM
ejpam-3142	194	13	)	)	PUNCT
ejpam-3142	194	14	,	,	PUNCT
ejpam-3142	194	15	79	79	NUM
ejpam-3142	194	16	-	-	SYM
ejpam-3142	194	17	89	89	NUM
ejpam-3142	194	18	84	84	NUM
ejpam-3142	194	19	theorem	theorem	VERB
ejpam-3142	194	20	3.4	3.4	NUM
ejpam-3142	194	21	.	.	PUNCT
ejpam-3142	195	1	let	let	VERB
ejpam-3142	195	2	r	r	PRON
ejpam-3142	195	3	be	be	AUX
ejpam-3142	195	4	a	a	DET
ejpam-3142	195	5	prime	prime	ADJ
ejpam-3142	195	6	ring	ring	NOUN
ejpam-3142	195	7	and	and	CCONJ
ejpam-3142	195	8	i	i	PRON
ejpam-3142	195	9	a	a	DET
ejpam-3142	195	10	nonzero	nonzero	NOUN
ejpam-3142	195	11	ideal	ideal	NOUN
ejpam-3142	195	12	of	of	ADP
ejpam-3142	195	13	r.	r.	PROPN
ejpam-3142	195	14	suppose	suppose	VERB
ejpam-3142	195	15	that	that	SCONJ
ejpam-3142	195	16	r	r	NOUN
ejpam-3142	195	17	admits	admit	VERB
ejpam-3142	195	18	a	a	DET
ejpam-3142	195	19	generalized	generalized	ADJ
ejpam-3142	195	20	derivation	derivation	NOUN
ejpam-3142	195	21	f	f	PROPN
ejpam-3142	195	22	with	with	ADP
ejpam-3142	195	23	associated	associated	ADJ
ejpam-3142	195	24	derivation	derivation	NOUN
ejpam-3142	195	25	d	d	ADP
ejpam-3142	195	26	such	such	ADJ
ejpam-3142	195	27	that	that	DET
ejpam-3142	195	28	d(z(r	d(z(r	PROPN
ejpam-3142	195	29	)	)	PUNCT
ejpam-3142	195	30	)	)	PUNCT
ejpam-3142	196	1	6=	6=	ADP
ejpam-3142	196	2	0	0	X
ejpam-3142	196	3	.	.	PUNCT
ejpam-3142	197	1	further	far	ADV
ejpam-3142	197	2	,	,	PUNCT
ejpam-3142	197	3	if	if	SCONJ
ejpam-3142	197	4	r	r	NOUN
ejpam-3142	197	5	satisfies	satisfy	VERB
ejpam-3142	197	6	any	any	DET
ejpam-3142	197	7	one	one	NUM
ejpam-3142	197	8	of	of	ADP
ejpam-3142	197	9	the	the	DET
ejpam-3142	197	10	following	following	ADJ
ejpam-3142	197	11	conditions	condition	NOUN
ejpam-3142	197	12	:	:	PUNCT
ejpam-3142	197	13	(	(	PUNCT
ejpam-3142	197	14	i	i	NOUN
ejpam-3142	197	15	)	)	PUNCT
ejpam-3142	197	16	f	f	PROPN
ejpam-3142	197	17	(	(	PUNCT
ejpam-3142	197	18	x	x	SYM
ejpam-3142	197	19	◦	◦	VERB
ejpam-3142	197	20	y)−	y)−	PROPN
ejpam-3142	198	1	[	[	X
ejpam-3142	198	2	x	x	X
ejpam-3142	198	3	,	,	PUNCT
ejpam-3142	198	4	y	y	PROPN
ejpam-3142	198	5	]	]	X
ejpam-3142	198	6	∈	∈	PROPN
ejpam-3142	198	7	z(r	z(r	PROPN
ejpam-3142	198	8	)	)	PUNCT
ejpam-3142	198	9	for	for	ADP
ejpam-3142	198	10	all	all	DET
ejpam-3142	198	11	x	x	NOUN
ejpam-3142	198	12	,	,	PUNCT
ejpam-3142	198	13	y	y	PROPN
ejpam-3142	198	14	∈	∈	PROPN
ejpam-3142	198	15	i	i	PRON
ejpam-3142	198	16	,	,	PUNCT
ejpam-3142	198	17	or	or	CCONJ
ejpam-3142	198	18	(	(	PUNCT
ejpam-3142	198	19	ii	ii	PROPN
ejpam-3142	198	20	)	)	PUNCT
ejpam-3142	198	21	f	f	NOUN
ejpam-3142	198	22	(	(	PUNCT
ejpam-3142	198	23	x	x	SYM
ejpam-3142	198	24	◦	◦	VERB
ejpam-3142	198	25	y	y	NOUN
ejpam-3142	198	26	)	)	PUNCT
ejpam-3142	199	1	+	+	CCONJ
ejpam-3142	200	1	[	[	X
ejpam-3142	200	2	x	x	X
ejpam-3142	200	3	,	,	PUNCT
ejpam-3142	200	4	y	y	PROPN
ejpam-3142	200	5	]	]	X
ejpam-3142	200	6	∈	∈	PROPN
ejpam-3142	200	7	z(r	z(r	PROPN
ejpam-3142	200	8	)	)	PUNCT
ejpam-3142	200	9	for	for	ADP
ejpam-3142	200	10	all	all	DET
ejpam-3142	200	11	x	x	NOUN
ejpam-3142	200	12	,	,	PUNCT
ejpam-3142	200	13	y	y	PROPN
ejpam-3142	200	14	∈	∈	PROPN
ejpam-3142	200	15	i	i	PRON
ejpam-3142	200	16	,	,	PUNCT
ejpam-3142	200	17	then	then	ADV
ejpam-3142	200	18	r	r	NOUN
ejpam-3142	200	19	is	be	AUX
ejpam-3142	200	20	commutative	commutative	ADJ
ejpam-3142	200	21	.	.	PUNCT
ejpam-3142	201	1	proof	proof	NOUN
ejpam-3142	201	2	.	.	PUNCT
ejpam-3142	202	1	(	(	PUNCT
ejpam-3142	202	2	i	i	NOUN
ejpam-3142	202	3	)	)	PUNCT
ejpam-3142	202	4	by	by	ADP
ejpam-3142	202	5	hypothesis	hypothesis	NOUN
ejpam-3142	202	6	we	we	PRON
ejpam-3142	202	7	have	have	VERB
ejpam-3142	202	8	f	f	X
ejpam-3142	202	9	(	(	PUNCT
ejpam-3142	202	10	x	x	SYM
ejpam-3142	202	11	◦	◦	VERB
ejpam-3142	202	12	y	y	NOUN
ejpam-3142	202	13	)	)	PUNCT
ejpam-3142	202	14	−	−	PROPN
ejpam-3142	203	1	[	[	X
ejpam-3142	203	2	x	x	X
ejpam-3142	203	3	,	,	PUNCT
ejpam-3142	203	4	y	y	PROPN
ejpam-3142	203	5	]	]	X
ejpam-3142	203	6	∈	∈	PROPN
ejpam-3142	203	7	z(r	z(r	PROPN
ejpam-3142	203	8	)	)	PUNCT
ejpam-3142	203	9	for	for	ADP
ejpam-3142	203	10	all	all	DET
ejpam-3142	203	11	x	x	NOUN
ejpam-3142	203	12	,	,	PUNCT
ejpam-3142	203	13	y	y	PROPN
ejpam-3142	203	14	∈	∈	PROPN
ejpam-3142	203	15	i.	i.	NOUN
ejpam-3142	203	16	if	if	SCONJ
ejpam-3142	203	17	f	f	PROPN
ejpam-3142	203	18	=	=	SYM
ejpam-3142	203	19	0	0	PROPN
ejpam-3142	203	20	,	,	PUNCT
ejpam-3142	203	21	then	then	ADV
ejpam-3142	203	22	[	[	X
ejpam-3142	203	23	x	x	X
ejpam-3142	203	24	,	,	PUNCT
ejpam-3142	203	25	y	y	PROPN
ejpam-3142	203	26	]	]	X
ejpam-3142	203	27	∈	∈	PROPN
ejpam-3142	203	28	z(r	z(r	PROPN
ejpam-3142	203	29	)	)	PUNCT
ejpam-3142	203	30	for	for	ADP
ejpam-3142	203	31	all	all	DET
ejpam-3142	203	32	x	x	NOUN
ejpam-3142	203	33	,	,	PUNCT
ejpam-3142	203	34	y	y	PROPN
ejpam-3142	203	35	∈	∈	PROPN
ejpam-3142	204	1	i	i	PRON
ejpam-3142	204	2	,	,	PUNCT
ejpam-3142	204	3	and	and	CCONJ
ejpam-3142	204	4	hence	hence	ADV
ejpam-3142	204	5	by	by	ADP
ejpam-3142	204	6	lemma	lemma	PROPN
ejpam-3142	204	7	2.5(a	2.5(a	NUM
ejpam-3142	204	8	)	)	PUNCT
ejpam-3142	204	9	,	,	PUNCT
ejpam-3142	204	10	we	we	PRON
ejpam-3142	204	11	get	get	VERB
ejpam-3142	204	12	the	the	DET
ejpam-3142	204	13	required	require	VERB
ejpam-3142	204	14	result	result	NOUN
ejpam-3142	204	15	.	.	PUNCT
ejpam-3142	205	1	therefore	therefore	ADV
ejpam-3142	205	2	we	we	PRON
ejpam-3142	205	3	shall	shall	AUX
ejpam-3142	205	4	assume	assume	VERB
ejpam-3142	205	5	that	that	SCONJ
ejpam-3142	205	6	f	f	PROPN
ejpam-3142	205	7	6=	6=	PROPN
ejpam-3142	205	8	0	0	NUM
ejpam-3142	205	9	,	,	PUNCT
ejpam-3142	205	10	then	then	ADV
ejpam-3142	205	11	we	we	PRON
ejpam-3142	205	12	have	have	VERB
ejpam-3142	205	13	for	for	ADP
ejpam-3142	205	14	any	any	DET
ejpam-3142	205	15	x	x	NOUN
ejpam-3142	205	16	,	,	PUNCT
ejpam-3142	205	17	y	y	PROPN
ejpam-3142	205	18	∈	∈	PROPN
ejpam-3142	206	1	i	i	PRON
ejpam-3142	206	2	f	f	X
ejpam-3142	206	3	(	(	PUNCT
ejpam-3142	206	4	x	x	SYM
ejpam-3142	206	5	◦	◦	VERB
ejpam-3142	206	6	y)−	y)−	PROPN
ejpam-3142	207	1	[	[	X
ejpam-3142	207	2	x	x	X
ejpam-3142	207	3	,	,	PUNCT
ejpam-3142	207	4	y	y	PROPN
ejpam-3142	207	5	]	]	X
ejpam-3142	207	6	∈	∈	PROPN
ejpam-3142	207	7	z(r	z(r	PROPN
ejpam-3142	207	8	)	)	PUNCT
ejpam-3142	207	9	.	.	PUNCT
ejpam-3142	208	1	(	(	PUNCT
ejpam-3142	208	2	5	5	X
ejpam-3142	208	3	)	)	PUNCT
ejpam-3142	208	4	since	since	SCONJ
ejpam-3142	208	5	d(z(r	d(z(r	PROPN
ejpam-3142	208	6	)	)	PUNCT
ejpam-3142	208	7	)	)	PUNCT
ejpam-3142	209	1	6=	6=	ADP
ejpam-3142	209	2	0	0	NUM
ejpam-3142	209	3	,	,	PUNCT
ejpam-3142	209	4	then	then	ADV
ejpam-3142	209	5	there	there	PRON
ejpam-3142	209	6	exists	exist	VERB
ejpam-3142	209	7	z	z	PROPN
ejpam-3142	209	8	∈	∈	PROPN
ejpam-3142	209	9	z(r	z(r	PROPN
ejpam-3142	209	10	)	)	PUNCT
ejpam-3142	209	11	such	such	ADJ
ejpam-3142	209	12	that	that	SCONJ
ejpam-3142	209	13	d(z	d(z	NOUN
ejpam-3142	209	14	)	)	PUNCT
ejpam-3142	209	15	6=	6=	ADP
ejpam-3142	209	16	0	0	X
ejpam-3142	209	17	.	.	PUNCT
ejpam-3142	210	1	replace	replace	VERB
ejpam-3142	210	2	y	y	PROPN
ejpam-3142	210	3	by	by	ADP
ejpam-3142	210	4	zy	zy	PROPN
ejpam-3142	210	5	in	in	ADP
ejpam-3142	210	6	(	(	PUNCT
ejpam-3142	210	7	5	5	NUM
ejpam-3142	210	8	)	)	PUNCT
ejpam-3142	210	9	to	to	PART
ejpam-3142	210	10	get	get	VERB
ejpam-3142	210	11	zf	zf	PROPN
ejpam-3142	210	12	(	(	PUNCT
ejpam-3142	210	13	x	x	SYM
ejpam-3142	210	14	◦	◦	VERB
ejpam-3142	210	15	y	y	NOUN
ejpam-3142	210	16	)	)	PUNCT
ejpam-3142	211	1	+	+	NOUN
ejpam-3142	211	2	d(z)(x	d(z)(x	AUX
ejpam-3142	211	3	◦	◦	VERB
ejpam-3142	211	4	y)−	y)−	PROPN
ejpam-3142	211	5	z[x	z[x	NOUN
ejpam-3142	211	6	,	,	PUNCT
ejpam-3142	211	7	y	y	PROPN
ejpam-3142	211	8	]	]	X
ejpam-3142	211	9	∈	∈	PROPN
ejpam-3142	211	10	z(r	z(r	PROPN
ejpam-3142	211	11	)	)	PUNCT
ejpam-3142	211	12	,	,	PUNCT
ejpam-3142	211	13	for	for	ADP
ejpam-3142	211	14	all	all	DET
ejpam-3142	211	15	x	x	NOUN
ejpam-3142	211	16	,	,	PUNCT
ejpam-3142	211	17	y	y	PROPN
ejpam-3142	211	18	∈	∈	PROPN
ejpam-3142	211	19	i	i	PRON
ejpam-3142	211	20	,	,	PUNCT
ejpam-3142	211	21	and	and	CCONJ
ejpam-3142	211	22	hence	hence	ADV
ejpam-3142	211	23	by	by	ADP
ejpam-3142	211	24	(	(	PUNCT
ejpam-3142	211	25	5	5	NUM
ejpam-3142	211	26	)	)	PUNCT
ejpam-3142	211	27	,	,	PUNCT
ejpam-3142	211	28	we	we	PRON
ejpam-3142	211	29	find	find	VERB
ejpam-3142	211	30	that	that	SCONJ
ejpam-3142	211	31	d(z)(x	d(z)(x	NUM
ejpam-3142	211	32	◦	◦	VERB
ejpam-3142	211	33	y	y	NOUN
ejpam-3142	211	34	)	)	PUNCT
ejpam-3142	211	35	∈	∈	PROPN
ejpam-3142	211	36	z(r	z(r	PROPN
ejpam-3142	211	37	)	)	PUNCT
ejpam-3142	211	38	for	for	ADP
ejpam-3142	211	39	all	all	DET
ejpam-3142	211	40	x	x	NOUN
ejpam-3142	211	41	,	,	PUNCT
ejpam-3142	211	42	y	y	PROPN
ejpam-3142	211	43	∈	∈	PROPN
ejpam-3142	211	44	i.	i.	NOUN
ejpam-3142	211	45	thus	thus	ADV
ejpam-3142	211	46	,	,	PUNCT
ejpam-3142	211	47	lemma	lemma	PROPN
ejpam-3142	211	48	2.1	2.1	NUM
ejpam-3142	211	49	and	and	CCONJ
ejpam-3142	211	50	remark	remark	VERB
ejpam-3142	211	51	2.2	2.2	NUM
ejpam-3142	211	52	gives	give	VERB
ejpam-3142	211	53	that	that	PRON
ejpam-3142	211	54	x	x	PROPN
ejpam-3142	211	55	◦	◦	NOUN
ejpam-3142	211	56	y	y	PROPN
ejpam-3142	211	57	∈	∈	PROPN
ejpam-3142	211	58	z(r	z(r	PROPN
ejpam-3142	211	59	)	)	PUNCT
ejpam-3142	211	60	and	and	CCONJ
ejpam-3142	211	61	hence	hence	ADV
ejpam-3142	211	62	by	by	ADP
ejpam-3142	211	63	lemma	lemma	PROPN
ejpam-3142	211	64	2.5(b	2.5(b	NUM
ejpam-3142	211	65	)	)	PUNCT
ejpam-3142	211	66	we	we	PRON
ejpam-3142	211	67	get	get	VERB
ejpam-3142	211	68	the	the	DET
ejpam-3142	211	69	required	require	VERB
ejpam-3142	211	70	result	result	NOUN
ejpam-3142	211	71	.	.	PUNCT
ejpam-3142	212	1	(	(	PUNCT
ejpam-3142	212	2	ii	ii	NOUN
ejpam-3142	212	3	)	)	PUNCT
ejpam-3142	212	4	using	use	VERB
ejpam-3142	212	5	the	the	DET
ejpam-3142	212	6	same	same	ADJ
ejpam-3142	212	7	trick	trick	NOUN
ejpam-3142	212	8	as	as	SCONJ
ejpam-3142	212	9	used	use	VERB
ejpam-3142	212	10	in	in	ADP
ejpam-3142	212	11	(	(	PUNCT
ejpam-3142	212	12	i	i	NOUN
ejpam-3142	212	13	)	)	PUNCT
ejpam-3142	212	14	,	,	PUNCT
ejpam-3142	212	15	result	result	NOUN
ejpam-3142	212	16	follows	follow	VERB
ejpam-3142	212	17	.	.	PUNCT
ejpam-3142	213	1	theorem	theorem	ADJ
ejpam-3142	213	2	3.5	3.5	NUM
ejpam-3142	213	3	.	.	PUNCT
ejpam-3142	214	1	let	let	VERB
ejpam-3142	214	2	r	r	PRON
ejpam-3142	214	3	be	be	AUX
ejpam-3142	214	4	a	a	DET
ejpam-3142	214	5	prime	prime	ADJ
ejpam-3142	214	6	ring	ring	NOUN
ejpam-3142	214	7	and	and	CCONJ
ejpam-3142	214	8	i	i	PRON
ejpam-3142	214	9	a	a	DET
ejpam-3142	214	10	nonzero	nonzero	NOUN
ejpam-3142	214	11	left	leave	VERB
ejpam-3142	214	12	ideal	ideal	NOUN
ejpam-3142	214	13	of	of	ADP
ejpam-3142	214	14	r	r	NOUN
ejpam-3142	214	15	such	such	ADJ
ejpam-3142	214	16	that	that	SCONJ
ejpam-3142	214	17	i∩z(r	i∩z(r	PRON
ejpam-3142	214	18	)	)	PUNCT
ejpam-3142	214	19	6=	6=	ADP
ejpam-3142	214	20	0	0	X
ejpam-3142	214	21	.	.	PUNCT
ejpam-3142	214	22	suppose	suppose	VERB
ejpam-3142	214	23	that	that	SCONJ
ejpam-3142	214	24	r	r	NOUN
ejpam-3142	214	25	admits	admit	VERB
ejpam-3142	214	26	a	a	DET
ejpam-3142	214	27	generalized	generalized	ADJ
ejpam-3142	214	28	derivation	derivation	NOUN
ejpam-3142	214	29	f	f	PROPN
ejpam-3142	214	30	with	with	ADP
ejpam-3142	214	31	associated	associated	ADJ
ejpam-3142	214	32	derivation	derivation	NOUN
ejpam-3142	214	33	d	d	ADP
ejpam-3142	214	34	such	such	ADJ
ejpam-3142	214	35	that	that	DET
ejpam-3142	214	36	d(z(r	d(z(r	PROPN
ejpam-3142	214	37	)	)	PUNCT
ejpam-3142	214	38	)	)	PUNCT
ejpam-3142	215	1	6=	6=	ADP
ejpam-3142	215	2	0	0	X
ejpam-3142	215	3	.	.	PUNCT
ejpam-3142	216	1	further	far	ADV
ejpam-3142	216	2	,	,	PUNCT
ejpam-3142	216	3	if	if	SCONJ
ejpam-3142	216	4	r	r	NOUN
ejpam-3142	216	5	satisfies	satisfy	VERB
ejpam-3142	216	6	any	any	DET
ejpam-3142	216	7	one	one	NUM
ejpam-3142	216	8	of	of	ADP
ejpam-3142	216	9	the	the	DET
ejpam-3142	216	10	following	following	ADJ
ejpam-3142	216	11	conditions	condition	NOUN
ejpam-3142	216	12	:	:	PUNCT
ejpam-3142	216	13	(	(	PUNCT
ejpam-3142	216	14	i	i	NOUN
ejpam-3142	216	15	)	)	PUNCT
ejpam-3142	217	1	[	[	X
ejpam-3142	217	2	f	f	X
ejpam-3142	217	3	(	(	PUNCT
ejpam-3142	217	4	x	x	NOUN
ejpam-3142	217	5	)	)	PUNCT
ejpam-3142	217	6	,	,	PUNCT
ejpam-3142	217	7	f	f	PROPN
ejpam-3142	217	8	(	(	PUNCT
ejpam-3142	217	9	y)]−	y)]−	NOUN
ejpam-3142	217	10	x	x	PUNCT
ejpam-3142	217	11	◦	◦	NOUN
ejpam-3142	217	12	y	y	PROPN
ejpam-3142	217	13	∈	∈	PROPN
ejpam-3142	217	14	z(r	z(r	PROPN
ejpam-3142	217	15	)	)	PUNCT
ejpam-3142	217	16	,	,	PUNCT
ejpam-3142	217	17	for	for	ADP
ejpam-3142	217	18	all	all	DET
ejpam-3142	217	19	x	x	NOUN
ejpam-3142	217	20	,	,	PUNCT
ejpam-3142	217	21	y	y	PROPN
ejpam-3142	217	22	∈	∈	PROPN
ejpam-3142	218	1	i	i	PRON
ejpam-3142	218	2	,	,	PUNCT
ejpam-3142	218	3	or	or	CCONJ
ejpam-3142	218	4	(	(	PUNCT
ejpam-3142	218	5	ii	ii	NOUN
ejpam-3142	218	6	)	)	PUNCT
ejpam-3142	219	1	[	[	X
ejpam-3142	219	2	f	f	X
ejpam-3142	219	3	(	(	PUNCT
ejpam-3142	219	4	x	x	NOUN
ejpam-3142	219	5	)	)	PUNCT
ejpam-3142	219	6	,	,	PUNCT
ejpam-3142	219	7	f	f	PROPN
ejpam-3142	219	8	(	(	PUNCT
ejpam-3142	219	9	y	y	PROPN
ejpam-3142	219	10	)	)	PUNCT
ejpam-3142	219	11	]	]	PUNCT
ejpam-3142	220	1	+	+	CCONJ
ejpam-3142	220	2	x	x	PUNCT
ejpam-3142	220	3	◦	◦	NOUN
ejpam-3142	220	4	y	y	PROPN
ejpam-3142	220	5	∈	∈	PROPN
ejpam-3142	220	6	z(r	z(r	PROPN
ejpam-3142	220	7	)	)	PUNCT
ejpam-3142	220	8	,	,	PUNCT
ejpam-3142	220	9	for	for	ADP
ejpam-3142	220	10	all	all	DET
ejpam-3142	220	11	x	x	NOUN
ejpam-3142	220	12	,	,	PUNCT
ejpam-3142	220	13	y	y	PROPN
ejpam-3142	220	14	∈	∈	PROPN
ejpam-3142	221	1	i	i	PRON
ejpam-3142	221	2	,	,	PUNCT
ejpam-3142	221	3	then	then	ADV
ejpam-3142	221	4	r	r	NOUN
ejpam-3142	221	5	is	be	AUX
ejpam-3142	221	6	commutative	commutative	ADJ
ejpam-3142	221	7	.	.	PUNCT
ejpam-3142	222	1	proof	proof	NOUN
ejpam-3142	222	2	.	.	PUNCT
ejpam-3142	223	1	(	(	PUNCT
ejpam-3142	223	2	i	i	NOUN
ejpam-3142	223	3	)	)	PUNCT
ejpam-3142	223	4	by	by	ADP
ejpam-3142	223	5	hypothesis	hypothesis	NOUN
ejpam-3142	223	6	we	we	PRON
ejpam-3142	223	7	have	have	VERB
ejpam-3142	223	8	[	[	X
ejpam-3142	223	9	f	f	X
ejpam-3142	223	10	(	(	PUNCT
ejpam-3142	223	11	x	x	NOUN
ejpam-3142	223	12	)	)	PUNCT
ejpam-3142	223	13	,	,	PUNCT
ejpam-3142	223	14	f	f	PROPN
ejpam-3142	223	15	(	(	PUNCT
ejpam-3142	223	16	y	y	PROPN
ejpam-3142	223	17	)	)	PUNCT
ejpam-3142	223	18	]	]	PUNCT
ejpam-3142	224	1	−	−	NOUN
ejpam-3142	224	2	x	x	PUNCT
ejpam-3142	224	3	◦	◦	VERB
ejpam-3142	224	4	y	y	PROPN
ejpam-3142	224	5	∈	∈	PROPN
ejpam-3142	224	6	z(r	z(r	PROPN
ejpam-3142	224	7	)	)	PUNCT
ejpam-3142	224	8	for	for	ADP
ejpam-3142	224	9	all	all	DET
ejpam-3142	224	10	x	x	NOUN
ejpam-3142	224	11	,	,	PUNCT
ejpam-3142	224	12	y	y	PROPN
ejpam-3142	224	13	∈	∈	PROPN
ejpam-3142	224	14	i.	i.	NOUN
ejpam-3142	224	15	if	if	SCONJ
ejpam-3142	224	16	f	f	PROPN
ejpam-3142	224	17	=	=	SYM
ejpam-3142	224	18	0	0	PROPN
ejpam-3142	224	19	,	,	PUNCT
ejpam-3142	224	20	then	then	ADV
ejpam-3142	224	21	x	x	PART
ejpam-3142	224	22	◦	◦	NOUN
ejpam-3142	224	23	y	y	PROPN
ejpam-3142	224	24	∈	∈	PROPN
ejpam-3142	224	25	z(r	z(r	PROPN
ejpam-3142	224	26	)	)	PUNCT
ejpam-3142	224	27	for	for	ADP
ejpam-3142	224	28	all	all	DET
ejpam-3142	224	29	x	x	NOUN
ejpam-3142	224	30	,	,	PUNCT
ejpam-3142	224	31	y	y	PROPN
ejpam-3142	224	32	∈	∈	PROPN
ejpam-3142	225	1	i	i	PRON
ejpam-3142	225	2	,	,	PUNCT
ejpam-3142	225	3	and	and	CCONJ
ejpam-3142	225	4	hence	hence	ADV
ejpam-3142	225	5	we	we	PRON
ejpam-3142	225	6	get	get	VERB
ejpam-3142	225	7	the	the	DET
ejpam-3142	225	8	required	require	VERB
ejpam-3142	225	9	result	result	NOUN
ejpam-3142	225	10	by	by	ADP
ejpam-3142	225	11	lemma	lemma	PROPN
ejpam-3142	225	12	2.5(b	2.5(b	NUM
ejpam-3142	225	13	)	)	PUNCT
ejpam-3142	225	14	.	.	PUNCT
ejpam-3142	226	1	therefore	therefore	ADV
ejpam-3142	226	2	we	we	PRON
ejpam-3142	226	3	shall	shall	AUX
ejpam-3142	226	4	assume	assume	VERB
ejpam-3142	226	5	that	that	SCONJ
ejpam-3142	226	6	f	f	PROPN
ejpam-3142	226	7	6=	6=	PROPN
ejpam-3142	226	8	0	0	NUM
ejpam-3142	226	9	,	,	PUNCT
ejpam-3142	226	10	then	then	ADV
ejpam-3142	226	11	for	for	ADP
ejpam-3142	226	12	any	any	DET
ejpam-3142	226	13	x	x	NOUN
ejpam-3142	226	14	,	,	PUNCT
ejpam-3142	226	15	y	y	PROPN
ejpam-3142	226	16	∈	∈	PROPN
ejpam-3142	226	17	i	i	PRON
ejpam-3142	226	18	we	we	PRON
ejpam-3142	226	19	have	have	VERB
ejpam-3142	226	20	[	[	X
ejpam-3142	226	21	f	f	X
ejpam-3142	226	22	(	(	PUNCT
ejpam-3142	226	23	x	x	NOUN
ejpam-3142	226	24	)	)	PUNCT
ejpam-3142	226	25	,	,	PUNCT
ejpam-3142	226	26	f	f	PROPN
ejpam-3142	226	27	(	(	PUNCT
ejpam-3142	226	28	y)]−	y)]−	NOUN
ejpam-3142	226	29	x	x	PUNCT
ejpam-3142	226	30	◦	◦	NOUN
ejpam-3142	226	31	y	y	PROPN
ejpam-3142	226	32	∈	∈	PROPN
ejpam-3142	226	33	z(r	z(r	PROPN
ejpam-3142	226	34	)	)	PUNCT
ejpam-3142	226	35	.	.	PUNCT
ejpam-3142	227	1	(	(	PUNCT
ejpam-3142	227	2	6	6	NUM
ejpam-3142	227	3	)	)	PUNCT
ejpam-3142	227	4	since	since	SCONJ
ejpam-3142	227	5	d(z(r	d(z(r	PROPN
ejpam-3142	227	6	)	)	PUNCT
ejpam-3142	227	7	)	)	PUNCT
ejpam-3142	228	1	6=	6=	ADP
ejpam-3142	228	2	0	0	NUM
ejpam-3142	228	3	,	,	PUNCT
ejpam-3142	228	4	then	then	ADV
ejpam-3142	228	5	there	there	PRON
ejpam-3142	228	6	exists	exist	VERB
ejpam-3142	228	7	z	z	PROPN
ejpam-3142	228	8	∈	∈	PROPN
ejpam-3142	228	9	z(r	z(r	PROPN
ejpam-3142	228	10	)	)	PUNCT
ejpam-3142	228	11	such	such	ADJ
ejpam-3142	228	12	that	that	SCONJ
ejpam-3142	228	13	d(z	d(z	NOUN
ejpam-3142	228	14	)	)	PUNCT
ejpam-3142	228	15	6=	6=	ADP
ejpam-3142	228	16	0	0	X
ejpam-3142	228	17	.	.	X
ejpam-3142	229	1	replacing	replace	VERB
ejpam-3142	229	2	y	y	PRON
ejpam-3142	229	3	by	by	ADP
ejpam-3142	229	4	zy	zy	PROPN
ejpam-3142	229	5	in	in	ADP
ejpam-3142	229	6	(	(	PUNCT
ejpam-3142	229	7	6	6	NUM
ejpam-3142	229	8	)	)	PUNCT
ejpam-3142	229	9	and	and	CCONJ
ejpam-3142	229	10	using	use	VERB
ejpam-3142	229	11	(	(	PUNCT
ejpam-3142	229	12	6	6	NUM
ejpam-3142	229	13	)	)	PUNCT
ejpam-3142	229	14	,	,	PUNCT
ejpam-3142	229	15	we	we	PRON
ejpam-3142	229	16	get	get	VERB
ejpam-3142	229	17	d(z)[f	d(z)[f	NOUN
ejpam-3142	229	18	(	(	PUNCT
ejpam-3142	229	19	x	x	NOUN
ejpam-3142	229	20	)	)	PUNCT
ejpam-3142	229	21	,	,	PUNCT
ejpam-3142	229	22	y	y	PROPN
ejpam-3142	229	23	]	]	PUNCT
ejpam-3142	230	1	+	+	CCONJ
ejpam-3142	230	2	[	[	X
ejpam-3142	230	3	f	f	X
ejpam-3142	230	4	(	(	PUNCT
ejpam-3142	230	5	x	x	NOUN
ejpam-3142	230	6	)	)	PUNCT
ejpam-3142	230	7	,	,	PUNCT
ejpam-3142	230	8	d(z)]y	d(z)]y	PROPN
ejpam-3142	230	9	∈	∈	PROPN
ejpam-3142	230	10	z(r	z(r	PROPN
ejpam-3142	230	11	)	)	PUNCT
ejpam-3142	230	12	.	.	PUNCT
ejpam-3142	231	1	now	now	ADV
ejpam-3142	231	2	,	,	PUNCT
ejpam-3142	231	3	since	since	SCONJ
ejpam-3142	231	4	z	z	PROPN
ejpam-3142	231	5	∈	∈	PROPN
ejpam-3142	231	6	z(r	z(r	PROPN
ejpam-3142	231	7	)	)	PUNCT
ejpam-3142	231	8	then	then	ADV
ejpam-3142	231	9	by	by	ADP
ejpam-3142	231	10	lemma	lemma	PROPN
ejpam-3142	231	11	2.1	2.1	NUM
ejpam-3142	231	12	we	we	PRON
ejpam-3142	231	13	have	have	VERB
ejpam-3142	231	14	d(z)[f	d(z)[f	NOUN
ejpam-3142	231	15	(	(	PUNCT
ejpam-3142	231	16	x	x	NOUN
ejpam-3142	231	17	)	)	PUNCT
ejpam-3142	231	18	,	,	PUNCT
ejpam-3142	231	19	y	y	PROPN
ejpam-3142	231	20	]	]	X
ejpam-3142	231	21	∈	∈	PROPN
ejpam-3142	231	22	z(r	z(r	PROPN
ejpam-3142	231	23	)	)	PUNCT
ejpam-3142	231	24	and	and	CCONJ
ejpam-3142	231	25	hence	hence	ADV
ejpam-3142	231	26	by	by	ADP
ejpam-3142	231	27	remark	remark	NOUN
ejpam-3142	231	28	2.2	2.2	NUM
ejpam-3142	231	29	,	,	PUNCT
ejpam-3142	231	30	we	we	PRON
ejpam-3142	231	31	find	find	VERB
ejpam-3142	231	32	that	that	SCONJ
ejpam-3142	231	33	[	[	X
ejpam-3142	231	34	f	f	X
ejpam-3142	231	35	(	(	PUNCT
ejpam-3142	231	36	x	x	NOUN
ejpam-3142	231	37	)	)	PUNCT
ejpam-3142	231	38	,	,	PUNCT
ejpam-3142	231	39	y	y	PROPN
ejpam-3142	231	40	]	]	X
ejpam-3142	231	41	∈	∈	PROPN
ejpam-3142	231	42	z(r	z(r	PROPN
ejpam-3142	231	43	)	)	PUNCT
ejpam-3142	231	44	for	for	ADP
ejpam-3142	231	45	all	all	DET
ejpam-3142	231	46	x	x	NOUN
ejpam-3142	231	47	,	,	PUNCT
ejpam-3142	231	48	y	y	PROPN
ejpam-3142	231	49	∈	∈	PROPN
ejpam-3142	231	50	i.	i.	NOUN
ejpam-3142	231	51	in	in	ADP
ejpam-3142	231	52	particular	particular	ADJ
ejpam-3142	231	53	[	[	X
ejpam-3142	231	54	f	f	X
ejpam-3142	231	55	(	(	PUNCT
ejpam-3142	231	56	x	x	NOUN
ejpam-3142	231	57	)	)	PUNCT
ejpam-3142	231	58	,	,	PUNCT
ejpam-3142	231	59	x	x	X
ejpam-3142	231	60	]	]	X
ejpam-3142	231	61	∈	∈	PROPN
ejpam-3142	231	62	z(r	z(r	PROPN
ejpam-3142	231	63	)	)	PUNCT
ejpam-3142	231	64	for	for	ADP
ejpam-3142	231	65	all	all	DET
ejpam-3142	231	66	x	x	SYM
ejpam-3142	231	67	∈	∈	PROPN
ejpam-3142	231	68	i	i	PRON
ejpam-3142	231	69	and	and	CCONJ
ejpam-3142	231	70	hence	hence	ADV
ejpam-3142	231	71	by	by	ADP
ejpam-3142	231	72	lemma	lemma	PROPN
ejpam-3142	231	73	2.2	2.2	NUM
ejpam-3142	231	74	,	,	PUNCT
ejpam-3142	231	75	r	r	NOUN
ejpam-3142	231	76	is	be	AUX
ejpam-3142	231	77	commutative	commutative	ADJ
ejpam-3142	231	78	.	.	PUNCT
ejpam-3142	232	1	(	(	PUNCT
ejpam-3142	232	2	ii	ii	NOUN
ejpam-3142	232	3	)	)	PUNCT
ejpam-3142	232	4	using	use	VERB
ejpam-3142	232	5	similar	similar	ADJ
ejpam-3142	232	6	arguments	argument	NOUN
ejpam-3142	232	7	as	as	ADP
ejpam-3142	232	8	(	(	PUNCT
ejpam-3142	232	9	i	i	NOUN
ejpam-3142	232	10	)	)	PUNCT
ejpam-3142	232	11	it	it	PRON
ejpam-3142	232	12	follows	follow	VERB
ejpam-3142	232	13	.	.	PUNCT
ejpam-3142	233	1	m.	m.	NOUN
ejpam-3142	233	2	k.	k.	PROPN
ejpam-3142	234	1	abu	abu	PROPN
ejpam-3142	235	1	nawas	nawas	PROPN
ejpam-3142	235	2	,	,	PUNCT
ejpam-3142	235	3	r.	r.	PROPN
ejpam-3142	235	4	m.	m.	PROPN
ejpam-3142	235	5	al	al	PROPN
ejpam-3142	235	6	-	-	PUNCT
ejpam-3142	235	7	omary	omary	ADJ
ejpam-3142	235	8	/	/	SYM
ejpam-3142	235	9	eur	eur	PROPN
ejpam-3142	235	10	.	.	PUNCT
ejpam-3142	236	1	j.	j.	PROPN
ejpam-3142	236	2	pure	pure	PROPN
ejpam-3142	236	3	appl	appl	PROPN
ejpam-3142	236	4	.	.	PROPN
ejpam-3142	236	5	math	math	PROPN
ejpam-3142	236	6	,	,	PUNCT
ejpam-3142	236	7	11	11	NUM
ejpam-3142	236	8	(	(	PUNCT
ejpam-3142	236	9	1	1	NUM
ejpam-3142	236	10	)	)	PUNCT
ejpam-3142	236	11	(	(	PUNCT
ejpam-3142	236	12	2018	2018	NUM
ejpam-3142	236	13	)	)	PUNCT
ejpam-3142	236	14	,	,	PUNCT
ejpam-3142	236	15	79	79	NUM
ejpam-3142	236	16	-	-	SYM
ejpam-3142	236	17	89	89	NUM
ejpam-3142	236	18	85	85	NUM
ejpam-3142	236	19	theorem	theorem	NOUN
ejpam-3142	236	20	3.6	3.6	NUM
ejpam-3142	236	21	.	.	PUNCT
ejpam-3142	237	1	let	let	VERB
ejpam-3142	237	2	r	r	PRON
ejpam-3142	237	3	be	be	AUX
ejpam-3142	237	4	a	a	DET
ejpam-3142	237	5	prime	prime	ADJ
ejpam-3142	237	6	ring	ring	NOUN
ejpam-3142	237	7	and	and	CCONJ
ejpam-3142	237	8	i	i	PRON
ejpam-3142	237	9	a	a	DET
ejpam-3142	237	10	nonzero	nonzero	NOUN
ejpam-3142	237	11	left	leave	VERB
ejpam-3142	237	12	ideal	ideal	NOUN
ejpam-3142	237	13	of	of	ADP
ejpam-3142	237	14	r	r	NOUN
ejpam-3142	237	15	such	such	ADJ
ejpam-3142	237	16	that	that	SCONJ
ejpam-3142	237	17	i∩z(r	i∩z(r	PRON
ejpam-3142	237	18	)	)	PUNCT
ejpam-3142	237	19	6=	6=	ADP
ejpam-3142	237	20	0	0	X
ejpam-3142	237	21	.	.	PUNCT
ejpam-3142	237	22	suppose	suppose	VERB
ejpam-3142	237	23	that	that	SCONJ
ejpam-3142	237	24	r	r	NOUN
ejpam-3142	237	25	admits	admit	VERB
ejpam-3142	237	26	a	a	DET
ejpam-3142	237	27	generalized	generalized	ADJ
ejpam-3142	237	28	derivations	derivation	NOUN
ejpam-3142	237	29	f	f	NOUN
ejpam-3142	237	30	and	and	CCONJ
ejpam-3142	237	31	g	g	NOUN
ejpam-3142	237	32	with	with	ADP
ejpam-3142	237	33	associated	associated	ADJ
ejpam-3142	237	34	derivations	derivation	NOUN
ejpam-3142	237	35	d	d	NOUN
ejpam-3142	237	36	and	and	CCONJ
ejpam-3142	237	37	g	g	NOUN
ejpam-3142	237	38	respectively	respectively	ADV
ejpam-3142	237	39	,	,	PUNCT
ejpam-3142	237	40	such	such	ADJ
ejpam-3142	237	41	that	that	SCONJ
ejpam-3142	237	42	g(z(r	g(z(r	PROPN
ejpam-3142	237	43	)	)	PUNCT
ejpam-3142	237	44	)	)	PUNCT
ejpam-3142	238	1	6=	6=	ADP
ejpam-3142	238	2	0	0	X
ejpam-3142	238	3	.	.	PUNCT
ejpam-3142	239	1	further	far	ADV
ejpam-3142	239	2	,	,	PUNCT
ejpam-3142	239	3	if	if	SCONJ
ejpam-3142	239	4	r	r	NOUN
ejpam-3142	239	5	satisfies	satisfy	VERB
ejpam-3142	239	6	any	any	DET
ejpam-3142	239	7	one	one	NUM
ejpam-3142	239	8	of	of	ADP
ejpam-3142	239	9	the	the	DET
ejpam-3142	239	10	following	following	ADJ
ejpam-3142	239	11	conditions	condition	NOUN
ejpam-3142	239	12	:	:	PUNCT
ejpam-3142	239	13	(	(	PUNCT
ejpam-3142	239	14	i	i	NOUN
ejpam-3142	239	15	)	)	PUNCT
ejpam-3142	240	1	[	[	X
ejpam-3142	240	2	f	f	X
ejpam-3142	240	3	(	(	PUNCT
ejpam-3142	240	4	x	x	NOUN
ejpam-3142	240	5	)	)	PUNCT
ejpam-3142	240	6	,	,	PUNCT
ejpam-3142	240	7	g(y)]−	g(y)]−	PROPN
ejpam-3142	241	1	[	[	X
ejpam-3142	241	2	x	x	X
ejpam-3142	241	3	,	,	PUNCT
ejpam-3142	241	4	y	y	PROPN
ejpam-3142	241	5	]	]	X
ejpam-3142	241	6	∈	∈	PROPN
ejpam-3142	241	7	z(r	z(r	PROPN
ejpam-3142	241	8	)	)	PUNCT
ejpam-3142	241	9	,	,	PUNCT
ejpam-3142	241	10	for	for	ADP
ejpam-3142	241	11	all	all	DET
ejpam-3142	241	12	x	x	NOUN
ejpam-3142	241	13	,	,	PUNCT
ejpam-3142	241	14	y	y	PROPN
ejpam-3142	241	15	∈	∈	PROPN
ejpam-3142	242	1	i	i	PRON
ejpam-3142	242	2	,	,	PUNCT
ejpam-3142	242	3	or	or	CCONJ
ejpam-3142	242	4	(	(	PUNCT
ejpam-3142	242	5	ii	ii	NOUN
ejpam-3142	242	6	)	)	PUNCT
ejpam-3142	243	1	[	[	X
ejpam-3142	243	2	f	f	X
ejpam-3142	243	3	(	(	PUNCT
ejpam-3142	243	4	x	x	NOUN
ejpam-3142	243	5	)	)	PUNCT
ejpam-3142	243	6	,	,	PUNCT
ejpam-3142	243	7	g(y	g(y	PROPN
ejpam-3142	243	8	)	)	PUNCT
ejpam-3142	243	9	]	]	PUNCT
ejpam-3142	244	1	+	+	CCONJ
ejpam-3142	244	2	[	[	X
ejpam-3142	244	3	x	x	X
ejpam-3142	244	4	,	,	PUNCT
ejpam-3142	244	5	y	y	PROPN
ejpam-3142	244	6	]	]	X
ejpam-3142	244	7	∈	∈	PROPN
ejpam-3142	244	8	z(r	z(r	PROPN
ejpam-3142	244	9	)	)	PUNCT
ejpam-3142	244	10	,	,	PUNCT
ejpam-3142	244	11	for	for	ADP
ejpam-3142	244	12	all	all	DET
ejpam-3142	244	13	x	x	NOUN
ejpam-3142	244	14	,	,	PUNCT
ejpam-3142	244	15	y	y	PROPN
ejpam-3142	244	16	∈	∈	PROPN
ejpam-3142	245	1	i	i	PRON
ejpam-3142	245	2	,	,	PUNCT
ejpam-3142	245	3	then	then	ADV
ejpam-3142	245	4	r	r	NOUN
ejpam-3142	245	5	is	be	AUX
ejpam-3142	245	6	commutative	commutative	ADJ
ejpam-3142	245	7	.	.	PUNCT
ejpam-3142	246	1	proof	proof	NOUN
ejpam-3142	246	2	.	.	PUNCT
ejpam-3142	247	1	given	give	VERB
ejpam-3142	247	2	that	that	PRON
ejpam-3142	247	3	f	f	PROPN
ejpam-3142	247	4	and	and	CCONJ
ejpam-3142	247	5	g	g	PROPN
ejpam-3142	247	6	are	be	AUX
ejpam-3142	247	7	generalized	generalized	ADJ
ejpam-3142	247	8	derivations	derivation	NOUN
ejpam-3142	247	9	of	of	ADP
ejpam-3142	247	10	r	r	NOUN
ejpam-3142	247	11	such	such	ADJ
ejpam-3142	247	12	that	that	SCONJ
ejpam-3142	247	13	[	[	X
ejpam-3142	247	14	f	f	X
ejpam-3142	247	15	(	(	PUNCT
ejpam-3142	247	16	x	x	NOUN
ejpam-3142	247	17	)	)	PUNCT
ejpam-3142	247	18	,	,	PUNCT
ejpam-3142	247	19	g(y)]−[x	g(y)]−[x	PROPN
ejpam-3142	247	20	,	,	PUNCT
ejpam-3142	247	21	y	y	PROPN
ejpam-3142	247	22	]	]	X
ejpam-3142	247	23	∈	∈	PROPN
ejpam-3142	247	24	z(r	z(r	PROPN
ejpam-3142	247	25	)	)	PUNCT
ejpam-3142	247	26	for	for	ADP
ejpam-3142	247	27	all	all	DET
ejpam-3142	247	28	x	x	NOUN
ejpam-3142	247	29	,	,	PUNCT
ejpam-3142	247	30	y	y	PROPN
ejpam-3142	247	31	∈	∈	PROPN
ejpam-3142	247	32	i.	i.	NOUN
ejpam-3142	247	33	if	if	SCONJ
ejpam-3142	247	34	f	f	PROPN
ejpam-3142	247	35	=	=	SYM
ejpam-3142	247	36	0	0	PUNCT
ejpam-3142	247	37	(	(	PUNCT
ejpam-3142	247	38	or	or	CCONJ
ejpam-3142	247	39	g	g	NOUN
ejpam-3142	247	40	=	=	SYM
ejpam-3142	247	41	0	0	NUM
ejpam-3142	247	42	)	)	PUNCT
ejpam-3142	247	43	,	,	PUNCT
ejpam-3142	247	44	then	then	ADV
ejpam-3142	247	45	[	[	X
ejpam-3142	247	46	x	x	X
ejpam-3142	247	47	,	,	PUNCT
ejpam-3142	247	48	y	y	PROPN
ejpam-3142	247	49	]	]	X
ejpam-3142	247	50	∈	∈	PROPN
ejpam-3142	247	51	z(r	z(r	PROPN
ejpam-3142	247	52	)	)	PUNCT
ejpam-3142	247	53	for	for	ADP
ejpam-3142	247	54	all	all	DET
ejpam-3142	247	55	x	x	NOUN
ejpam-3142	247	56	,	,	PUNCT
ejpam-3142	247	57	y	y	PROPN
ejpam-3142	247	58	∈	∈	PROPN
ejpam-3142	247	59	i	i	PRON
ejpam-3142	247	60	,	,	PUNCT
ejpam-3142	247	61	and	and	CCONJ
ejpam-3142	247	62	hence	hence	ADV
ejpam-3142	247	63	by	by	ADP
ejpam-3142	247	64	lemma	lemma	PROPN
ejpam-3142	247	65	2.5	2.5	NUM
ejpam-3142	247	66	(	(	PUNCT
ejpam-3142	247	67	a	a	NOUN
ejpam-3142	247	68	)	)	PUNCT
ejpam-3142	247	69	,	,	PUNCT
ejpam-3142	247	70	r	r	NOUN
ejpam-3142	247	71	is	be	AUX
ejpam-3142	247	72	a	a	DET
ejpam-3142	247	73	commutative	commutative	ADJ
ejpam-3142	247	74	.	.	PUNCT
ejpam-3142	248	1	therefore	therefore	ADV
ejpam-3142	248	2	,	,	PUNCT
ejpam-3142	248	3	we	we	PRON
ejpam-3142	248	4	shall	shall	AUX
ejpam-3142	248	5	assume	assume	VERB
ejpam-3142	248	6	that	that	SCONJ
ejpam-3142	248	7	f	f	PROPN
ejpam-3142	249	1	6=	6=	ADP
ejpam-3142	249	2	0	0	NUM
ejpam-3142	249	3	(	(	PUNCT
ejpam-3142	249	4	and	and	CCONJ
ejpam-3142	249	5	g	g	PROPN
ejpam-3142	249	6	6=	6=	PROPN
ejpam-3142	249	7	0	0	NUM
ejpam-3142	249	8	)	)	PUNCT
ejpam-3142	249	9	.	.	PUNCT
ejpam-3142	250	1	for	for	ADP
ejpam-3142	250	2	any	any	DET
ejpam-3142	250	3	x	x	NOUN
ejpam-3142	250	4	,	,	PUNCT
ejpam-3142	250	5	y	y	PROPN
ejpam-3142	250	6	∈	∈	PROPN
ejpam-3142	250	7	i	i	PRON
ejpam-3142	250	8	we	we	PRON
ejpam-3142	250	9	have	have	VERB
ejpam-3142	250	10	[	[	X
ejpam-3142	250	11	f	f	X
ejpam-3142	250	12	(	(	PUNCT
ejpam-3142	250	13	x	x	NOUN
ejpam-3142	250	14	)	)	PUNCT
ejpam-3142	250	15	,	,	PUNCT
ejpam-3142	250	16	g(y)]−	g(y)]−	PROPN
ejpam-3142	251	1	[	[	X
ejpam-3142	251	2	x	x	X
ejpam-3142	251	3	,	,	PUNCT
ejpam-3142	251	4	y	y	PROPN
ejpam-3142	251	5	]	]	X
ejpam-3142	251	6	∈	∈	PROPN
ejpam-3142	251	7	z(r	z(r	PROPN
ejpam-3142	251	8	)	)	PUNCT
ejpam-3142	251	9	.	.	PUNCT
ejpam-3142	252	1	(	(	PUNCT
ejpam-3142	252	2	7	7	X
ejpam-3142	252	3	)	)	PUNCT
ejpam-3142	252	4	since	since	SCONJ
ejpam-3142	252	5	g(z(r	g(z(r	ADJ
ejpam-3142	252	6	)	)	PUNCT
ejpam-3142	252	7	)	)	PUNCT
ejpam-3142	252	8	6=	6=	ADP
ejpam-3142	252	9	0	0	NUM
ejpam-3142	252	10	,	,	PUNCT
ejpam-3142	252	11	then	then	ADV
ejpam-3142	252	12	there	there	PRON
ejpam-3142	252	13	exists	exist	VERB
ejpam-3142	252	14	z	z	PROPN
ejpam-3142	252	15	∈	∈	PROPN
ejpam-3142	252	16	z(r	z(r	PROPN
ejpam-3142	252	17	)	)	PUNCT
ejpam-3142	253	1	such	such	ADJ
ejpam-3142	253	2	that	that	SCONJ
ejpam-3142	253	3	g(z	g(z	PROPN
ejpam-3142	253	4	)	)	PUNCT
ejpam-3142	253	5	6=	6=	ADP
ejpam-3142	253	6	0	0	X
ejpam-3142	253	7	.	.	X
ejpam-3142	254	1	replacing	replace	VERB
ejpam-3142	254	2	y	y	PRON
ejpam-3142	254	3	by	by	ADP
ejpam-3142	254	4	zy	zy	PROPN
ejpam-3142	254	5	in	in	ADP
ejpam-3142	254	6	(	(	PUNCT
ejpam-3142	254	7	7	7	NUM
ejpam-3142	254	8	)	)	PUNCT
ejpam-3142	254	9	and	and	CCONJ
ejpam-3142	254	10	using	use	VERB
ejpam-3142	254	11	(	(	PUNCT
ejpam-3142	254	12	7	7	NUM
ejpam-3142	254	13	)	)	PUNCT
ejpam-3142	254	14	,	,	PUNCT
ejpam-3142	254	15	we	we	PRON
ejpam-3142	254	16	get	get	VERB
ejpam-3142	254	17	g(z)[f	g(z)[f	NOUN
ejpam-3142	254	18	(	(	PUNCT
ejpam-3142	254	19	x	x	NOUN
ejpam-3142	254	20	)	)	PUNCT
ejpam-3142	254	21	,	,	PUNCT
ejpam-3142	254	22	y	y	PROPN
ejpam-3142	254	23	]	]	PUNCT
ejpam-3142	255	1	+	+	CCONJ
ejpam-3142	255	2	[	[	X
ejpam-3142	255	3	f	f	X
ejpam-3142	255	4	(	(	PUNCT
ejpam-3142	255	5	x	x	NOUN
ejpam-3142	255	6	)	)	PUNCT
ejpam-3142	255	7	,	,	PUNCT
ejpam-3142	255	8	g(z)]y	g(z)]y	PROPN
ejpam-3142	255	9	∈	∈	PROPN
ejpam-3142	255	10	z(r	z(r	PROPN
ejpam-3142	255	11	)	)	PUNCT
ejpam-3142	255	12	for	for	ADP
ejpam-3142	255	13	all	all	DET
ejpam-3142	255	14	x	x	NOUN
ejpam-3142	255	15	,	,	PUNCT
ejpam-3142	255	16	y	y	PROPN
ejpam-3142	255	17	∈	∈	PROPN
ejpam-3142	255	18	i	i	PRON
ejpam-3142	255	19	,	,	PUNCT
ejpam-3142	255	20	since	since	SCONJ
ejpam-3142	255	21	by	by	ADP
ejpam-3142	255	22	lemma	lemma	PROPN
ejpam-3142	255	23	2.1	2.1	NUM
ejpam-3142	255	24	,	,	PUNCT
ejpam-3142	255	25	g(z	g(z	PROPN
ejpam-3142	255	26	)	)	PUNCT
ejpam-3142	255	27	∈	∈	PROPN
ejpam-3142	255	28	z(r	z(r	PROPN
ejpam-3142	255	29	)	)	PUNCT
ejpam-3142	255	30	so	so	SCONJ
ejpam-3142	255	31	we	we	PRON
ejpam-3142	255	32	find	find	VERB
ejpam-3142	255	33	that	that	DET
ejpam-3142	255	34	g(z)[f	g(z)[f	NOUN
ejpam-3142	255	35	(	(	PUNCT
ejpam-3142	255	36	x	x	NOUN
ejpam-3142	255	37	)	)	PUNCT
ejpam-3142	255	38	,	,	PUNCT
ejpam-3142	255	39	y	y	PROPN
ejpam-3142	255	40	]	]	X
ejpam-3142	255	41	∈	∈	PROPN
ejpam-3142	255	42	z(r	z(r	PROPN
ejpam-3142	255	43	)	)	PUNCT
ejpam-3142	255	44	.	.	PUNCT
ejpam-3142	256	1	thus	thus	ADV
ejpam-3142	256	2	,	,	PUNCT
ejpam-3142	256	3	by	by	ADP
ejpam-3142	256	4	remark	remark	NOUN
ejpam-3142	256	5	2.2	2.2	NUM
ejpam-3142	256	6	,	,	PUNCT
ejpam-3142	256	7	we	we	PRON
ejpam-3142	256	8	find	find	VERB
ejpam-3142	256	9	that	that	SCONJ
ejpam-3142	256	10	[	[	X
ejpam-3142	256	11	f	f	X
ejpam-3142	256	12	(	(	PUNCT
ejpam-3142	256	13	x	x	NOUN
ejpam-3142	256	14	)	)	PUNCT
ejpam-3142	256	15	,	,	PUNCT
ejpam-3142	256	16	y	y	PROPN
ejpam-3142	256	17	]	]	X
ejpam-3142	256	18	∈	∈	PROPN
ejpam-3142	256	19	z(r	z(r	PROPN
ejpam-3142	256	20	)	)	PUNCT
ejpam-3142	256	21	for	for	ADP
ejpam-3142	256	22	all	all	DET
ejpam-3142	256	23	x	x	NOUN
ejpam-3142	256	24	,	,	PUNCT
ejpam-3142	256	25	y	y	PROPN
ejpam-3142	256	26	∈	∈	PROPN
ejpam-3142	256	27	i.	i.	NOUN
ejpam-3142	256	28	in	in	ADP
ejpam-3142	256	29	particular	particular	ADJ
ejpam-3142	256	30	[	[	X
ejpam-3142	256	31	f	f	X
ejpam-3142	256	32	(	(	PUNCT
ejpam-3142	256	33	x	x	NOUN
ejpam-3142	256	34	)	)	PUNCT
ejpam-3142	256	35	,	,	PUNCT
ejpam-3142	256	36	x	x	X
ejpam-3142	256	37	]	]	X
ejpam-3142	256	38	∈	∈	PROPN
ejpam-3142	256	39	z(r	z(r	PROPN
ejpam-3142	256	40	)	)	PUNCT
ejpam-3142	256	41	for	for	ADP
ejpam-3142	256	42	all	all	DET
ejpam-3142	256	43	x	x	SYM
ejpam-3142	256	44	∈	∈	PROPN
ejpam-3142	256	45	i.	i.	NOUN
ejpam-3142	256	46	hence	hence	ADV
ejpam-3142	256	47	,	,	PUNCT
ejpam-3142	256	48	r	r	NOUN
ejpam-3142	256	49	is	be	AUX
ejpam-3142	256	50	commutative	commutative	ADJ
ejpam-3142	256	51	by	by	ADP
ejpam-3142	256	52	lemma	lemma	PROPN
ejpam-3142	256	53	2.2	2.2	NUM
ejpam-3142	256	54	.	.	PUNCT
ejpam-3142	257	1	(	(	PUNCT
ejpam-3142	257	2	ii	ii	NOUN
ejpam-3142	257	3	)	)	PUNCT
ejpam-3142	257	4	using	use	VERB
ejpam-3142	257	5	the	the	DET
ejpam-3142	257	6	same	same	ADJ
ejpam-3142	257	7	technique	technique	NOUN
ejpam-3142	257	8	as	as	ADP
ejpam-3142	257	9	above	above	ADV
ejpam-3142	257	10	we	we	PRON
ejpam-3142	257	11	get	get	VERB
ejpam-3142	257	12	the	the	DET
ejpam-3142	257	13	required	require	VERB
ejpam-3142	257	14	result	result	NOUN
ejpam-3142	257	15	.	.	PUNCT
ejpam-3142	258	1	theorem	theorem	VERB
ejpam-3142	258	2	3.7	3.7	NUM
ejpam-3142	258	3	.	.	PUNCT
ejpam-3142	259	1	let	let	VERB
ejpam-3142	259	2	r	r	PRON
ejpam-3142	259	3	be	be	AUX
ejpam-3142	259	4	a	a	DET
ejpam-3142	259	5	prime	prime	ADJ
ejpam-3142	259	6	ring	ring	NOUN
ejpam-3142	259	7	and	and	CCONJ
ejpam-3142	259	8	i	i	PRON
ejpam-3142	259	9	a	a	DET
ejpam-3142	259	10	nonzero	nonzero	NOUN
ejpam-3142	259	11	left	leave	VERB
ejpam-3142	259	12	ideal	ideal	NOUN
ejpam-3142	259	13	of	of	ADP
ejpam-3142	259	14	r	r	NOUN
ejpam-3142	259	15	such	such	ADJ
ejpam-3142	259	16	that	that	SCONJ
ejpam-3142	259	17	i∩z(r	i∩z(r	PRON
ejpam-3142	259	18	)	)	PUNCT
ejpam-3142	259	19	6=	6=	ADP
ejpam-3142	259	20	0	0	X
ejpam-3142	259	21	.	.	PUNCT
ejpam-3142	259	22	suppose	suppose	VERB
ejpam-3142	259	23	that	that	SCONJ
ejpam-3142	259	24	r	r	NOUN
ejpam-3142	259	25	admits	admit	VERB
ejpam-3142	259	26	a	a	DET
ejpam-3142	259	27	generalized	generalized	ADJ
ejpam-3142	259	28	derivations	derivation	NOUN
ejpam-3142	259	29	f	f	NOUN
ejpam-3142	259	30	and	and	CCONJ
ejpam-3142	259	31	g	g	NOUN
ejpam-3142	259	32	with	with	ADP
ejpam-3142	259	33	associated	associated	ADJ
ejpam-3142	259	34	derivations	derivation	NOUN
ejpam-3142	259	35	d	d	NOUN
ejpam-3142	259	36	and	and	CCONJ
ejpam-3142	259	37	g	g	NOUN
ejpam-3142	259	38	respectively	respectively	ADV
ejpam-3142	259	39	,	,	PUNCT
ejpam-3142	259	40	such	such	ADJ
ejpam-3142	259	41	that	that	SCONJ
ejpam-3142	259	42	{	{	PUNCT
ejpam-3142	259	43	z	z	NOUN
ejpam-3142	259	44	∈	∈	PROPN
ejpam-3142	259	45	z(r	z(r	PROPN
ejpam-3142	259	46	)	)	PUNCT
ejpam-3142	259	47	|	|	ADV
ejpam-3142	259	48	d(z	d(z	NOUN
ejpam-3142	259	49	)	)	PUNCT
ejpam-3142	260	1	=	=	PUNCT
ejpam-3142	260	2	g(z	g(z	PROPN
ejpam-3142	260	3	)	)	PUNCT
ejpam-3142	261	1	6=	6=	ADP
ejpam-3142	261	2	0	0	NUM
ejpam-3142	261	3	}	}	PUNCT
ejpam-3142	261	4	6=	6=	NUM
ejpam-3142	261	5	φ	φ	PROPN
ejpam-3142	261	6	.	.	PUNCT
ejpam-3142	262	1	further	far	ADV
ejpam-3142	262	2	,	,	PUNCT
ejpam-3142	262	3	if	if	SCONJ
ejpam-3142	262	4	r	r	NOUN
ejpam-3142	262	5	satisfies	satisfy	VERB
ejpam-3142	262	6	any	any	DET
ejpam-3142	262	7	one	one	NUM
ejpam-3142	262	8	of	of	ADP
ejpam-3142	262	9	the	the	DET
ejpam-3142	262	10	following	following	ADJ
ejpam-3142	262	11	conditions	condition	NOUN
ejpam-3142	262	12	:	:	PUNCT
ejpam-3142	262	13	(	(	PUNCT
ejpam-3142	262	14	i	i	NOUN
ejpam-3142	262	15	)	)	PUNCT
ejpam-3142	263	1	[	[	X
ejpam-3142	263	2	f	f	X
ejpam-3142	263	3	(	(	PUNCT
ejpam-3142	263	4	x	x	NOUN
ejpam-3142	263	5	)	)	PUNCT
ejpam-3142	263	6	,	,	PUNCT
ejpam-3142	263	7	x]−	x]−	PUNCT
ejpam-3142	264	1	[	[	X
ejpam-3142	264	2	x	x	X
ejpam-3142	264	3	,	,	PUNCT
ejpam-3142	264	4	g(x	g(x	NOUN
ejpam-3142	264	5	)	)	PUNCT
ejpam-3142	264	6	]	]	PUNCT
ejpam-3142	264	7	∈	∈	PROPN
ejpam-3142	264	8	z(r	z(r	PROPN
ejpam-3142	264	9	)	)	PUNCT
ejpam-3142	264	10	,	,	PUNCT
ejpam-3142	264	11	for	for	ADP
ejpam-3142	264	12	all	all	DET
ejpam-3142	264	13	x	x	SYM
ejpam-3142	264	14	∈	∈	PROPN
ejpam-3142	264	15	i	i	PRON
ejpam-3142	264	16	,	,	PUNCT
ejpam-3142	264	17	or	or	CCONJ
ejpam-3142	264	18	(	(	PUNCT
ejpam-3142	264	19	ii	ii	NOUN
ejpam-3142	264	20	)	)	PUNCT
ejpam-3142	265	1	[	[	X
ejpam-3142	265	2	f	f	X
ejpam-3142	265	3	(	(	PUNCT
ejpam-3142	265	4	x	x	NOUN
ejpam-3142	265	5	)	)	PUNCT
ejpam-3142	265	6	,	,	PUNCT
ejpam-3142	265	7	x	x	X
ejpam-3142	265	8	]	]	X
ejpam-3142	266	1	+	+	CCONJ
ejpam-3142	266	2	[	[	X
ejpam-3142	266	3	x	x	X
ejpam-3142	266	4	,	,	PUNCT
ejpam-3142	266	5	g(x	g(x	NOUN
ejpam-3142	266	6	)	)	PUNCT
ejpam-3142	266	7	]	]	PUNCT
ejpam-3142	266	8	∈	∈	PROPN
ejpam-3142	266	9	z(r	z(r	PROPN
ejpam-3142	266	10	)	)	PUNCT
ejpam-3142	266	11	,	,	PUNCT
ejpam-3142	266	12	for	for	ADP
ejpam-3142	266	13	all	all	PRON
ejpam-3142	266	14	x	x	SYM
ejpam-3142	266	15	∈	∈	PROPN
ejpam-3142	266	16	i	i	PRON
ejpam-3142	266	17	,	,	PUNCT
ejpam-3142	266	18	then	then	ADV
ejpam-3142	266	19	r	r	NOUN
ejpam-3142	266	20	is	be	AUX
ejpam-3142	266	21	commutative	commutative	ADJ
ejpam-3142	266	22	.	.	PUNCT
ejpam-3142	267	1	proof	proof	NOUN
ejpam-3142	267	2	.	.	PUNCT
ejpam-3142	268	1	(	(	PUNCT
ejpam-3142	268	2	i	i	NOUN
ejpam-3142	268	3	)	)	PUNCT
ejpam-3142	268	4	it	it	PRON
ejpam-3142	268	5	is	be	AUX
ejpam-3142	268	6	given	give	VERB
ejpam-3142	268	7	that	that	SCONJ
ejpam-3142	268	8	f	f	PROPN
ejpam-3142	268	9	and	and	CCONJ
ejpam-3142	268	10	g	g	PROPN
ejpam-3142	268	11	are	be	AUX
ejpam-3142	268	12	generalized	generalized	ADJ
ejpam-3142	268	13	derivations	derivation	NOUN
ejpam-3142	268	14	of	of	ADP
ejpam-3142	268	15	r	r	NOUN
ejpam-3142	268	16	such	such	ADJ
ejpam-3142	268	17	that	that	SCONJ
ejpam-3142	269	1	[	[	X
ejpam-3142	269	2	f	f	X
ejpam-3142	269	3	(	(	PUNCT
ejpam-3142	269	4	x	x	NOUN
ejpam-3142	269	5	)	)	PUNCT
ejpam-3142	269	6	,	,	PUNCT
ejpam-3142	269	7	x]−	x]−	PUNCT
ejpam-3142	270	1	[	[	X
ejpam-3142	270	2	x	x	X
ejpam-3142	270	3	,	,	PUNCT
ejpam-3142	270	4	g(x	g(x	NOUN
ejpam-3142	270	5	)	)	PUNCT
ejpam-3142	270	6	]	]	PUNCT
ejpam-3142	270	7	∈	∈	PROPN
ejpam-3142	270	8	z(r	z(r	PROPN
ejpam-3142	270	9	)	)	PUNCT
ejpam-3142	270	10	for	for	ADP
ejpam-3142	270	11	all	all	DET
ejpam-3142	270	12	x	x	SYM
ejpam-3142	270	13	∈	∈	PROPN
ejpam-3142	270	14	i.	i.	NOUN
ejpam-3142	270	15	if	if	SCONJ
ejpam-3142	270	16	g	g	PROPN
ejpam-3142	270	17	=	=	NOUN
ejpam-3142	270	18	0	0	PUNCT
ejpam-3142	271	1	then	then	ADV
ejpam-3142	271	2	[	[	X
ejpam-3142	271	3	f	f	X
ejpam-3142	271	4	(	(	PUNCT
ejpam-3142	271	5	x	x	NOUN
ejpam-3142	271	6	)	)	PUNCT
ejpam-3142	271	7	,	,	PUNCT
ejpam-3142	271	8	x	x	X
ejpam-3142	271	9	]	]	X
ejpam-3142	271	10	∈	∈	PROPN
ejpam-3142	271	11	z(r	z(r	PROPN
ejpam-3142	271	12	)	)	PUNCT
ejpam-3142	271	13	for	for	ADP
ejpam-3142	271	14	all	all	DET
ejpam-3142	271	15	x	x	SYM
ejpam-3142	271	16	∈	∈	PROPN
ejpam-3142	271	17	i	i	PRON
ejpam-3142	271	18	,	,	PUNCT
ejpam-3142	271	19	(	(	PUNCT
ejpam-3142	271	20	or	or	CCONJ
ejpam-3142	271	21	if	if	SCONJ
ejpam-3142	271	22	f	f	PROPN
ejpam-3142	271	23	=	=	SYM
ejpam-3142	271	24	0	0	PROPN
ejpam-3142	271	25	,	,	PUNCT
ejpam-3142	271	26	then	then	ADV
ejpam-3142	271	27	−[x	−[x	PROPN
ejpam-3142	271	28	,	,	PUNCT
ejpam-3142	271	29	g(x	g(x	PROPN
ejpam-3142	271	30	)	)	PUNCT
ejpam-3142	271	31	]	]	PUNCT
ejpam-3142	271	32	∈	∈	PROPN
ejpam-3142	271	33	z(r	z(r	PROPN
ejpam-3142	271	34	)	)	PUNCT
ejpam-3142	271	35	)	)	PUNCT
ejpam-3142	271	36	and	and	CCONJ
ejpam-3142	271	37	hence	hence	ADV
ejpam-3142	271	38	in	in	ADP
ejpam-3142	271	39	both	both	CCONJ
ejpam-3142	271	40	the	the	DET
ejpam-3142	271	41	cases	case	NOUN
ejpam-3142	271	42	by	by	ADP
ejpam-3142	271	43	lemma	lemma	PROPN
ejpam-3142	271	44	2.2	2.2	NUM
ejpam-3142	271	45	,	,	PUNCT
ejpam-3142	271	46	we	we	PRON
ejpam-3142	271	47	get	get	VERB
ejpam-3142	271	48	the	the	DET
ejpam-3142	271	49	required	require	VERB
ejpam-3142	271	50	result	result	NOUN
ejpam-3142	271	51	.	.	PUNCT
ejpam-3142	272	1	henceforth	henceforth	ADV
ejpam-3142	272	2	,	,	PUNCT
ejpam-3142	272	3	we	we	PRON
ejpam-3142	272	4	shall	shall	AUX
ejpam-3142	272	5	assume	assume	VERB
ejpam-3142	272	6	that	that	SCONJ
ejpam-3142	272	7	f	f	PROPN
ejpam-3142	273	1	6=	6=	ADP
ejpam-3142	273	2	0	0	NUM
ejpam-3142	273	3	(	(	PUNCT
ejpam-3142	273	4	and	and	CCONJ
ejpam-3142	273	5	g	g	PROPN
ejpam-3142	273	6	6=	6=	PROPN
ejpam-3142	273	7	0	0	NUM
ejpam-3142	273	8	)	)	PUNCT
ejpam-3142	273	9	.	.	PUNCT
ejpam-3142	274	1	for	for	ADP
ejpam-3142	274	2	any	any	DET
ejpam-3142	274	3	x	x	SYM
ejpam-3142	274	4	∈	∈	PROPN
ejpam-3142	274	5	i	i	PRON
ejpam-3142	274	6	,	,	PUNCT
ejpam-3142	274	7	we	we	PRON
ejpam-3142	274	8	have	have	VERB
ejpam-3142	274	9	[	[	X
ejpam-3142	274	10	f	f	X
ejpam-3142	274	11	(	(	PUNCT
ejpam-3142	274	12	x	x	NOUN
ejpam-3142	274	13	)	)	PUNCT
ejpam-3142	274	14	,	,	PUNCT
ejpam-3142	274	15	x]−	x]−	PUNCT
ejpam-3142	275	1	[	[	X
ejpam-3142	275	2	x	x	X
ejpam-3142	275	3	,	,	PUNCT
ejpam-3142	275	4	g(x	g(x	NOUN
ejpam-3142	275	5	)	)	PUNCT
ejpam-3142	275	6	]	]	PUNCT
ejpam-3142	275	7	∈	∈	PROPN
ejpam-3142	275	8	z(r	z(r	PROPN
ejpam-3142	275	9	)	)	PUNCT
ejpam-3142	275	10	.	.	PUNCT
ejpam-3142	276	1	linearizing	linearize	VERB
ejpam-3142	276	2	the	the	DET
ejpam-3142	276	3	above	above	ADJ
ejpam-3142	276	4	expression	expression	NOUN
ejpam-3142	276	5	,	,	PUNCT
ejpam-3142	276	6	we	we	PRON
ejpam-3142	276	7	get	get	VERB
ejpam-3142	276	8	[	[	X
ejpam-3142	276	9	f	f	X
ejpam-3142	276	10	(	(	PUNCT
ejpam-3142	276	11	x	x	NOUN
ejpam-3142	276	12	)	)	PUNCT
ejpam-3142	276	13	,	,	PUNCT
ejpam-3142	276	14	y	y	PROPN
ejpam-3142	276	15	]	]	PUNCT
ejpam-3142	277	1	+	+	CCONJ
ejpam-3142	277	2	[	[	X
ejpam-3142	277	3	f	f	X
ejpam-3142	277	4	(	(	PUNCT
ejpam-3142	277	5	y	y	PROPN
ejpam-3142	277	6	)	)	PUNCT
ejpam-3142	277	7	,	,	PUNCT
ejpam-3142	277	8	x]−	x]−	PUNCT
ejpam-3142	278	1	[	[	X
ejpam-3142	278	2	x	x	X
ejpam-3142	278	3	,	,	PUNCT
ejpam-3142	278	4	g(y)]−	g(y)]−	PROPN
ejpam-3142	279	1	[	[	X
ejpam-3142	279	2	y	y	NOUN
ejpam-3142	279	3	,	,	PUNCT
ejpam-3142	279	4	g(x	g(x	NOUN
ejpam-3142	279	5	)	)	PUNCT
ejpam-3142	279	6	]	]	PUNCT
ejpam-3142	280	1	∈	∈	PROPN
ejpam-3142	280	2	z(r	z(r	PROPN
ejpam-3142	280	3	)	)	PUNCT
ejpam-3142	280	4	.	.	PUNCT
ejpam-3142	281	1	(	(	PUNCT
ejpam-3142	281	2	8)	8)	NUM
ejpam-3142	281	3	m.	m.	NOUN
ejpam-3142	281	4	k.	k.	PROPN
ejpam-3142	282	1	abu	abu	PROPN
ejpam-3142	282	2	nawas	nawas	PROPN
ejpam-3142	282	3	,	,	PUNCT
ejpam-3142	282	4	r.	r.	PROPN
ejpam-3142	282	5	m.	m.	PROPN
ejpam-3142	283	1	al	al	PROPN
ejpam-3142	283	2	-	-	PUNCT
ejpam-3142	283	3	omary	omary	ADJ
ejpam-3142	283	4	/	/	SYM
ejpam-3142	283	5	eur	eur	PROPN
ejpam-3142	283	6	.	.	PUNCT
ejpam-3142	284	1	j.	j.	PROPN
ejpam-3142	284	2	pure	pure	PROPN
ejpam-3142	284	3	appl	appl	PROPN
ejpam-3142	284	4	.	.	PROPN
ejpam-3142	284	5	math	math	PROPN
ejpam-3142	284	6	,	,	PUNCT
ejpam-3142	284	7	11	11	NUM
ejpam-3142	284	8	(	(	PUNCT
ejpam-3142	284	9	1	1	NUM
ejpam-3142	284	10	)	)	PUNCT
ejpam-3142	284	11	(	(	PUNCT
ejpam-3142	284	12	2018	2018	NUM
ejpam-3142	284	13	)	)	PUNCT
ejpam-3142	284	14	,	,	PUNCT
ejpam-3142	284	15	79	79	NUM
ejpam-3142	284	16	-	-	SYM
ejpam-3142	284	17	89	89	NUM
ejpam-3142	284	18	86	86	NUM
ejpam-3142	284	19	since	since	SCONJ
ejpam-3142	284	20	{	{	PUNCT
ejpam-3142	284	21	z	z	PROPN
ejpam-3142	284	22	∈	∈	PROPN
ejpam-3142	284	23	z(r	z(r	PROPN
ejpam-3142	284	24	)	)	PUNCT
ejpam-3142	284	25	|	|	ADV
ejpam-3142	284	26	d(z	d(z	NOUN
ejpam-3142	284	27	)	)	PUNCT
ejpam-3142	284	28	=	=	PUNCT
ejpam-3142	285	1	g(z	g(z	PROPN
ejpam-3142	285	2	)	)	PUNCT
ejpam-3142	286	1	6=	6=	ADP
ejpam-3142	286	2	0	0	NUM
ejpam-3142	286	3	}	}	PUNCT
ejpam-3142	286	4	6=	6=	NUM
ejpam-3142	286	5	φ	φ	NUM
ejpam-3142	286	6	.	.	PUNCT
ejpam-3142	287	1	replacing	replace	VERB
ejpam-3142	287	2	y	y	PRON
ejpam-3142	287	3	by	by	ADP
ejpam-3142	287	4	zy	zy	PROPN
ejpam-3142	287	5	in	in	ADP
ejpam-3142	287	6	(	(	PUNCT
ejpam-3142	287	7	8)	8)	NUM
ejpam-3142	287	8	and	and	CCONJ
ejpam-3142	287	9	using	use	VERB
ejpam-3142	287	10	(	(	PUNCT
ejpam-3142	287	11	8)	8)	NUM
ejpam-3142	287	12	,	,	PUNCT
ejpam-3142	287	13	we	we	PRON
ejpam-3142	287	14	find	find	VERB
ejpam-3142	287	15	that	that	PRON
ejpam-3142	287	16	d(z)[y	d(z)[y	ADJ
ejpam-3142	287	17	,	,	PUNCT
ejpam-3142	287	18	x]+[d(z	x]+[d(z	NUM
ejpam-3142	287	19	)	)	PUNCT
ejpam-3142	287	20	,	,	PUNCT
ejpam-3142	287	21	x]y−g(z)[x	x]y−g(z)[x	PROPN
ejpam-3142	287	22	,	,	PUNCT
ejpam-3142	287	23	y]−[x	y]−[x	PROPN
ejpam-3142	287	24	,	,	PUNCT
ejpam-3142	287	25	g(z)]y	g(z)]y	PROPN
ejpam-3142	287	26	∈	∈	PROPN
ejpam-3142	287	27	z(r	z(r	PROPN
ejpam-3142	287	28	)	)	PUNCT
ejpam-3142	287	29	for	for	ADP
ejpam-3142	287	30	all	all	DET
ejpam-3142	287	31	x	x	NOUN
ejpam-3142	287	32	,	,	PUNCT
ejpam-3142	287	33	y	y	PROPN
ejpam-3142	287	34	∈	∈	PROPN
ejpam-3142	287	35	i.	i.	NOUN
ejpam-3142	287	36	since	since	SCONJ
ejpam-3142	287	37	z	z	PROPN
ejpam-3142	287	38	∈	∈	PROPN
ejpam-3142	287	39	z(r	z(r	PROPN
ejpam-3142	287	40	)	)	PUNCT
ejpam-3142	287	41	and	and	CCONJ
ejpam-3142	287	42	hence	hence	ADV
ejpam-3142	287	43	by	by	ADP
ejpam-3142	287	44	lemma	lemma	PROPN
ejpam-3142	287	45	2.1	2.1	NUM
ejpam-3142	287	46	,	,	PUNCT
ejpam-3142	287	47	d(z	d(z	PROPN
ejpam-3142	287	48	)	)	PUNCT
ejpam-3142	287	49	∈	∈	PROPN
ejpam-3142	287	50	z(r	z(r	PROPN
ejpam-3142	287	51	)	)	PUNCT
ejpam-3142	287	52	and	and	CCONJ
ejpam-3142	287	53	g(z	g(z	PROPN
ejpam-3142	287	54	)	)	PUNCT
ejpam-3142	287	55	∈	∈	PROPN
ejpam-3142	287	56	z(r	z(r	PROPN
ejpam-3142	287	57	)	)	PUNCT
ejpam-3142	287	58	and	and	CCONJ
ejpam-3142	287	59	therefore	therefore	ADV
ejpam-3142	287	60	(	(	PUNCT
ejpam-3142	287	61	d(z	d(z	X
ejpam-3142	287	62	)	)	PUNCT
ejpam-3142	287	63	+	+	PUNCT
ejpam-3142	287	64	g(z	g(z	ADJ
ejpam-3142	287	65	)	)	PUNCT
ejpam-3142	287	66	)	)	PUNCT
ejpam-3142	288	1	∈	∈	PROPN
ejpam-3142	288	2	z(r	z(r	PROPN
ejpam-3142	288	3	)	)	PUNCT
ejpam-3142	288	4	.	.	PUNCT
ejpam-3142	289	1	thus	thus	ADV
ejpam-3142	289	2	,	,	PUNCT
ejpam-3142	289	3	we	we	PRON
ejpam-3142	289	4	find	find	VERB
ejpam-3142	289	5	that	that	SCONJ
ejpam-3142	289	6	(	(	PUNCT
ejpam-3142	289	7	d(z)+g(z))[y	d(z)+g(z))[y	NOUN
ejpam-3142	289	8	,	,	PUNCT
ejpam-3142	289	9	x	x	X
ejpam-3142	289	10	]	]	X
ejpam-3142	289	11	∈	∈	PROPN
ejpam-3142	289	12	z(r	z(r	PROPN
ejpam-3142	289	13	)	)	PUNCT
ejpam-3142	289	14	and	and	CCONJ
ejpam-3142	289	15	hence	hence	ADV
ejpam-3142	289	16	by	by	ADP
ejpam-3142	289	17	remark	remark	NOUN
ejpam-3142	289	18	2.2	2.2	NUM
ejpam-3142	289	19	,	,	PUNCT
ejpam-3142	289	20	we	we	PRON
ejpam-3142	289	21	get	get	VERB
ejpam-3142	289	22	[	[	X
ejpam-3142	289	23	y	y	NOUN
ejpam-3142	289	24	,	,	PUNCT
ejpam-3142	289	25	x	x	X
ejpam-3142	289	26	]	]	X
ejpam-3142	289	27	∈	∈	PROPN
ejpam-3142	289	28	z(r	z(r	PROPN
ejpam-3142	289	29	)	)	PUNCT
ejpam-3142	289	30	for	for	ADP
ejpam-3142	289	31	all	all	DET
ejpam-3142	289	32	x	x	NOUN
ejpam-3142	289	33	,	,	PUNCT
ejpam-3142	289	34	y	y	PROPN
ejpam-3142	289	35	∈	∈	PROPN
ejpam-3142	289	36	i	i	PRON
ejpam-3142	289	37	and	and	CCONJ
ejpam-3142	289	38	hence	hence	ADV
ejpam-3142	289	39	by	by	ADP
ejpam-3142	289	40	lemma	lemma	PROPN
ejpam-3142	289	41	2.5	2.5	NUM
ejpam-3142	289	42	(	(	PUNCT
ejpam-3142	289	43	a	a	NOUN
ejpam-3142	289	44	)	)	PUNCT
ejpam-3142	289	45	,	,	PUNCT
ejpam-3142	289	46	we	we	PRON
ejpam-3142	289	47	get	get	VERB
ejpam-3142	289	48	the	the	DET
ejpam-3142	289	49	required	require	VERB
ejpam-3142	289	50	result	result	NOUN
ejpam-3142	289	51	.	.	PUNCT
ejpam-3142	290	1	(	(	PUNCT
ejpam-3142	290	2	ii	ii	NOUN
ejpam-3142	290	3	)	)	PUNCT
ejpam-3142	290	4	using	use	VERB
ejpam-3142	290	5	similar	similar	ADJ
ejpam-3142	290	6	arguments	argument	NOUN
ejpam-3142	290	7	as	as	ADP
ejpam-3142	290	8	above	above	ADP
ejpam-3142	290	9	it	it	PRON
ejpam-3142	290	10	follows	follow	VERB
ejpam-3142	290	11	.	.	PUNCT
ejpam-3142	291	1	theorem	theorem	VERB
ejpam-3142	291	2	3.8	3.8	NUM
ejpam-3142	291	3	.	.	PUNCT
ejpam-3142	292	1	let	let	VERB
ejpam-3142	292	2	r	r	PRON
ejpam-3142	292	3	be	be	AUX
ejpam-3142	292	4	a	a	DET
ejpam-3142	292	5	prime	prime	ADJ
ejpam-3142	292	6	ring	ring	NOUN
ejpam-3142	292	7	and	and	CCONJ
ejpam-3142	292	8	i	i	PRON
ejpam-3142	292	9	a	a	DET
ejpam-3142	292	10	nonzero	nonzero	NOUN
ejpam-3142	292	11	ideal	ideal	NOUN
ejpam-3142	292	12	of	of	ADP
ejpam-3142	292	13	r.	r.	PROPN
ejpam-3142	292	14	suppose	suppose	VERB
ejpam-3142	292	15	that	that	SCONJ
ejpam-3142	292	16	r	r	NOUN
ejpam-3142	292	17	admits	admit	VERB
ejpam-3142	292	18	a	a	DET
ejpam-3142	292	19	generalized	generalized	ADJ
ejpam-3142	292	20	derivations	derivation	NOUN
ejpam-3142	292	21	f	f	NOUN
ejpam-3142	292	22	and	and	CCONJ
ejpam-3142	292	23	g	g	NOUN
ejpam-3142	292	24	with	with	ADP
ejpam-3142	292	25	associated	associated	ADJ
ejpam-3142	292	26	derivations	derivation	NOUN
ejpam-3142	292	27	d	d	NOUN
ejpam-3142	292	28	and	and	CCONJ
ejpam-3142	292	29	g	g	NOUN
ejpam-3142	292	30	respectively	respectively	ADV
ejpam-3142	292	31	,	,	PUNCT
ejpam-3142	292	32	such	such	ADJ
ejpam-3142	292	33	that	that	SCONJ
ejpam-3142	292	34	{	{	PUNCT
ejpam-3142	292	35	z	z	NOUN
ejpam-3142	292	36	∈	∈	PROPN
ejpam-3142	292	37	z(r	z(r	PROPN
ejpam-3142	292	38	)	)	PUNCT
ejpam-3142	292	39	|	|	ADV
ejpam-3142	292	40	d(z	d(z	NOUN
ejpam-3142	292	41	)	)	PUNCT
ejpam-3142	292	42	=	=	PUNCT
ejpam-3142	293	1	g(z	g(z	PROPN
ejpam-3142	293	2	)	)	PUNCT
ejpam-3142	294	1	6=	6=	ADP
ejpam-3142	294	2	0	0	NUM
ejpam-3142	294	3	}	}	PUNCT
ejpam-3142	294	4	6=	6=	NUM
ejpam-3142	294	5	φ	φ	PROPN
ejpam-3142	294	6	.	.	PUNCT
ejpam-3142	295	1	further	far	ADV
ejpam-3142	295	2	,	,	PUNCT
ejpam-3142	295	3	if	if	SCONJ
ejpam-3142	295	4	r	r	NOUN
ejpam-3142	295	5	satisfies	satisfy	VERB
ejpam-3142	295	6	any	any	DET
ejpam-3142	295	7	one	one	NUM
ejpam-3142	295	8	of	of	ADP
ejpam-3142	295	9	the	the	DET
ejpam-3142	295	10	following	following	ADJ
ejpam-3142	295	11	conditions	condition	NOUN
ejpam-3142	295	12	:	:	PUNCT
ejpam-3142	295	13	(	(	PUNCT
ejpam-3142	295	14	i	i	NOUN
ejpam-3142	295	15	)	)	PUNCT
ejpam-3142	295	16	f	f	PROPN
ejpam-3142	295	17	(	(	PUNCT
ejpam-3142	295	18	x	x	X
ejpam-3142	295	19	)	)	PUNCT
ejpam-3142	295	20	◦	◦	NOUN
ejpam-3142	295	21	x−	x−	PROPN
ejpam-3142	295	22	x	x	SYM
ejpam-3142	295	23	◦	◦	NOUN
ejpam-3142	295	24	g(x	g(x	NOUN
ejpam-3142	295	25	)	)	PUNCT
ejpam-3142	295	26	∈	∈	PROPN
ejpam-3142	295	27	z(r	z(r	PROPN
ejpam-3142	295	28	)	)	PUNCT
ejpam-3142	295	29	,	,	PUNCT
ejpam-3142	295	30	for	for	ADP
ejpam-3142	295	31	all	all	DET
ejpam-3142	295	32	x	x	SYM
ejpam-3142	295	33	∈	∈	PROPN
ejpam-3142	295	34	i	i	PRON
ejpam-3142	295	35	,	,	PUNCT
ejpam-3142	295	36	or	or	CCONJ
ejpam-3142	295	37	(	(	PUNCT
ejpam-3142	295	38	ii	ii	PROPN
ejpam-3142	295	39	)	)	PUNCT
ejpam-3142	295	40	f	f	PROPN
ejpam-3142	295	41	(	(	PUNCT
ejpam-3142	295	42	x	x	X
ejpam-3142	295	43	)	)	PUNCT
ejpam-3142	295	44	◦	◦	NOUN
ejpam-3142	295	45	x+	x+	ADJ
ejpam-3142	295	46	x	x	SYM
ejpam-3142	295	47	◦	◦	NOUN
ejpam-3142	295	48	g(x	g(x	NOUN
ejpam-3142	295	49	)	)	PUNCT
ejpam-3142	295	50	∈	∈	PROPN
ejpam-3142	295	51	z(r	z(r	PROPN
ejpam-3142	295	52	)	)	PUNCT
ejpam-3142	295	53	,	,	PUNCT
ejpam-3142	295	54	for	for	ADP
ejpam-3142	295	55	all	all	PRON
ejpam-3142	295	56	x	x	SYM
ejpam-3142	295	57	∈	∈	PROPN
ejpam-3142	295	58	i	i	PRON
ejpam-3142	295	59	,	,	PUNCT
ejpam-3142	295	60	then	then	ADV
ejpam-3142	295	61	r	r	NOUN
ejpam-3142	295	62	is	be	AUX
ejpam-3142	295	63	commutative	commutative	ADJ
ejpam-3142	295	64	.	.	PUNCT
ejpam-3142	296	1	proof	proof	NOUN
ejpam-3142	296	2	.	.	PUNCT
ejpam-3142	297	1	(	(	PUNCT
ejpam-3142	297	2	i	i	NOUN
ejpam-3142	297	3	)	)	PUNCT
ejpam-3142	297	4	it	it	PRON
ejpam-3142	297	5	is	be	AUX
ejpam-3142	297	6	given	give	VERB
ejpam-3142	297	7	that	that	SCONJ
ejpam-3142	297	8	f	f	PROPN
ejpam-3142	297	9	and	and	CCONJ
ejpam-3142	297	10	g	g	PROPN
ejpam-3142	297	11	are	be	AUX
ejpam-3142	297	12	generalized	generalized	ADJ
ejpam-3142	297	13	derivations	derivation	NOUN
ejpam-3142	297	14	of	of	ADP
ejpam-3142	297	15	r	r	NOUN
ejpam-3142	298	1	such	such	ADJ
ejpam-3142	298	2	that	that	SCONJ
ejpam-3142	298	3	f	f	PROPN
ejpam-3142	298	4	(	(	PUNCT
ejpam-3142	298	5	x)	x)	PROPN
ejpam-3142	298	6	◦	◦	NOUN
ejpam-3142	298	7	x−x	x−x	X
ejpam-3142	298	8	◦	◦	VERB
ejpam-3142	298	9	g(x	g(x	NOUN
ejpam-3142	298	10	)	)	PUNCT
ejpam-3142	298	11	∈	∈	PROPN
ejpam-3142	298	12	z(r	z(r	PROPN
ejpam-3142	298	13	)	)	PUNCT
ejpam-3142	298	14	for	for	ADP
ejpam-3142	298	15	all	all	DET
ejpam-3142	298	16	x	x	SYM
ejpam-3142	298	17	∈	∈	PROPN
ejpam-3142	298	18	i.	i.	NOUN
ejpam-3142	298	19	if	if	SCONJ
ejpam-3142	298	20	f	f	PROPN
ejpam-3142	298	21	=	=	SYM
ejpam-3142	298	22	0	0	PROPN
ejpam-3142	298	23	,	,	PUNCT
ejpam-3142	298	24	then	then	ADV
ejpam-3142	298	25	f	f	PROPN
ejpam-3142	298	26	(	(	PUNCT
ejpam-3142	298	27	x	x	X
ejpam-3142	298	28	)	)	PUNCT
ejpam-3142	298	29	◦	◦	NOUN
ejpam-3142	298	30	x	x	SYM
ejpam-3142	298	31	∈	∈	PROPN
ejpam-3142	298	32	z(r	z(r	PROPN
ejpam-3142	298	33	)	)	PUNCT
ejpam-3142	298	34	for	for	ADP
ejpam-3142	298	35	all	all	DET
ejpam-3142	298	36	x	x	SYM
ejpam-3142	298	37	∈	∈	PROPN
ejpam-3142	298	38	i	i	PRON
ejpam-3142	298	39	,	,	PUNCT
ejpam-3142	298	40	(	(	PUNCT
ejpam-3142	298	41	or	or	CCONJ
ejpam-3142	298	42	if	if	SCONJ
ejpam-3142	298	43	g	g	NOUN
ejpam-3142	298	44	=	=	SYM
ejpam-3142	298	45	0	0	NUM
ejpam-3142	298	46	,	,	PUNCT
ejpam-3142	298	47	then	then	ADV
ejpam-3142	298	48	−(x	−(x	PROPN
ejpam-3142	298	49	◦	◦	NOUN
ejpam-3142	298	50	g(x	g(x	NOUN
ejpam-3142	298	51	)	)	PUNCT
ejpam-3142	298	52	)	)	PUNCT
ejpam-3142	299	1	∈	∈	PROPN
ejpam-3142	299	2	z(r	z(r	PROPN
ejpam-3142	299	3	)	)	PUNCT
ejpam-3142	299	4	and	and	CCONJ
ejpam-3142	299	5	hence	hence	ADV
ejpam-3142	299	6	in	in	ADP
ejpam-3142	299	7	both	both	CCONJ
ejpam-3142	299	8	the	the	DET
ejpam-3142	299	9	cases	case	NOUN
ejpam-3142	299	10	by	by	ADP
ejpam-3142	299	11	theorem	theorem	NOUN
ejpam-3142	299	12	3.1	3.1	NUM
ejpam-3142	299	13	we	we	PRON
ejpam-3142	299	14	get	get	VERB
ejpam-3142	299	15	the	the	DET
ejpam-3142	299	16	required	require	VERB
ejpam-3142	299	17	result	result	NOUN
ejpam-3142	299	18	.	.	PUNCT
ejpam-3142	300	1	henceforth	henceforth	ADV
ejpam-3142	300	2	,	,	PUNCT
ejpam-3142	300	3	we	we	PRON
ejpam-3142	300	4	shall	shall	AUX
ejpam-3142	300	5	assume	assume	VERB
ejpam-3142	300	6	that	that	SCONJ
ejpam-3142	300	7	g	g	PROPN
ejpam-3142	300	8	6=	6=	PRON
ejpam-3142	300	9	0	0	NUM
ejpam-3142	300	10	(	(	PUNCT
ejpam-3142	300	11	and	and	CCONJ
ejpam-3142	300	12	f	f	PROPN
ejpam-3142	300	13	6=	6=	PROPN
ejpam-3142	300	14	0	0	NUM
ejpam-3142	300	15	)	)	PUNCT
ejpam-3142	300	16	.	.	PUNCT
ejpam-3142	301	1	for	for	ADP
ejpam-3142	301	2	any	any	DET
ejpam-3142	301	3	x	x	SYM
ejpam-3142	301	4	∈	∈	PROPN
ejpam-3142	301	5	i	i	PRON
ejpam-3142	301	6	,	,	PUNCT
ejpam-3142	301	7	we	we	PRON
ejpam-3142	301	8	have	have	VERB
ejpam-3142	301	9	f	f	PROPN
ejpam-3142	301	10	(	(	PUNCT
ejpam-3142	301	11	x	x	X
ejpam-3142	301	12	)	)	PUNCT
ejpam-3142	301	13	◦	◦	NOUN
ejpam-3142	301	14	x−	x−	PROPN
ejpam-3142	301	15	x	x	SYM
ejpam-3142	301	16	◦	◦	NOUN
ejpam-3142	301	17	g(x	g(x	NOUN
ejpam-3142	301	18	)	)	PUNCT
ejpam-3142	301	19	∈	∈	PROPN
ejpam-3142	301	20	z(r	z(r	PROPN
ejpam-3142	301	21	)	)	PUNCT
ejpam-3142	301	22	.	.	PUNCT
ejpam-3142	302	1	linearizing	linearize	VERB
ejpam-3142	302	2	the	the	DET
ejpam-3142	302	3	last	last	ADJ
ejpam-3142	302	4	expression	expression	NOUN
ejpam-3142	302	5	,	,	PUNCT
ejpam-3142	302	6	to	to	PART
ejpam-3142	302	7	get	get	VERB
ejpam-3142	302	8	f	f	PROPN
ejpam-3142	302	9	(	(	PUNCT
ejpam-3142	302	10	x	x	NOUN
ejpam-3142	302	11	)	)	PUNCT
ejpam-3142	302	12	◦	◦	NOUN
ejpam-3142	302	13	y	y	PROPN
ejpam-3142	302	14	+	+	NUM
ejpam-3142	302	15	f	f	X
ejpam-3142	302	16	(	(	PUNCT
ejpam-3142	302	17	y	y	NOUN
ejpam-3142	302	18	)	)	PUNCT
ejpam-3142	302	19	◦	◦	NOUN
ejpam-3142	302	20	x−	x−	PROPN
ejpam-3142	302	21	x	x	SYM
ejpam-3142	302	22	◦	◦	VERB
ejpam-3142	302	23	g(y)−	g(y)−	PROPN
ejpam-3142	302	24	y	y	PROPN
ejpam-3142	302	25	◦	◦	NOUN
ejpam-3142	302	26	g(x	g(x	NOUN
ejpam-3142	302	27	)	)	PUNCT
ejpam-3142	302	28	∈	∈	PROPN
ejpam-3142	302	29	z(r	z(r	PROPN
ejpam-3142	302	30	)	)	PUNCT
ejpam-3142	302	31	.	.	PUNCT
ejpam-3142	303	1	(	(	PUNCT
ejpam-3142	303	2	9	9	X
ejpam-3142	303	3	)	)	PUNCT
ejpam-3142	303	4	since	since	SCONJ
ejpam-3142	303	5	{	{	PUNCT
ejpam-3142	303	6	z	z	PROPN
ejpam-3142	303	7	∈	∈	PROPN
ejpam-3142	303	8	z(r	z(r	PROPN
ejpam-3142	303	9	)	)	PUNCT
ejpam-3142	303	10	|	|	ADV
ejpam-3142	303	11	d(z	d(z	NOUN
ejpam-3142	303	12	)	)	PUNCT
ejpam-3142	303	13	=	=	PUNCT
ejpam-3142	304	1	g(z	g(z	PROPN
ejpam-3142	304	2	)	)	PUNCT
ejpam-3142	305	1	6=	6=	ADP
ejpam-3142	305	2	0	0	NUM
ejpam-3142	305	3	}	}	PUNCT
ejpam-3142	305	4	6=	6=	NUM
ejpam-3142	305	5	φ	φ	PROPN
ejpam-3142	305	6	.	.	PUNCT
ejpam-3142	306	1	replace	replace	VERB
ejpam-3142	306	2	y	y	PROPN
ejpam-3142	306	3	by	by	ADP
ejpam-3142	306	4	zy	zy	PROPN
ejpam-3142	306	5	in	in	ADP
ejpam-3142	306	6	(	(	PUNCT
ejpam-3142	306	7	9	9	NUM
ejpam-3142	306	8	)	)	PUNCT
ejpam-3142	306	9	and	and	CCONJ
ejpam-3142	306	10	use	use	NOUN
ejpam-3142	306	11	(	(	PUNCT
ejpam-3142	306	12	9	9	NUM
ejpam-3142	306	13	)	)	PUNCT
ejpam-3142	306	14	,	,	PUNCT
ejpam-3142	306	15	to	to	PART
ejpam-3142	306	16	get	get	VERB
ejpam-3142	306	17	d(z)(y	d(z)(y	PUNCT
ejpam-3142	306	18	◦	◦	VERB
ejpam-3142	306	19	x)−	x)−	PROPN
ejpam-3142	307	1	[	[	X
ejpam-3142	307	2	d(z	d(z	NOUN
ejpam-3142	307	3	)	)	PUNCT
ejpam-3142	307	4	,	,	PUNCT
ejpam-3142	307	5	x]y−	x]y−	PROPN
ejpam-3142	307	6	g(z)(x	g(z)(x	PUNCT
ejpam-3142	307	7	◦	◦	VERB
ejpam-3142	307	8	y)−	y)−	PROPN
ejpam-3142	307	9	[	[	X
ejpam-3142	307	10	x	x	X
ejpam-3142	307	11	,	,	PUNCT
ejpam-3142	307	12	g(z)]y	g(z)]y	PROPN
ejpam-3142	307	13	∈	∈	PROPN
ejpam-3142	307	14	z(r	z(r	PROPN
ejpam-3142	307	15	)	)	PUNCT
ejpam-3142	307	16	for	for	ADP
ejpam-3142	307	17	all	all	DET
ejpam-3142	307	18	x	x	NOUN
ejpam-3142	307	19	,	,	PUNCT
ejpam-3142	307	20	y	y	PROPN
ejpam-3142	307	21	∈	∈	PROPN
ejpam-3142	307	22	i.	i.	NOUN
ejpam-3142	307	23	hence	hence	ADV
ejpam-3142	307	24	,	,	PUNCT
ejpam-3142	307	25	by	by	ADP
ejpam-3142	307	26	lemma	lemma	PROPN
ejpam-3142	307	27	2.1	2.1	NUM
ejpam-3142	307	28	we	we	PRON
ejpam-3142	307	29	find	find	VERB
ejpam-3142	307	30	that	that	SCONJ
ejpam-3142	307	31	d(z	d(z	NOUN
ejpam-3142	307	32	)	)	PUNCT
ejpam-3142	307	33	∈	∈	PROPN
ejpam-3142	307	34	z(r	z(r	PROPN
ejpam-3142	307	35	)	)	PUNCT
ejpam-3142	307	36	and	and	CCONJ
ejpam-3142	307	37	g(z	g(z	PROPN
ejpam-3142	307	38	)	)	PUNCT
ejpam-3142	307	39	∈	∈	PROPN
ejpam-3142	307	40	z(r	z(r	PROPN
ejpam-3142	307	41	)	)	PUNCT
ejpam-3142	307	42	and	and	CCONJ
ejpam-3142	307	43	therefore	therefore	ADV
ejpam-3142	307	44	d(z	d(z	PROPN
ejpam-3142	307	45	)	)	PUNCT
ejpam-3142	307	46	−	−	ADP
ejpam-3142	308	1	g(z	g(z	PROPN
ejpam-3142	308	2	)	)	PUNCT
ejpam-3142	308	3	∈	∈	PROPN
ejpam-3142	308	4	z(r	z(r	PROPN
ejpam-3142	308	5	)	)	PUNCT
ejpam-3142	308	6	.	.	PUNCT
ejpam-3142	309	1	thus	thus	ADV
ejpam-3142	309	2	,	,	PUNCT
ejpam-3142	309	3	we	we	PRON
ejpam-3142	309	4	obtain	obtain	VERB
ejpam-3142	309	5	(	(	PUNCT
ejpam-3142	309	6	d(z)−	d(z)−	PROPN
ejpam-3142	309	7	g(z))(y	g(z))(y	PROPN
ejpam-3142	309	8	◦	◦	NOUN
ejpam-3142	309	9	x	x	SYM
ejpam-3142	309	10	)	)	PUNCT
ejpam-3142	309	11	∈	∈	PROPN
ejpam-3142	309	12	z(r	z(r	PROPN
ejpam-3142	309	13	)	)	PUNCT
ejpam-3142	309	14	and	and	CCONJ
ejpam-3142	309	15	by	by	ADP
ejpam-3142	309	16	remark	remark	NOUN
ejpam-3142	309	17	2.2	2.2	NUM
ejpam-3142	309	18	it	it	PRON
ejpam-3142	309	19	follows	follow	VERB
ejpam-3142	309	20	that	that	SCONJ
ejpam-3142	309	21	y	y	PROPN
ejpam-3142	309	22	◦	◦	NOUN
ejpam-3142	309	23	x	x	X
ejpam-3142	309	24	∈	∈	PROPN
ejpam-3142	309	25	z(r	z(r	PROPN
ejpam-3142	309	26	)	)	PUNCT
ejpam-3142	309	27	for	for	ADP
ejpam-3142	309	28	all	all	DET
ejpam-3142	309	29	x	x	NOUN
ejpam-3142	309	30	,	,	PUNCT
ejpam-3142	309	31	y	y	PROPN
ejpam-3142	309	32	∈	∈	PROPN
ejpam-3142	310	1	i	i	PRON
ejpam-3142	310	2	and	and	CCONJ
ejpam-3142	310	3	hence	hence	ADV
ejpam-3142	310	4	r	r	NOUN
ejpam-3142	310	5	is	be	AUX
ejpam-3142	310	6	commutative	commutative	ADJ
ejpam-3142	310	7	by	by	ADP
ejpam-3142	310	8	lemma	lemma	PROPN
ejpam-3142	310	9	2.5	2.5	NUM
ejpam-3142	310	10	(	(	PUNCT
ejpam-3142	310	11	b	b	NOUN
ejpam-3142	310	12	)	)	PUNCT
ejpam-3142	310	13	.	.	PUNCT
ejpam-3142	311	1	(	(	PUNCT
ejpam-3142	311	2	ii	ii	NOUN
ejpam-3142	311	3	)	)	PUNCT
ejpam-3142	311	4	using	use	VERB
ejpam-3142	311	5	similar	similar	ADJ
ejpam-3142	311	6	arguments	argument	NOUN
ejpam-3142	311	7	as	as	SCONJ
ejpam-3142	311	8	above	above	ADP
ejpam-3142	311	9	it	it	PRON
ejpam-3142	311	10	follows	follow	VERB
ejpam-3142	311	11	.	.	PUNCT
ejpam-3142	312	1	in	in	ADP
ejpam-3142	312	2	the	the	DET
ejpam-3142	312	3	next	next	ADJ
ejpam-3142	312	4	theorem	theorem	NOUN
ejpam-3142	312	5	,	,	PUNCT
ejpam-3142	312	6	we	we	PRON
ejpam-3142	312	7	consider	consider	VERB
ejpam-3142	312	8	two	two	NUM
ejpam-3142	312	9	identities	identity	NOUN
ejpam-3142	312	10	involving	involve	VERB
ejpam-3142	312	11	generalized	generalized	ADJ
ejpam-3142	312	12	(	(	PUNCT
ejpam-3142	312	13	α	α	NOUN
ejpam-3142	312	14	,	,	PUNCT
ejpam-3142	312	15	β)−derivation	β)−derivation	NOUN
ejpam-3142	312	16	f	f	PROPN
ejpam-3142	312	17	associated	associate	VERB
ejpam-3142	312	18	with	with	ADP
ejpam-3142	312	19	(	(	PUNCT
ejpam-3142	312	20	α	α	X
ejpam-3142	312	21	,	,	PUNCT
ejpam-3142	312	22	β)−derivation	β)−derivation	NOUN
ejpam-3142	312	23	d	d	NOUN
ejpam-3142	312	24	,	,	PUNCT
ejpam-3142	312	25	such	such	ADJ
ejpam-3142	312	26	that	that	SCONJ
ejpam-3142	312	27	r	r	NOUN
ejpam-3142	312	28	is	be	AUX
ejpam-3142	312	29	a	a	DET
ejpam-3142	312	30	prime	prime	ADJ
ejpam-3142	312	31	ring	ring	NOUN
ejpam-3142	312	32	with	with	ADP
ejpam-3142	312	33	involution	involution	NOUN
ejpam-3142	312	34	∗	∗	NOUN
ejpam-3142	312	35	,	,	PUNCT
ejpam-3142	312	36	and	and	CCONJ
ejpam-3142	312	37	we	we	PRON
ejpam-3142	312	38	show	show	VERB
ejpam-3142	312	39	that	that	SCONJ
ejpam-3142	312	40	r	r	NOUN
ejpam-3142	312	41	is	be	AUX
ejpam-3142	312	42	commutative	commutative	ADJ
ejpam-3142	312	43	.	.	PUNCT
ejpam-3142	313	1	theorem	theorem	VERB
ejpam-3142	313	2	3.9	3.9	NUM
ejpam-3142	313	3	.	.	PUNCT
ejpam-3142	314	1	let	let	VERB
ejpam-3142	314	2	r	r	PRON
ejpam-3142	314	3	be	be	AUX
ejpam-3142	314	4	a	a	DET
ejpam-3142	314	5	2	2	NUM
ejpam-3142	314	6	-	-	PUNCT
ejpam-3142	314	7	torsion	torsion	NOUN
ejpam-3142	314	8	free	free	ADJ
ejpam-3142	314	9	∗−prime	∗−prime	NOUN
ejpam-3142	314	10	ring	ring	NOUN
ejpam-3142	314	11	and	and	CCONJ
ejpam-3142	314	12	α	α	NOUN
ejpam-3142	314	13	,	,	PUNCT
ejpam-3142	314	14	β	β	X
ejpam-3142	314	15	be	be	VERB
ejpam-3142	314	16	automorphisms	automorphisms	PROPN
ejpam-3142	314	17	on	on	ADP
ejpam-3142	314	18	r.	r.	PROPN
ejpam-3142	314	19	if	if	SCONJ
ejpam-3142	314	20	r	r	NOUN
ejpam-3142	314	21	admits	admit	VERB
ejpam-3142	314	22	a	a	DET
ejpam-3142	314	23	generalized	generalized	ADJ
ejpam-3142	314	24	(	(	PUNCT
ejpam-3142	314	25	α	α	NOUN
ejpam-3142	314	26	,	,	PUNCT
ejpam-3142	314	27	β)-derivation	β)-derivation	PUNCT
ejpam-3142	314	28	f	f	PROPN
ejpam-3142	314	29	associated	associate	VERB
ejpam-3142	314	30	with	with	ADP
ejpam-3142	314	31	a	a	DET
ejpam-3142	314	32	nonzero	nonzero	X
ejpam-3142	314	33	(	(	PUNCT
ejpam-3142	314	34	α	α	NOUN
ejpam-3142	314	35	,	,	PUNCT
ejpam-3142	314	36	β)−derivation	β)−derivation	NOUN
ejpam-3142	314	37	d	d	ADP
ejpam-3142	314	38	such	such	ADJ
ejpam-3142	314	39	that	that	SCONJ
ejpam-3142	314	40	either	either	DET
ejpam-3142	314	41	m.	m.	NOUN
ejpam-3142	315	1	k.	k.	PROPN
ejpam-3142	316	1	abu	abu	PROPN
ejpam-3142	317	1	nawas	nawas	PROPN
ejpam-3142	317	2	,	,	PUNCT
ejpam-3142	317	3	r.	r.	PROPN
ejpam-3142	317	4	m.	m.	PROPN
ejpam-3142	317	5	al	al	PROPN
ejpam-3142	317	6	-	-	PUNCT
ejpam-3142	317	7	omary	omary	ADJ
ejpam-3142	317	8	/	/	SYM
ejpam-3142	317	9	eur	eur	PROPN
ejpam-3142	317	10	.	.	PUNCT
ejpam-3142	318	1	j.	j.	PROPN
ejpam-3142	318	2	pure	pure	PROPN
ejpam-3142	318	3	appl	appl	PROPN
ejpam-3142	318	4	.	.	PROPN
ejpam-3142	318	5	math	math	PROPN
ejpam-3142	318	6	,	,	PUNCT
ejpam-3142	318	7	11	11	NUM
ejpam-3142	318	8	(	(	PUNCT
ejpam-3142	318	9	1	1	NUM
ejpam-3142	318	10	)	)	PUNCT
ejpam-3142	318	11	(	(	PUNCT
ejpam-3142	318	12	2018	2018	NUM
ejpam-3142	318	13	)	)	PUNCT
ejpam-3142	318	14	,	,	PUNCT
ejpam-3142	318	15	79	79	NUM
ejpam-3142	318	16	-	-	SYM
ejpam-3142	318	17	89	89	NUM
ejpam-3142	318	18	87	87	NUM
ejpam-3142	318	19	(	(	PUNCT
ejpam-3142	318	20	i	i	NOUN
ejpam-3142	318	21	)	)	PUNCT
ejpam-3142	318	22	f	f	PROPN
ejpam-3142	319	1	[	[	X
ejpam-3142	319	2	x	x	X
ejpam-3142	319	3	,	,	PUNCT
ejpam-3142	319	4	y]−	y]−	VERB
ejpam-3142	319	5	[	[	X
ejpam-3142	319	6	f	f	X
ejpam-3142	319	7	(	(	PUNCT
ejpam-3142	319	8	x	x	NOUN
ejpam-3142	319	9	)	)	PUNCT
ejpam-3142	319	10	,	,	PUNCT
ejpam-3142	319	11	y]α	y]α	NOUN
ejpam-3142	319	12	,	,	PUNCT
ejpam-3142	319	13	β	β	X
ejpam-3142	319	14	=	=	PUNCT
ejpam-3142	320	1	[	[	X
ejpam-3142	320	2	d(y	d(y	NOUN
ejpam-3142	320	3	)	)	PUNCT
ejpam-3142	320	4	,	,	PUNCT
ejpam-3142	320	5	x]α	x]α	PROPN
ejpam-3142	320	6	,	,	PUNCT
ejpam-3142	320	7	β	β	VERB
ejpam-3142	320	8	for	for	ADP
ejpam-3142	320	9	all	all	DET
ejpam-3142	320	10	x	x	NOUN
ejpam-3142	320	11	,	,	PUNCT
ejpam-3142	320	12	y	y	PROPN
ejpam-3142	320	13	∈	∈	PROPN
ejpam-3142	320	14	r	r	NOUN
ejpam-3142	320	15	,	,	PUNCT
ejpam-3142	320	16	or	or	CCONJ
ejpam-3142	320	17	(	(	PUNCT
ejpam-3142	320	18	ii	ii	NOUN
ejpam-3142	320	19	)	)	PUNCT
ejpam-3142	320	20	f	f	PROPN
ejpam-3142	321	1	[	[	X
ejpam-3142	321	2	x	x	X
ejpam-3142	321	3	,	,	PUNCT
ejpam-3142	321	4	y]−	y]−	PRON
ejpam-3142	321	5	(	(	PUNCT
ejpam-3142	321	6	f	f	PROPN
ejpam-3142	321	7	(	(	PUNCT
ejpam-3142	321	8	x	x	NOUN
ejpam-3142	321	9	)	)	PUNCT
ejpam-3142	321	10	◦	◦	NOUN
ejpam-3142	321	11	y)α	y)α	NOUN
ejpam-3142	321	12	,	,	PUNCT
ejpam-3142	321	13	β	β	X
ejpam-3142	321	14	=	=	PUNCT
ejpam-3142	322	1	[	[	X
ejpam-3142	322	2	d(y	d(y	NOUN
ejpam-3142	322	3	)	)	PUNCT
ejpam-3142	322	4	,	,	PUNCT
ejpam-3142	322	5	x]α	x]α	PROPN
ejpam-3142	322	6	,	,	PUNCT
ejpam-3142	322	7	β	β	VERB
ejpam-3142	322	8	for	for	ADP
ejpam-3142	322	9	all	all	DET
ejpam-3142	322	10	x	x	NOUN
ejpam-3142	322	11	,	,	PUNCT
ejpam-3142	322	12	y	y	PROPN
ejpam-3142	322	13	∈	∈	PROPN
ejpam-3142	322	14	r	r	NOUN
ejpam-3142	322	15	,	,	PUNCT
ejpam-3142	322	16	then	then	ADV
ejpam-3142	322	17	r	r	NOUN
ejpam-3142	322	18	is	be	AUX
ejpam-3142	322	19	commutative	commutative	ADJ
ejpam-3142	322	20	.	.	PUNCT
ejpam-3142	323	1	proof	proof	NOUN
ejpam-3142	323	2	.	.	PUNCT
ejpam-3142	324	1	(	(	PUNCT
ejpam-3142	324	2	i	i	NOUN
ejpam-3142	324	3	)	)	PUNCT
ejpam-3142	324	4	if	if	SCONJ
ejpam-3142	324	5	f	f	PROPN
ejpam-3142	324	6	=	=	SYM
ejpam-3142	324	7	0	0	PROPN
ejpam-3142	324	8	,	,	PUNCT
ejpam-3142	324	9	then	then	ADV
ejpam-3142	324	10	we	we	PRON
ejpam-3142	324	11	have	have	VERB
ejpam-3142	324	12	[	[	X
ejpam-3142	324	13	d(y	d(y	NOUN
ejpam-3142	324	14	)	)	PUNCT
ejpam-3142	324	15	,	,	PUNCT
ejpam-3142	324	16	x]α	x]α	PROPN
ejpam-3142	324	17	,	,	PUNCT
ejpam-3142	324	18	β	β	X
ejpam-3142	324	19	=	=	SYM
ejpam-3142	324	20	0	0	NUM
ejpam-3142	324	21	for	for	ADP
ejpam-3142	324	22	all	all	DET
ejpam-3142	324	23	x	x	NOUN
ejpam-3142	324	24	,	,	PUNCT
ejpam-3142	324	25	y	y	PROPN
ejpam-3142	324	26	∈	∈	PROPN
ejpam-3142	324	27	r.	r.	NOUN
ejpam-3142	324	28	replacing	replace	VERB
ejpam-3142	324	29	y	y	PRON
ejpam-3142	324	30	by	by	ADP
ejpam-3142	324	31	yx	yx	PROPN
ejpam-3142	324	32	in	in	ADP
ejpam-3142	324	33	the	the	DET
ejpam-3142	324	34	last	last	ADJ
ejpam-3142	324	35	expression	expression	NOUN
ejpam-3142	324	36	gives	give	VERB
ejpam-3142	324	37	β(y)[d(x	β(y)[d(x	PUNCT
ejpam-3142	324	38	)	)	PUNCT
ejpam-3142	324	39	,	,	PUNCT
ejpam-3142	324	40	x]α	x]α	PROPN
ejpam-3142	324	41	,	,	PUNCT
ejpam-3142	324	42	β	β	X
ejpam-3142	324	43	+	+	X
ejpam-3142	325	1	[	[	X
ejpam-3142	325	2	β(y	β(y	NOUN
ejpam-3142	325	3	)	)	PUNCT
ejpam-3142	325	4	,	,	PUNCT
ejpam-3142	325	5	β(x)]d(x	β(x)]d(x	NOUN
ejpam-3142	325	6	)	)	PUNCT
ejpam-3142	325	7	=	=	SYM
ejpam-3142	325	8	0	0	X
ejpam-3142	325	9	.	.	PUNCT
ejpam-3142	325	10	again	again	ADV
ejpam-3142	325	11	replacing	replace	VERB
ejpam-3142	325	12	y	y	PRON
ejpam-3142	325	13	by	by	ADP
ejpam-3142	325	14	zy	zy	PROPN
ejpam-3142	325	15	gives	give	VERB
ejpam-3142	325	16	[	[	PRON
ejpam-3142	325	17	β(z	β(z	PROPN
ejpam-3142	325	18	)	)	PUNCT
ejpam-3142	325	19	,	,	PUNCT
ejpam-3142	325	20	β(x)]β(y)d(x	β(x)]β(y)d(x	VERB
ejpam-3142	325	21	)	)	PUNCT
ejpam-3142	325	22	=	=	SYM
ejpam-3142	325	23	0	0	NUM
ejpam-3142	325	24	for	for	ADP
ejpam-3142	325	25	all	all	DET
ejpam-3142	325	26	x	x	NOUN
ejpam-3142	325	27	,	,	PUNCT
ejpam-3142	325	28	y	y	PROPN
ejpam-3142	325	29	,	,	PUNCT
ejpam-3142	325	30	z	z	PROPN
ejpam-3142	325	31	∈	∈	PROPN
ejpam-3142	325	32	r.	r.	NOUN
ejpam-3142	325	33	but	but	CCONJ
ejpam-3142	325	34	as	as	SCONJ
ejpam-3142	325	35	β	β	PROPN
ejpam-3142	325	36	is	be	AUX
ejpam-3142	325	37	an	an	DET
ejpam-3142	325	38	automorphism	automorphism	NOUN
ejpam-3142	325	39	on	on	ADP
ejpam-3142	325	40	r	r	NOUN
ejpam-3142	325	41	,	,	PUNCT
ejpam-3142	325	42	we	we	PRON
ejpam-3142	325	43	have	have	VERB
ejpam-3142	325	44	[	[	X
ejpam-3142	325	45	β(z	β(z	PROPN
ejpam-3142	325	46	)	)	PUNCT
ejpam-3142	325	47	,	,	PUNCT
ejpam-3142	325	48	β(x)]rd(x	β(x)]rd(x	PUNCT
ejpam-3142	325	49	)	)	PUNCT
ejpam-3142	325	50	=	=	SYM
ejpam-3142	325	51	0	0	NUM
ejpam-3142	325	52	for	for	ADP
ejpam-3142	325	53	all	all	DET
ejpam-3142	325	54	x	x	NOUN
ejpam-3142	325	55	,	,	PUNCT
ejpam-3142	325	56	z	z	PROPN
ejpam-3142	325	57	∈	∈	PROPN
ejpam-3142	325	58	r.	r.	PROPN
ejpam-3142	325	59	(	(	PUNCT
ejpam-3142	325	60	10	10	NUM
ejpam-3142	325	61	)	)	PUNCT
ejpam-3142	325	62	if	if	SCONJ
ejpam-3142	325	63	x	x	PROPN
ejpam-3142	325	64	∈	∈	PROPN
ejpam-3142	325	65	s∗(r	s∗(r	PROPN
ejpam-3142	325	66	)	)	PUNCT
ejpam-3142	325	67	∩	∩	NOUN
ejpam-3142	325	68	r	r	NOUN
ejpam-3142	325	69	,	,	PUNCT
ejpam-3142	325	70	then	then	ADV
ejpam-3142	325	71	β([z	β([z	NUM
ejpam-3142	325	72	,	,	PUNCT
ejpam-3142	325	73	x])rd(x	x])rd(x	PUNCT
ejpam-3142	325	74	)	)	PUNCT
ejpam-3142	325	75	=	=	SYM
ejpam-3142	325	76	β([z	β([z	NUM
ejpam-3142	325	77	,	,	PUNCT
ejpam-3142	325	78	x])∗rd(x	x])∗rd(x	PROPN
ejpam-3142	325	79	)	)	PUNCT
ejpam-3142	325	80	.	.	PUNCT
ejpam-3142	326	1	thus	thus	ADV
ejpam-3142	326	2	,	,	PUNCT
ejpam-3142	326	3	for	for	ADP
ejpam-3142	326	4	some	some	DET
ejpam-3142	326	5	x	x	SYM
ejpam-3142	326	6	∈	∈	PROPN
ejpam-3142	326	7	s∗(r	s∗(r	PROPN
ejpam-3142	326	8	)	)	PUNCT
ejpam-3142	326	9	∩	∩	ADJ
ejpam-3142	326	10	r	r	NOUN
ejpam-3142	326	11	,	,	PUNCT
ejpam-3142	326	12	the	the	DET
ejpam-3142	326	13	∗−primeness	∗−primeness	NUM
ejpam-3142	326	14	of	of	ADP
ejpam-3142	326	15	r	r	NOUN
ejpam-3142	326	16	yields	yield	NOUN
ejpam-3142	326	17	either	either	CCONJ
ejpam-3142	326	18	β([z	β([z	NUM
ejpam-3142	326	19	,	,	PUNCT
ejpam-3142	326	20	x	x	NOUN
ejpam-3142	326	21	]	]	X
ejpam-3142	326	22	)	)	PUNCT
ejpam-3142	326	23	=	=	SYM
ejpam-3142	326	24	0	0	NUM
ejpam-3142	326	25	or	or	CCONJ
ejpam-3142	326	26	d(x	d(x	PROPN
ejpam-3142	326	27	)	)	PUNCT
ejpam-3142	326	28	=	=	SYM
ejpam-3142	326	29	0	0	X
ejpam-3142	326	30	.	.	PUNCT
ejpam-3142	327	1	but	but	CCONJ
ejpam-3142	327	2	for	for	ADP
ejpam-3142	327	3	any	any	DET
ejpam-3142	327	4	x	x	SYM
ejpam-3142	327	5	∈	∈	PROPN
ejpam-3142	327	6	r	r	NOUN
ejpam-3142	327	7	,	,	PUNCT
ejpam-3142	327	8	x	x	PUNCT
ejpam-3142	327	9	−	−	NOUN
ejpam-3142	327	10	x∗	x∗	PROPN
ejpam-3142	327	11	∈	∈	PROPN
ejpam-3142	327	12	s∗(r	s∗(r	PROPN
ejpam-3142	327	13	)	)	PUNCT
ejpam-3142	327	14	∩	∩	PROPN
ejpam-3142	327	15	r.	r.	PROPN
ejpam-3142	327	16	thus	thus	ADV
ejpam-3142	327	17	,	,	PUNCT
ejpam-3142	327	18	for	for	ADP
ejpam-3142	327	19	some	some	DET
ejpam-3142	327	20	x	x	SYM
ejpam-3142	327	21	∈	∈	PROPN
ejpam-3142	327	22	r	r	NOUN
ejpam-3142	327	23	,	,	PUNCT
ejpam-3142	327	24	either	either	CCONJ
ejpam-3142	327	25	[	[	X
ejpam-3142	327	26	z	z	X
ejpam-3142	327	27	,	,	PUNCT
ejpam-3142	327	28	x	x	PUNCT
ejpam-3142	327	29	−	−	NOUN
ejpam-3142	327	30	x∗	x∗	X
ejpam-3142	327	31	]	]	X
ejpam-3142	327	32	=	=	SYM
ejpam-3142	327	33	0	0	NUM
ejpam-3142	327	34	or	or	CCONJ
ejpam-3142	327	35	d(x	d(x	NOUN
ejpam-3142	327	36	−	−	PROPN
ejpam-3142	327	37	x∗	x∗	PROPN
ejpam-3142	327	38	)	)	PUNCT
ejpam-3142	327	39	=	=	SYM
ejpam-3142	328	1	0	0	X
ejpam-3142	328	2	.	.	PUNCT
ejpam-3142	329	1	if	if	SCONJ
ejpam-3142	329	2	[	[	X
ejpam-3142	329	3	z	z	X
ejpam-3142	329	4	,	,	PUNCT
ejpam-3142	329	5	x	x	PUNCT
ejpam-3142	329	6	−	−	NOUN
ejpam-3142	329	7	x∗	x∗	X
ejpam-3142	329	8	]	]	X
ejpam-3142	329	9	=	=	SYM
ejpam-3142	329	10	0	0	NUM
ejpam-3142	329	11	,	,	PUNCT
ejpam-3142	329	12	then	then	ADV
ejpam-3142	329	13	equation	equation	NOUN
ejpam-3142	329	14	(	(	PUNCT
ejpam-3142	329	15	10	10	NUM
ejpam-3142	329	16	)	)	PUNCT
ejpam-3142	329	17	follows	follow	VERB
ejpam-3142	329	18	that	that	SCONJ
ejpam-3142	329	19	β([z	β([z	NOUN
ejpam-3142	329	20	,	,	PUNCT
ejpam-3142	329	21	x])rd(x	x])rd(x	NUM
ejpam-3142	329	22	)	)	PUNCT
ejpam-3142	329	23	=	=	SYM
ejpam-3142	329	24	0	0	PUNCT
ejpam-3142	330	1	=	=	SYM
ejpam-3142	330	2	β([z	β([z	NUM
ejpam-3142	330	3	,	,	PUNCT
ejpam-3142	330	4	x])∗rd(x	x])∗rd(x	PROPN
ejpam-3142	330	5	)	)	PUNCT
ejpam-3142	330	6	.	.	PUNCT
ejpam-3142	331	1	hence	hence	ADV
ejpam-3142	331	2	the	the	DET
ejpam-3142	331	3	∗−primeness	∗−primeness	NUM
ejpam-3142	331	4	of	of	ADP
ejpam-3142	331	5	r	r	NOUN
ejpam-3142	331	6	yields	yield	NOUN
ejpam-3142	331	7	either	either	CCONJ
ejpam-3142	331	8	β([z	β([z	NUM
ejpam-3142	331	9	,	,	PUNCT
ejpam-3142	331	10	x	x	NOUN
ejpam-3142	331	11	]	]	X
ejpam-3142	331	12	)	)	PUNCT
ejpam-3142	331	13	=	=	SYM
ejpam-3142	331	14	0	0	NUM
ejpam-3142	331	15	or	or	CCONJ
ejpam-3142	331	16	d(x	d(x	PROPN
ejpam-3142	331	17	)	)	PUNCT
ejpam-3142	332	1	=	=	SYM
ejpam-3142	332	2	0	0	X
ejpam-3142	332	3	.	.	PUNCT
ejpam-3142	333	1	if	if	SCONJ
ejpam-3142	333	2	d(x	d(x	PROPN
ejpam-3142	333	3	−	−	PROPN
ejpam-3142	333	4	x∗	x∗	PROPN
ejpam-3142	333	5	)	)	PUNCT
ejpam-3142	333	6	=	=	SYM
ejpam-3142	333	7	0	0	NUM
ejpam-3142	333	8	then	then	ADV
ejpam-3142	333	9	d(x	d(x	NOUN
ejpam-3142	333	10	)	)	PUNCT
ejpam-3142	333	11	=	=	PUNCT
ejpam-3142	334	1	(	(	PUNCT
ejpam-3142	334	2	d(x))∗	d(x))∗	NOUN
ejpam-3142	334	3	for	for	ADP
ejpam-3142	334	4	all	all	DET
ejpam-3142	334	5	x	x	PROPN
ejpam-3142	334	6	∈	∈	PROPN
ejpam-3142	334	7	r.	r.	PROPN
ejpam-3142	334	8	consequently	consequently	ADV
ejpam-3142	334	9	,	,	PUNCT
ejpam-3142	334	10	for	for	ADP
ejpam-3142	334	11	all	all	DET
ejpam-3142	334	12	x	x	NOUN
ejpam-3142	334	13	,	,	PUNCT
ejpam-3142	334	14	z	z	PROPN
ejpam-3142	334	15	∈	∈	PROPN
ejpam-3142	334	16	r	r	NOUN
ejpam-3142	334	17	,	,	PUNCT
ejpam-3142	334	18	either	either	CCONJ
ejpam-3142	334	19	β([z	β([z	NUM
ejpam-3142	334	20	,	,	PUNCT
ejpam-3142	334	21	x	x	NOUN
ejpam-3142	334	22	]	]	X
ejpam-3142	334	23	)	)	PUNCT
ejpam-3142	334	24	=	=	SYM
ejpam-3142	334	25	0	0	NUM
ejpam-3142	334	26	or	or	CCONJ
ejpam-3142	334	27	d(x	d(x	PROPN
ejpam-3142	334	28	)	)	PUNCT
ejpam-3142	335	1	=	=	SYM
ejpam-3142	335	2	0	0	X
ejpam-3142	335	3	.	.	PUNCT
ejpam-3142	336	1	let	let	VERB
ejpam-3142	336	2	a	a	DET
ejpam-3142	336	3	=	=	SYM
ejpam-3142	336	4	{	{	PUNCT
ejpam-3142	336	5	x	x	SYM
ejpam-3142	336	6	∈	∈	PROPN
ejpam-3142	336	7	r	r	NOUN
ejpam-3142	336	8	|	|	NOUN
ejpam-3142	336	9	d(x	d(x	NOUN
ejpam-3142	336	10	)	)	PUNCT
ejpam-3142	337	1	=	=	PUNCT
ejpam-3142	337	2	0	0	X
ejpam-3142	337	3	}	}	PUNCT
ejpam-3142	337	4	and	and	CCONJ
ejpam-3142	337	5	b	b	X
ejpam-3142	337	6	=	=	PRON
ejpam-3142	337	7	{	{	PUNCT
ejpam-3142	337	8	x	x	SYM
ejpam-3142	337	9	∈	∈	PROPN
ejpam-3142	337	10	r	r	NOUN
ejpam-3142	338	1	|	|	NOUN
ejpam-3142	339	1	[	[	X
ejpam-3142	339	2	z	z	X
ejpam-3142	339	3	,	,	PUNCT
ejpam-3142	339	4	x	x	X
ejpam-3142	339	5	]	]	X
ejpam-3142	339	6	=	=	PUNCT
ejpam-3142	339	7	0	0	NUM
ejpam-3142	339	8	}	}	PUNCT
ejpam-3142	339	9	.	.	PUNCT
ejpam-3142	340	1	then	then	ADV
ejpam-3142	340	2	a	a	PRON
ejpam-3142	340	3	and	and	CCONJ
ejpam-3142	340	4	b	b	NOUN
ejpam-3142	340	5	are	be	AUX
ejpam-3142	340	6	both	both	PRON
ejpam-3142	340	7	additive	additive	ADJ
ejpam-3142	340	8	subgroups	subgroup	NOUN
ejpam-3142	340	9	of	of	ADP
ejpam-3142	340	10	r	r	NOUN
ejpam-3142	340	11	whose	whose	DET
ejpam-3142	340	12	union	union	NOUN
ejpam-3142	340	13	is	be	AUX
ejpam-3142	340	14	r.	r.	PROPN
ejpam-3142	340	15	using	use	VERB
ejpam-3142	340	16	brauer	brauer	PROPN
ejpam-3142	340	17	’s	’s	PART
ejpam-3142	340	18	trick	trick	NOUN
ejpam-3142	340	19	we	we	PRON
ejpam-3142	340	20	have	have	VERB
ejpam-3142	340	21	either	either	CCONJ
ejpam-3142	340	22	a	a	DET
ejpam-3142	340	23	=	=	SYM
ejpam-3142	340	24	r	r	NOUN
ejpam-3142	340	25	or	or	CCONJ
ejpam-3142	340	26	b	b	NOUN
ejpam-3142	340	27	=	=	SYM
ejpam-3142	340	28	r.	r.	PROPN
ejpam-3142	340	29	if	if	SCONJ
ejpam-3142	340	30	a	a	DET
ejpam-3142	340	31	=	=	NOUN
ejpam-3142	340	32	r	r	NOUN
ejpam-3142	340	33	then	then	ADV
ejpam-3142	340	34	d(x	d(x	NOUN
ejpam-3142	340	35	)	)	PUNCT
ejpam-3142	341	1	=	=	SYM
ejpam-3142	341	2	0	0	NUM
ejpam-3142	341	3	for	for	ADP
ejpam-3142	341	4	all	all	DET
ejpam-3142	341	5	x	x	SYM
ejpam-3142	341	6	∈	∈	PROPN
ejpam-3142	341	7	r	r	NOUN
ejpam-3142	341	8	,	,	PUNCT
ejpam-3142	341	9	a	a	DET
ejpam-3142	341	10	contradiction	contradiction	NOUN
ejpam-3142	341	11	.	.	PUNCT
ejpam-3142	342	1	if	if	SCONJ
ejpam-3142	342	2	b	b	X
ejpam-3142	342	3	=	=	SYM
ejpam-3142	342	4	r	r	NOUN
ejpam-3142	342	5	,	,	PUNCT
ejpam-3142	342	6	then	then	ADV
ejpam-3142	342	7	[	[	X
ejpam-3142	342	8	z	z	X
ejpam-3142	342	9	,	,	PUNCT
ejpam-3142	342	10	x	x	X
ejpam-3142	342	11	]	]	X
ejpam-3142	342	12	=	=	SYM
ejpam-3142	342	13	0	0	NUM
ejpam-3142	342	14	for	for	ADP
ejpam-3142	342	15	all	all	DET
ejpam-3142	342	16	x	x	NOUN
ejpam-3142	342	17	,	,	PUNCT
ejpam-3142	342	18	z	z	PROPN
ejpam-3142	342	19	∈	∈	PROPN
ejpam-3142	342	20	r	r	NOUN
ejpam-3142	342	21	and	and	CCONJ
ejpam-3142	342	22	hence	hence	ADV
ejpam-3142	342	23	r	r	NOUN
ejpam-3142	342	24	is	be	AUX
ejpam-3142	342	25	commutative	commutative	ADJ
ejpam-3142	342	26	.	.	PUNCT
ejpam-3142	343	1	therefore	therefore	ADV
ejpam-3142	343	2	,	,	PUNCT
ejpam-3142	343	3	we	we	PRON
ejpam-3142	343	4	shall	shall	AUX
ejpam-3142	343	5	assume	assume	VERB
ejpam-3142	343	6	that	that	SCONJ
ejpam-3142	343	7	f	f	PROPN
ejpam-3142	343	8	6=	6=	PROPN
ejpam-3142	343	9	0	0	NUM
ejpam-3142	343	10	.	.	PUNCT
ejpam-3142	344	1	so	so	ADV
ejpam-3142	344	2	,	,	PUNCT
ejpam-3142	344	3	for	for	ADP
ejpam-3142	344	4	any	any	DET
ejpam-3142	344	5	x	x	NOUN
ejpam-3142	344	6	,	,	PUNCT
ejpam-3142	344	7	y	y	PROPN
ejpam-3142	344	8	∈	∈	PROPN
ejpam-3142	344	9	r	r	NOUN
ejpam-3142	344	10	,	,	PUNCT
ejpam-3142	344	11	we	we	PRON
ejpam-3142	344	12	have	have	VERB
ejpam-3142	344	13	f	f	PROPN
ejpam-3142	345	1	[	[	X
ejpam-3142	345	2	x	x	X
ejpam-3142	345	3	,	,	PUNCT
ejpam-3142	345	4	y]−	y]−	VERB
ejpam-3142	346	1	[	[	X
ejpam-3142	346	2	f	f	X
ejpam-3142	346	3	(	(	PUNCT
ejpam-3142	346	4	x	x	NOUN
ejpam-3142	346	5	)	)	PUNCT
ejpam-3142	346	6	,	,	PUNCT
ejpam-3142	346	7	y]α	y]α	NOUN
ejpam-3142	346	8	,	,	PUNCT
ejpam-3142	346	9	β	β	X
ejpam-3142	346	10	=	=	PUNCT
ejpam-3142	347	1	[	[	X
ejpam-3142	347	2	d(y	d(y	NOUN
ejpam-3142	347	3	)	)	PUNCT
ejpam-3142	347	4	,	,	PUNCT
ejpam-3142	347	5	x]α	x]α	PROPN
ejpam-3142	347	6	,	,	PUNCT
ejpam-3142	347	7	β	β	X
ejpam-3142	347	8	.	.	PUNCT
ejpam-3142	348	1	(	(	PUNCT
ejpam-3142	348	2	11	11	NUM
ejpam-3142	348	3	)	)	PUNCT
ejpam-3142	348	4	replacing	replace	VERB
ejpam-3142	348	5	y	y	PRON
ejpam-3142	348	6	by	by	ADP
ejpam-3142	348	7	yx	yx	PROPN
ejpam-3142	348	8	in	in	ADP
ejpam-3142	348	9	(	(	PUNCT
ejpam-3142	348	10	11	11	NUM
ejpam-3142	348	11	)	)	PUNCT
ejpam-3142	348	12	gives	give	VERB
ejpam-3142	348	13	β(y)[x	β(y)[x	NOUN
ejpam-3142	348	14	,	,	PUNCT
ejpam-3142	348	15	x]α	x]α	PROPN
ejpam-3142	348	16	,	,	PUNCT
ejpam-3142	348	17	β	β	PROPN
ejpam-3142	348	18	+	+	X
ejpam-3142	348	19	2β([x	2β([x	NUM
ejpam-3142	348	20	,	,	PUNCT
ejpam-3142	348	21	y])d(x	y])d(x	ADV
ejpam-3142	348	22	)	)	PUNCT
ejpam-3142	348	23	=	=	SYM
ejpam-3142	348	24	β(y)[d(x	β(y)[d(x	X
ejpam-3142	348	25	)	)	PUNCT
ejpam-3142	348	26	,	,	PUNCT
ejpam-3142	348	27	x]α	x]α	PROPN
ejpam-3142	348	28	,	,	PUNCT
ejpam-3142	348	29	β	β	X
ejpam-3142	348	30	,	,	PUNCT
ejpam-3142	348	31	for	for	ADP
ejpam-3142	348	32	all	all	DET
ejpam-3142	348	33	x	x	NOUN
ejpam-3142	348	34	,	,	PUNCT
ejpam-3142	348	35	y	y	PROPN
ejpam-3142	348	36	∈	∈	PROPN
ejpam-3142	348	37	r.	r.	PROPN
ejpam-3142	348	38	(	(	PUNCT
ejpam-3142	348	39	12	12	NUM
ejpam-3142	348	40	)	)	PUNCT
ejpam-3142	348	41	again	again	ADV
ejpam-3142	348	42	we	we	PRON
ejpam-3142	348	43	replace	replace	VERB
ejpam-3142	348	44	y	y	PROPN
ejpam-3142	348	45	by	by	ADP
ejpam-3142	348	46	wy	wy	PROPN
ejpam-3142	348	47	in	in	ADP
ejpam-3142	348	48	(	(	PUNCT
ejpam-3142	348	49	12	12	NUM
ejpam-3142	348	50	)	)	PUNCT
ejpam-3142	348	51	to	to	PART
ejpam-3142	348	52	get	get	VERB
ejpam-3142	348	53	2β([x	2β([x	NUM
ejpam-3142	348	54	,	,	PUNCT
ejpam-3142	348	55	w])β(y)d(x	w])β(y)d(x	PROPN
ejpam-3142	348	56	)	)	PUNCT
ejpam-3142	349	1	=	=	SYM
ejpam-3142	349	2	0	0	NUM
ejpam-3142	349	3	for	for	ADP
ejpam-3142	349	4	all	all	DET
ejpam-3142	349	5	x	x	NOUN
ejpam-3142	349	6	,	,	PUNCT
ejpam-3142	349	7	y	y	PROPN
ejpam-3142	349	8	,	,	PUNCT
ejpam-3142	349	9	w	w	PROPN
ejpam-3142	349	10	∈	∈	PROPN
ejpam-3142	349	11	r.	r.	NOUN
ejpam-3142	349	12	since	since	SCONJ
ejpam-3142	349	13	r	r	NOUN
ejpam-3142	349	14	is	be	AUX
ejpam-3142	349	15	a	a	DET
ejpam-3142	349	16	2	2	NUM
ejpam-3142	349	17	-	-	PUNCT
ejpam-3142	349	18	torsion	torsion	NOUN
ejpam-3142	349	19	free	free	ADJ
ejpam-3142	349	20	and	and	CCONJ
ejpam-3142	349	21	β	β	X
ejpam-3142	349	22	is	be	AUX
ejpam-3142	349	23	an	an	DET
ejpam-3142	349	24	automorphism	automorphism	NOUN
ejpam-3142	349	25	,	,	PUNCT
ejpam-3142	349	26	we	we	PRON
ejpam-3142	349	27	get	get	VERB
ejpam-3142	349	28	β([x	β([x	ADP
ejpam-3142	349	29	,	,	PUNCT
ejpam-3142	349	30	w])rd(x	w])rd(x	NOUN
ejpam-3142	349	31	)	)	PUNCT
ejpam-3142	349	32	=	=	PRON
ejpam-3142	349	33	{	{	PUNCT
ejpam-3142	349	34	0	0	NUM
ejpam-3142	349	35	}	}	PUNCT
ejpam-3142	349	36	,	,	PUNCT
ejpam-3142	349	37	for	for	ADP
ejpam-3142	349	38	all	all	DET
ejpam-3142	349	39	x	x	NOUN
ejpam-3142	349	40	,	,	PUNCT
ejpam-3142	349	41	w	w	PROPN
ejpam-3142	349	42	∈	∈	PROPN
ejpam-3142	349	43	r.	r.	PROPN
ejpam-3142	349	44	therefore	therefore	ADV
ejpam-3142	349	45	,	,	PUNCT
ejpam-3142	349	46	proceeding	proceed	VERB
ejpam-3142	349	47	in	in	ADP
ejpam-3142	349	48	the	the	DET
ejpam-3142	349	49	same	same	ADJ
ejpam-3142	349	50	way	way	NOUN
ejpam-3142	349	51	as	as	ADP
ejpam-3142	349	52	that	that	PRON
ejpam-3142	349	53	after	after	ADP
ejpam-3142	349	54	(	(	PUNCT
ejpam-3142	349	55	10	10	NUM
ejpam-3142	349	56	)	)	PUNCT
ejpam-3142	349	57	,	,	PUNCT
ejpam-3142	349	58	gives	give	VERB
ejpam-3142	349	59	the	the	DET
ejpam-3142	349	60	required	require	VERB
ejpam-3142	349	61	result	result	NOUN
ejpam-3142	349	62	.	.	PUNCT
ejpam-3142	350	1	(	(	PUNCT
ejpam-3142	350	2	ii	ii	NOUN
ejpam-3142	350	3	)	)	PUNCT
ejpam-3142	350	4	if	if	SCONJ
ejpam-3142	350	5	f	f	PROPN
ejpam-3142	350	6	=	=	SYM
ejpam-3142	350	7	0	0	PROPN
ejpam-3142	350	8	,	,	PUNCT
ejpam-3142	350	9	then	then	ADV
ejpam-3142	350	10	we	we	PRON
ejpam-3142	350	11	have	have	VERB
ejpam-3142	350	12	[	[	X
ejpam-3142	350	13	d(y	d(y	NOUN
ejpam-3142	350	14	)	)	PUNCT
ejpam-3142	350	15	,	,	PUNCT
ejpam-3142	350	16	x]α	x]α	PROPN
ejpam-3142	350	17	,	,	PUNCT
ejpam-3142	350	18	β	β	X
ejpam-3142	350	19	=	=	SYM
ejpam-3142	350	20	0	0	NUM
ejpam-3142	350	21	for	for	ADP
ejpam-3142	350	22	all	all	DET
ejpam-3142	350	23	x	x	NOUN
ejpam-3142	350	24	,	,	PUNCT
ejpam-3142	350	25	y	y	PROPN
ejpam-3142	350	26	∈	∈	PROPN
ejpam-3142	350	27	r.	r.	NOUN
ejpam-3142	350	28	applying	apply	VERB
ejpam-3142	350	29	the	the	DET
ejpam-3142	350	30	same	same	ADJ
ejpam-3142	350	31	techniques	technique	NOUN
ejpam-3142	350	32	as	as	ADP
ejpam-3142	350	33	that	that	PRON
ejpam-3142	350	34	used	use	VERB
ejpam-3142	350	35	above	above	ADV
ejpam-3142	350	36	to	to	PART
ejpam-3142	350	37	prove	prove	VERB
ejpam-3142	350	38	(	(	PUNCT
ejpam-3142	350	39	i	i	NOUN
ejpam-3142	350	40	)	)	PUNCT
ejpam-3142	350	41	yields	yield	VERB
ejpam-3142	350	42	the	the	DET
ejpam-3142	350	43	required	require	VERB
ejpam-3142	350	44	result	result	NOUN
ejpam-3142	350	45	.	.	PUNCT
ejpam-3142	351	1	henceforth	henceforth	ADV
ejpam-3142	351	2	,	,	PUNCT
ejpam-3142	351	3	we	we	PRON
ejpam-3142	351	4	shall	shall	AUX
ejpam-3142	351	5	assume	assume	VERB
ejpam-3142	351	6	that	that	SCONJ
ejpam-3142	351	7	f	f	PROPN
ejpam-3142	351	8	6=	6=	PROPN
ejpam-3142	351	9	0	0	NUM
ejpam-3142	351	10	.	.	PUNCT
ejpam-3142	352	1	so	so	ADV
ejpam-3142	352	2	,	,	PUNCT
ejpam-3142	352	3	for	for	ADP
ejpam-3142	352	4	all	all	DET
ejpam-3142	352	5	x	x	NOUN
ejpam-3142	352	6	,	,	PUNCT
ejpam-3142	352	7	y	y	PROPN
ejpam-3142	352	8	∈	∈	PROPN
ejpam-3142	352	9	r	r	NOUN
ejpam-3142	352	10	,	,	PUNCT
ejpam-3142	352	11	we	we	PRON
ejpam-3142	352	12	have	have	VERB
ejpam-3142	352	13	f	f	PROPN
ejpam-3142	353	1	[	[	X
ejpam-3142	353	2	x	x	X
ejpam-3142	353	3	,	,	PUNCT
ejpam-3142	353	4	y]−	y]−	PRON
ejpam-3142	353	5	(	(	PUNCT
ejpam-3142	353	6	f	f	PROPN
ejpam-3142	353	7	(	(	PUNCT
ejpam-3142	353	8	x	x	NOUN
ejpam-3142	353	9	)	)	PUNCT
ejpam-3142	353	10	◦	◦	NOUN
ejpam-3142	353	11	y)α	y)α	NOUN
ejpam-3142	353	12	,	,	PUNCT
ejpam-3142	353	13	β	β	X
ejpam-3142	353	14	=	=	PUNCT
ejpam-3142	354	1	[	[	X
ejpam-3142	354	2	d(y	d(y	NOUN
ejpam-3142	354	3	)	)	PUNCT
ejpam-3142	354	4	,	,	PUNCT
ejpam-3142	354	5	x]α	x]α	PROPN
ejpam-3142	354	6	,	,	PUNCT
ejpam-3142	354	7	β	β	X
ejpam-3142	354	8	.	.	PUNCT
ejpam-3142	355	1	(	(	PUNCT
ejpam-3142	355	2	13	13	NUM
ejpam-3142	355	3	)	)	PUNCT
ejpam-3142	355	4	replacing	replace	VERB
ejpam-3142	355	5	y	y	PRON
ejpam-3142	355	6	by	by	ADP
ejpam-3142	355	7	yx	yx	PROPN
ejpam-3142	355	8	in	in	ADP
ejpam-3142	355	9	(	(	PUNCT
ejpam-3142	355	10	13	13	NUM
ejpam-3142	355	11	)	)	PUNCT
ejpam-3142	355	12	gives	give	VERB
ejpam-3142	355	13	β(y)[x	β(y)[x	NOUN
ejpam-3142	355	14	,	,	PUNCT
ejpam-3142	355	15	x]α	x]α	PROPN
ejpam-3142	355	16	,	,	PUNCT
ejpam-3142	355	17	β	β	PROPN
ejpam-3142	355	18	+	+	X
ejpam-3142	355	19	2β([x	2β([x	NUM
ejpam-3142	355	20	,	,	PUNCT
ejpam-3142	355	21	y])d(x	y])d(x	ADV
ejpam-3142	355	22	)	)	PUNCT
ejpam-3142	355	23	=	=	SYM
ejpam-3142	355	24	β(y)[d(x	β(y)[d(x	X
ejpam-3142	355	25	)	)	PUNCT
ejpam-3142	355	26	,	,	PUNCT
ejpam-3142	355	27	x]α	x]α	PROPN
ejpam-3142	355	28	,	,	PUNCT
ejpam-3142	355	29	β	β	X
ejpam-3142	355	30	.	.	PUNCT
ejpam-3142	356	1	(	(	PUNCT
ejpam-3142	356	2	14	14	NUM
ejpam-3142	356	3	)	)	PUNCT
ejpam-3142	356	4	again	again	ADV
ejpam-3142	356	5	,	,	PUNCT
ejpam-3142	356	6	we	we	PRON
ejpam-3142	356	7	replace	replace	VERB
ejpam-3142	356	8	y	y	PROPN
ejpam-3142	356	9	by	by	ADP
ejpam-3142	356	10	wy	wy	PROPN
ejpam-3142	356	11	in	in	ADP
ejpam-3142	356	12	(	(	PUNCT
ejpam-3142	356	13	14	14	NUM
ejpam-3142	356	14	)	)	PUNCT
ejpam-3142	356	15	to	to	PART
ejpam-3142	356	16	get	get	VERB
ejpam-3142	356	17	2β([x	2β([x	NUM
ejpam-3142	356	18	,	,	PUNCT
ejpam-3142	356	19	w])β(y)d(x	w])β(y)d(x	PROPN
ejpam-3142	356	20	)	)	PUNCT
ejpam-3142	357	1	=	=	SYM
ejpam-3142	357	2	0	0	NUM
ejpam-3142	357	3	for	for	ADP
ejpam-3142	357	4	all	all	DET
ejpam-3142	357	5	x	x	NOUN
ejpam-3142	357	6	,	,	PUNCT
ejpam-3142	357	7	y	y	PROPN
ejpam-3142	357	8	∈	∈	PROPN
ejpam-3142	357	9	r.	r.	PROPN
ejpam-3142	357	10	since	since	SCONJ
ejpam-3142	357	11	r	r	NOUN
ejpam-3142	357	12	is	be	AUX
ejpam-3142	357	13	a	a	DET
ejpam-3142	357	14	2	2	NUM
ejpam-3142	357	15	-	-	PUNCT
ejpam-3142	357	16	torsion	torsion	NOUN
ejpam-3142	357	17	free	free	ADJ
ejpam-3142	357	18	and	and	CCONJ
ejpam-3142	357	19	β	β	X
ejpam-3142	357	20	is	be	AUX
ejpam-3142	357	21	an	an	DET
ejpam-3142	357	22	automorphism	automorphism	NOUN
ejpam-3142	357	23	on	on	ADP
ejpam-3142	357	24	r	r	NOUN
ejpam-3142	357	25	,	,	PUNCT
ejpam-3142	357	26	we	we	PRON
ejpam-3142	357	27	get	get	VERB
ejpam-3142	357	28	β([x	β([x	ADP
ejpam-3142	357	29	,	,	PUNCT
ejpam-3142	357	30	w])rd(x	w])rd(x	NOUN
ejpam-3142	357	31	)	)	PUNCT
ejpam-3142	357	32	=	=	PRON
ejpam-3142	357	33	{	{	PUNCT
ejpam-3142	357	34	0	0	NUM
ejpam-3142	357	35	}	}	PUNCT
ejpam-3142	357	36	,	,	PUNCT
ejpam-3142	357	37	for	for	ADP
ejpam-3142	357	38	all	all	DET
ejpam-3142	357	39	x	x	NOUN
ejpam-3142	357	40	,	,	PUNCT
ejpam-3142	357	41	w	w	PROPN
ejpam-3142	357	42	∈	∈	PROPN
ejpam-3142	357	43	r.	r.	NOUN
ejpam-3142	357	44	(	(	PUNCT
ejpam-3142	357	45	15	15	NUM
ejpam-3142	357	46	)	)	PUNCT
ejpam-3142	357	47	now	now	ADV
ejpam-3142	357	48	,	,	PUNCT
ejpam-3142	357	49	using	use	VERB
ejpam-3142	357	50	similar	similar	ADJ
ejpam-3142	357	51	techniques	technique	NOUN
ejpam-3142	357	52	as	as	SCONJ
ejpam-3142	357	53	that	that	PRON
ejpam-3142	357	54	after	after	ADP
ejpam-3142	357	55	equation	equation	NOUN
ejpam-3142	357	56	(	(	PUNCT
ejpam-3142	357	57	10	10	NUM
ejpam-3142	357	58	)	)	PUNCT
ejpam-3142	357	59	,	,	PUNCT
ejpam-3142	357	60	we	we	PRON
ejpam-3142	357	61	get	get	VERB
ejpam-3142	357	62	the	the	DET
ejpam-3142	357	63	required	require	VERB
ejpam-3142	357	64	result	result	NOUN
ejpam-3142	357	65	.	.	PUNCT
ejpam-3142	358	1	references	reference	NOUN
ejpam-3142	358	2	88	88	NUM
ejpam-3142	358	3	acknowledgement	acknowledgement	NOUN
ejpam-3142	358	4	this	this	DET
ejpam-3142	358	5	paper	paper	NOUN
ejpam-3142	358	6	was	be	AUX
ejpam-3142	358	7	financially	financially	ADV
ejpam-3142	358	8	supported	support	VERB
ejpam-3142	358	9	by	by	ADP
ejpam-3142	358	10	the	the	DET
ejpam-3142	358	11	deanship	deanship	NOUN
ejpam-3142	358	12	of	of	ADP
ejpam-3142	358	13	scientific	scientific	ADJ
ejpam-3142	358	14	research	research	NOUN
ejpam-3142	358	15	,	,	PUNCT
ejpam-3142	358	16	northern	northern	ADJ
ejpam-3142	358	17	border	border	NOUN
ejpam-3142	358	18	university	university	NOUN
ejpam-3142	358	19	,	,	PUNCT
ejpam-3142	358	20	under	under	ADP
ejpam-3142	358	21	the	the	DET
ejpam-3142	358	22	project	project	NOUN
ejpam-3142	358	23	no	no	NOUN
ejpam-3142	358	24	.	.	PUNCT
ejpam-3142	359	1	435	435	NUM
ejpam-3142	359	2	-	-	PUNCT
ejpam-3142	359	3	062	062	NUM
ejpam-3142	359	4	-	-	SYM
ejpam-3142	359	5	7	7	NUM
ejpam-3142	359	6	.	.	PUNCT
ejpam-3142	360	1	the	the	DET
ejpam-3142	360	2	authors	author	NOUN
ejpam-3142	360	3	would	would	AUX
ejpam-3142	360	4	like	like	VERB
ejpam-3142	360	5	to	to	PART
ejpam-3142	360	6	thank	thank	VERB
ejpam-3142	360	7	the	the	DET
ejpam-3142	360	8	deanship	deanship	NOUN
ejpam-3142	360	9	of	of	ADP
ejpam-3142	360	10	scientific	scientific	ADJ
ejpam-3142	360	11	research	research	NOUN
ejpam-3142	360	12	for	for	ADP
ejpam-3142	360	13	their	their	PRON
ejpam-3142	360	14	financial	financial	ADJ
ejpam-3142	360	15	support	support	NOUN
ejpam-3142	360	16	.	.	PUNCT
ejpam-3142	361	1	the	the	DET
ejpam-3142	361	2	authors	author	NOUN
ejpam-3142	361	3	also	also	ADV
ejpam-3142	361	4	would	would	AUX
ejpam-3142	361	5	like	like	VERB
ejpam-3142	361	6	to	to	PART
ejpam-3142	361	7	thank	thank	VERB
ejpam-3142	361	8	professor	professor	PROPN
ejpam-3142	361	9	nadeem	nadeem	PROPN
ejpam-3142	361	10	ur	ur	PROPN
ejpam-3142	361	11	rehman	rehman	PROPN
ejpam-3142	361	12	for	for	ADP
ejpam-3142	361	13	many	many	ADJ
ejpam-3142	361	14	useful	useful	ADJ
ejpam-3142	361	15	comments	comment	NOUN
ejpam-3142	361	16	.	.	PUNCT
ejpam-3142	362	1	references	reference	NOUN
ejpam-3142	362	2	[	[	X
ejpam-3142	362	3	1	1	NUM
ejpam-3142	362	4	]	]	PUNCT
ejpam-3142	362	5	m.	m.	NOUN
ejpam-3142	363	1	k.	k.	PROPN
ejpam-3142	363	2	abu	abu	PROPN
ejpam-3142	364	1	nawas	nawas	INTJ
ejpam-3142	364	2	and	and	CCONJ
ejpam-3142	364	3	r.	r.	PROPN
ejpam-3142	364	4	m.	m.	PROPN
ejpam-3142	365	1	al	al	PROPN
ejpam-3142	365	2	-	-	PUNCT
ejpam-3142	365	3	omary	omary	NOUN
ejpam-3142	365	4	.	.	PUNCT
ejpam-3142	366	1	on	on	ADP
ejpam-3142	366	2	commutativity	commutativity	NOUN
ejpam-3142	366	3	of	of	ADP
ejpam-3142	366	4	∗-prime	∗-prime	PROPN
ejpam-3142	366	5	rings	ring	NOUN
ejpam-3142	366	6	with	with	ADP
ejpam-3142	366	7	generalized	generalized	ADJ
ejpam-3142	366	8	(	(	PUNCT
ejpam-3142	366	9	α	α	NOUN
ejpam-3142	366	10	,	,	PUNCT
ejpam-3142	366	11	β)-derivations	β)-derivation	NOUN
ejpam-3142	366	12	.	.	PUNCT
ejpam-3142	367	1	ultra	ultra	ADJ
ejpam-3142	367	2	engineer	engineer	NOUN
ejpam-3142	367	3	,	,	PUNCT
ejpam-3142	367	4	3(1):1	3(1):1	PROPN
ejpam-3142	367	5	-	-	SYM
ejpam-3142	367	6	5	5	NUM
ejpam-3142	367	7	,	,	PUNCT
ejpam-3142	367	8	(	(	PUNCT
ejpam-3142	367	9	2015	2015	NUM
ejpam-3142	367	10	)	)	PUNCT
ejpam-3142	367	11	.	.	PUNCT
ejpam-3142	368	1	[	[	X
ejpam-3142	368	2	2	2	NUM
ejpam-3142	368	3	]	]	X
ejpam-3142	368	4	r.	r.	PROPN
ejpam-3142	368	5	m.	m.	PROPN
ejpam-3142	368	6	al	al	PROPN
ejpam-3142	368	7	-	-	PUNCT
ejpam-3142	368	8	omary	omary	NOUN
ejpam-3142	368	9	,	,	PUNCT
ejpam-3142	368	10	and	and	CCONJ
ejpam-3142	368	11	n.	n.	PROPN
ejpam-3142	368	12	rehman	rehman	PROPN
ejpam-3142	368	13	.	.	PUNCT
ejpam-3142	369	1	lie	lie	NOUN
ejpam-3142	369	2	ideals	ideal	NOUN
ejpam-3142	369	3	and	and	CCONJ
ejpam-3142	369	4	centralizing	centralize	VERB
ejpam-3142	369	5	mappings	mapping	NOUN
ejpam-3142	369	6	with	with	ADP
ejpam-3142	369	7	generalized	generalized	ADJ
ejpam-3142	369	8	derivations	derivation	NOUN
ejpam-3142	369	9	.	.	PUNCT
ejpam-3142	370	1	journal	journal	NOUN
ejpam-3142	370	2	of	of	ADP
ejpam-3142	370	3	scientific	scientific	ADJ
ejpam-3142	370	4	research	research	NOUN
ejpam-3142	370	5	and	and	CCONJ
ejpam-3142	370	6	reports	report	NOUN
ejpam-3142	370	7	,	,	PUNCT
ejpam-3142	370	8	11(3):1	11(3):1	NUM
ejpam-3142	370	9	-	-	SYM
ejpam-3142	370	10	8	8	NUM
ejpam-3142	370	11	,	,	PUNCT
ejpam-3142	370	12	(	(	PUNCT
ejpam-3142	370	13	2016	2016	NUM
ejpam-3142	370	14	)	)	PUNCT
ejpam-3142	370	15	.	.	PUNCT
ejpam-3142	371	1	[	[	X
ejpam-3142	371	2	3	3	X
ejpam-3142	371	3	]	]	PUNCT
ejpam-3142	371	4	m.	m.	NOUN
ejpam-3142	371	5	ashraf	ashraf	PROPN
ejpam-3142	371	6	,	,	PUNCT
ejpam-3142	371	7	a.	a.	PROPN
ejpam-3142	371	8	ali	ali	PROPN
ejpam-3142	371	9	and	and	CCONJ
ejpam-3142	371	10	s.	s.	PROPN
ejpam-3142	371	11	ali	ali	PROPN
ejpam-3142	371	12	.	.	PUNCT
ejpam-3142	372	1	some	some	DET
ejpam-3142	372	2	commutativity	commutativity	NOUN
ejpam-3142	372	3	theorems	theorem	VERB
ejpam-3142	372	4	for	for	ADP
ejpam-3142	372	5	rings	ring	NOUN
ejpam-3142	372	6	with	with	ADP
ejpam-3142	372	7	generalized	generalized	ADJ
ejpam-3142	372	8	derivations	derivation	NOUN
ejpam-3142	372	9	.	.	PUNCT
ejpam-3142	373	1	southeast	southeast	ADJ
ejpam-3142	373	2	asian	asian	ADJ
ejpam-3142	373	3	bull	bull	PROPN
ejpam-3142	373	4	.	.	PUNCT
ejpam-3142	374	1	math	math	NOUN
ejpam-3142	374	2	.	.	PUNCT
ejpam-3142	375	1	,	,	PUNCT
ejpam-3142	375	2	32(2):415	32(2):415	NOUN
ejpam-3142	375	3	-	-	SYM
ejpam-3142	375	4	421	421	NUM
ejpam-3142	375	5	,	,	PUNCT
ejpam-3142	375	6	(	(	PUNCT
ejpam-3142	375	7	2007	2007	NUM
ejpam-3142	375	8	)	)	PUNCT
ejpam-3142	375	9	.	.	PUNCT
ejpam-3142	376	1	[	[	X
ejpam-3142	376	2	4	4	X
ejpam-3142	376	3	]	]	PUNCT
ejpam-3142	376	4	m.	m.	NOUN
ejpam-3142	376	5	ashraf	ashraf	PROPN
ejpam-3142	376	6	and	and	CCONJ
ejpam-3142	376	7	a.	a.	PROPN
ejpam-3142	376	8	khan	khan	PROPN
ejpam-3142	376	9	.	.	PUNCT
ejpam-3142	377	1	commutativity	commutativity	NOUN
ejpam-3142	377	2	*	*	PUNCT
ejpam-3142	377	3	-prime	-prime	NOUN
ejpam-3142	377	4	rings	ring	NOUN
ejpam-3142	377	5	with	with	ADP
ejpam-3142	377	6	generalized	generalized	ADJ
ejpam-3142	377	7	derivations	derivation	NOUN
ejpam-3142	377	8	.	.	PUNCT
ejpam-3142	378	1	rend	rend	VERB
ejpam-3142	378	2	.	.	PUNCT
ejpam-3142	379	1	sem	sem	PROPN
ejpam-3142	379	2	.	.	PUNCT
ejpam-3142	379	3	mat	mat	PROPN
ejpam-3142	379	4	.	.	PROPN
ejpam-3142	379	5	univ	univ	PROPN
ejpam-3142	379	6	.	.	PUNCT
ejpam-3142	379	7	padova	padova	PROPN
ejpam-3142	379	8	,	,	PUNCT
ejpam-3142	379	9	125:71	125:71	PROPN
ejpam-3142	379	10	-	-	SYM
ejpam-3142	379	11	79	79	NUM
ejpam-3142	379	12	,	,	PUNCT
ejpam-3142	379	13	(	(	PUNCT
ejpam-3142	379	14	2011	2011	NUM
ejpam-3142	379	15	)	)	PUNCT
ejpam-3142	379	16	.	.	PUNCT
ejpam-3142	380	1	[	[	X
ejpam-3142	380	2	5	5	X
ejpam-3142	380	3	]	]	PUNCT
ejpam-3142	380	4	m.	m.	NOUN
ejpam-3142	380	5	ashraf	ashraf	NOUN
ejpam-3142	380	6	and	and	CCONJ
ejpam-3142	380	7	n.	n.	PROPN
ejpam-3142	380	8	rehman	rehman	PROPN
ejpam-3142	380	9	.	.	PUNCT
ejpam-3142	381	1	on	on	ADP
ejpam-3142	381	2	commutativity	commutativity	NOUN
ejpam-3142	381	3	of	of	ADP
ejpam-3142	381	4	rings	ring	NOUN
ejpam-3142	381	5	with	with	ADP
ejpam-3142	381	6	derivations	derivation	NOUN
ejpam-3142	381	7	.	.	PUNCT
ejpam-3142	382	1	results	result	VERB
ejpam-3142	382	2	math	math	PROPN
ejpam-3142	382	3	.	.	PUNCT
ejpam-3142	382	4	,	,	PUNCT
ejpam-3142	382	5	42:3	42:3	NUM
ejpam-3142	382	6	-	-	SYM
ejpam-3142	382	7	8	8	NUM
ejpam-3142	382	8	,	,	PUNCT
ejpam-3142	382	9	(	(	PUNCT
ejpam-3142	382	10	2002	2002	NUM
ejpam-3142	382	11	)	)	PUNCT
ejpam-3142	382	12	.	.	PUNCT
ejpam-3142	383	1	[	[	X
ejpam-3142	383	2	6	6	NUM
ejpam-3142	383	3	]	]	PUNCT
ejpam-3142	383	4	a.	a.	NOUN
ejpam-3142	383	5	asif	asif	NOUN
ejpam-3142	383	6	and	and	CCONJ
ejpam-3142	383	7	t.	t.	NOUN
ejpam-3142	383	8	shah	shah	NOUN
ejpam-3142	383	9	.	.	PUNCT
ejpam-3142	384	1	centralizing	centralize	VERB
ejpam-3142	384	2	and	and	CCONJ
ejpam-3142	384	3	commuting	commute	VERB
ejpam-3142	384	4	generalized	generalized	ADJ
ejpam-3142	384	5	derivation	derivation	NOUN
ejpam-3142	384	6	on	on	ADP
ejpam-3142	384	7	prime	prime	ADJ
ejpam-3142	384	8	rings	ring	NOUN
ejpam-3142	384	9	.	.	PUNCT
ejpam-3142	385	1	matema	matema	PROPN
ejpam-3142	385	2	.	.	PUNCT
ejpam-3142	385	3	,	,	PUNCT
ejpam-3142	385	4	60:1	60:1	PROPN
ejpam-3142	385	5	-	-	SYM
ejpam-3142	385	6	2	2	NUM
ejpam-3142	385	7	,	,	PUNCT
ejpam-3142	385	8	(	(	PUNCT
ejpam-3142	385	9	2008	2008	NUM
ejpam-3142	385	10	)	)	PUNCT
ejpam-3142	385	11	.	.	PUNCT
ejpam-3142	386	1	[	[	X
ejpam-3142	386	2	7	7	X
ejpam-3142	386	3	]	]	X
ejpam-3142	386	4	h.	h.	PROPN
ejpam-3142	386	5	e.	e.	PROPN
ejpam-3142	386	6	bell	bell	PROPN
ejpam-3142	386	7	and	and	CCONJ
ejpam-3142	386	8	w.s	w.s	PROPN
ejpam-3142	386	9	.	.	PROPN
ejpam-3142	386	10	martindale	martindale	PROPN
ejpam-3142	386	11	.	.	PUNCT
ejpam-3142	387	1	centralizing	centralize	VERB
ejpam-3142	387	2	and	and	CCONJ
ejpam-3142	387	3	commuting	commute	VERB
ejpam-3142	387	4	generalized	generalized	ADJ
ejpam-3142	387	5	derivation	derivation	NOUN
ejpam-3142	387	6	on	on	ADP
ejpam-3142	387	7	prime	prime	ADJ
ejpam-3142	387	8	rings	ring	NOUN
ejpam-3142	387	9	.	.	PUNCT
ejpam-3142	388	1	centralizing	centralize	VERB
ejpam-3142	388	2	mapping	mapping	NOUN
ejpam-3142	388	3	of	of	ADP
ejpam-3142	388	4	semiprime	semiprime	NOUN
ejpam-3142	388	5	rings	ring	NOUN
ejpam-3142	388	6	.	.	PUNCT
ejpam-3142	389	1	canda	canda	PROPN
ejpam-3142	389	2	.	.	PUNCT
ejpam-3142	389	3	math	math	NOUN
ejpam-3142	389	4	.	.	PUNCT
ejpam-3142	390	1	bull	bull	PROPN
ejpam-3142	390	2	.	.	PUNCT
ejpam-3142	390	3	,	,	PUNCT
ejpam-3142	390	4	30:92	30:92	NUM
ejpam-3142	390	5	-	-	SYM
ejpam-3142	390	6	101	101	NUM
ejpam-3142	390	7	,	,	PUNCT
ejpam-3142	390	8	(	(	PUNCT
ejpam-3142	390	9	1987	1987	NUM
ejpam-3142	390	10	)	)	PUNCT
ejpam-3142	390	11	.	.	PUNCT
ejpam-3142	391	1	[	[	X
ejpam-3142	391	2	8	8	X
ejpam-3142	391	3	]	]	X
ejpam-3142	391	4	h.	h.	PROPN
ejpam-3142	391	5	e.	e.	PROPN
ejpam-3142	391	6	bell	bell	PROPN
ejpam-3142	391	7	and	and	CCONJ
ejpam-3142	391	8	n.	n.	PROPN
ejpam-3142	391	9	rehman	rehman	PROPN
ejpam-3142	391	10	.	.	PUNCT
ejpam-3142	392	1	generalized	generalized	ADJ
ejpam-3142	392	2	derivations	derivation	NOUN
ejpam-3142	392	3	with	with	ADP
ejpam-3142	392	4	commutativity	commutativity	NOUN
ejpam-3142	392	5	and	and	CCONJ
ejpam-3142	392	6	anti	anti	ADJ
ejpam-3142	392	7	-	-	ADJ
ejpam-3142	392	8	commutativity	commutativity	ADJ
ejpam-3142	392	9	conditions	condition	NOUN
ejpam-3142	392	10	.	.	PUNCT
ejpam-3142	393	1	math	math	NOUN
ejpam-3142	393	2	.	.	PUNCT
ejpam-3142	394	1	j.	j.	PROPN
ejpam-3142	394	2	okayama	okayama	PROPN
ejpam-3142	394	3	univ	univ	PROPN
ejpam-3142	394	4	.	.	PROPN
ejpam-3142	394	5	,	,	PUNCT
ejpam-3142	394	6	49:139	49:139	NUM
ejpam-3142	394	7	-	-	SYM
ejpam-3142	394	8	147	147	NUM
ejpam-3142	394	9	,	,	PUNCT
ejpam-3142	394	10	(	(	PUNCT
ejpam-3142	394	11	2007	2007	NUM
ejpam-3142	394	12	)	)	PUNCT
ejpam-3142	394	13	.	.	PUNCT
ejpam-3142	395	1	[	[	X
ejpam-3142	395	2	9	9	NUM
ejpam-3142	395	3	]	]	X
ejpam-3142	395	4	m.	m.	NOUN
ejpam-3142	395	5	bresar	bresar	VERB
ejpam-3142	395	6	.	.	PUNCT
ejpam-3142	396	1	centralizing	centralize	VERB
ejpam-3142	396	2	mapping	mapping	NOUN
ejpam-3142	396	3	and	and	CCONJ
ejpam-3142	396	4	derivations	derivation	NOUN
ejpam-3142	396	5	in	in	ADP
ejpam-3142	396	6	prime	prime	ADJ
ejpam-3142	396	7	rings	ring	NOUN
ejpam-3142	396	8	.	.	PUNCT
ejpam-3142	397	1	j.algebra	j.algebra	PROPN
ejpam-3142	397	2	.	.	PROPN
ejpam-3142	397	3	,	,	PUNCT
ejpam-3142	397	4	156:385	156:385	PROPN
ejpam-3142	397	5	-	-	PUNCT
ejpam-3142	397	6	394	394	NUM
ejpam-3142	397	7	,	,	PUNCT
ejpam-3142	397	8	(	(	PUNCT
ejpam-3142	397	9	1993	1993	NUM
ejpam-3142	397	10	)	)	PUNCT
ejpam-3142	397	11	.	.	PUNCT
ejpam-3142	398	1	[	[	X
ejpam-3142	398	2	10	10	NUM
ejpam-3142	398	3	]	]	PUNCT
ejpam-3142	398	4	m.	m.	NOUN
ejpam-3142	398	5	el	el	PROPN
ejpam-3142	398	6	-	-	PUNCT
ejpam-3142	398	7	soufi	soufi	PROPN
ejpam-3142	398	8	and	and	CCONJ
ejpam-3142	398	9	a.	a.	NOUN
ejpam-3142	398	10	aboubakr	aboubakr	PROPN
ejpam-3142	398	11	.	.	PUNCT
ejpam-3142	399	1	generalized	generalized	ADJ
ejpam-3142	399	2	derivations	derivation	NOUN
ejpam-3142	399	3	on	on	ADP
ejpam-3142	399	4	jordan	jordan	PROPN
ejpam-3142	399	5	ideals	ideal	NOUN
ejpam-3142	399	6	in	in	ADP
ejpam-3142	399	7	prime	prime	ADJ
ejpam-3142	399	8	rings	ring	NOUN
ejpam-3142	399	9	.	.	PUNCT
ejpam-3142	400	1	turk	turk	PROPN
ejpam-3142	400	2	.	.	PUNCT
ejpam-3142	401	1	j.	j.	PROPN
ejpam-3142	401	2	math	math	PROPN
ejpam-3142	401	3	.	.	PUNCT
ejpam-3142	401	4	,	,	PUNCT
ejpam-3142	401	5	38:233	38:233	NUM
ejpam-3142	401	6	-	-	SYM
ejpam-3142	401	7	239	239	NUM
ejpam-3142	401	8	,	,	PUNCT
ejpam-3142	401	9	(	(	PUNCT
ejpam-3142	401	10	2014	2014	NUM
ejpam-3142	401	11	)	)	PUNCT
ejpam-3142	401	12	.	.	PUNCT
ejpam-3142	402	1	[	[	X
ejpam-3142	402	2	11	11	NUM
ejpam-3142	402	3	]	]	PUNCT
ejpam-3142	402	4	a.	a.	NOUN
ejpam-3142	402	5	ibraheem	ibraheem	NOUN
ejpam-3142	402	6	.	.	PUNCT
ejpam-3142	403	1	right	right	ADJ
ejpam-3142	403	2	ideals	ideal	NOUN
ejpam-3142	403	3	and	and	CCONJ
ejpam-3142	403	4	generalized	generalized	ADJ
ejpam-3142	403	5	reverse	reverse	ADJ
ejpam-3142	403	6	derivations	derivation	NOUN
ejpam-3142	403	7	on	on	ADP
ejpam-3142	403	8	prime	prime	ADJ
ejpam-3142	403	9	rings	ring	NOUN
ejpam-3142	403	10	.	.	PUNCT
ejpam-3142	404	1	american	american	PROPN
ejpam-3142	404	2	journal	journal	PROPN
ejpam-3142	404	3	of	of	ADP
ejpam-3142	404	4	computational	computational	ADJ
ejpam-3142	404	5	and	and	CCONJ
ejpam-3142	404	6	applied	applied	ADJ
ejpam-3142	404	7	mathematics	mathematic	NOUN
ejpam-3142	404	8	,	,	PUNCT
ejpam-3142	404	9	6(4):162	6(4):162	NUM
ejpam-3142	404	10	-	-	SYM
ejpam-3142	404	11	164	164	NUM
ejpam-3142	404	12	,	,	PUNCT
ejpam-3142	404	13	(	(	PUNCT
ejpam-3142	404	14	2016	2016	NUM
ejpam-3142	404	15	)	)	PUNCT
ejpam-3142	404	16	.	.	PUNCT
ejpam-3142	405	1	[	[	X
ejpam-3142	405	2	12	12	NUM
ejpam-3142	405	3	]	]	X
ejpam-3142	405	4	h.	h.	PROPN
ejpam-3142	405	5	marubayashi	marubayashi	PROPN
ejpam-3142	405	6	,	,	PUNCT
ejpam-3142	405	7	m.	m.	NOUN
ejpam-3142	405	8	ashraf	ashraf	PROPN
ejpam-3142	405	9	,	,	PUNCT
ejpam-3142	405	10	n.	n.	PROPN
ejpam-3142	405	11	rehman	rehman	PROPN
ejpam-3142	405	12	and	and	CCONJ
ejpam-3142	405	13	s.	s.	PROPN
ejpam-3142	405	14	ali	ali	PROPN
ejpam-3142	405	15	.	.	PROPN
ejpam-3142	406	1	on	on	ADP
ejpam-3142	406	2	generalized	generalized	ADJ
ejpam-3142	406	3	(	(	PUNCT
ejpam-3142	406	4	α	α	NOUN
ejpam-3142	406	5	,	,	PUNCT
ejpam-3142	406	6	β)derivations	β)derivation	NOUN
ejpam-3142	406	7	in	in	ADP
ejpam-3142	406	8	prime	prime	ADJ
ejpam-3142	406	9	rings	ring	NOUN
ejpam-3142	406	10	.	.	PUNCT
ejpam-3142	407	1	algebra	algebra	PROPN
ejpam-3142	407	2	colloquim	colloquim	VERB
ejpam-3142	407	3	,	,	PUNCT
ejpam-3142	407	4	17(1):865	17(1):865	PROPN
ejpam-3142	407	5	-	-	PUNCT
ejpam-3142	407	6	874	874	NUM
ejpam-3142	407	7	,	,	PUNCT
ejpam-3142	407	8	(	(	PUNCT
ejpam-3142	407	9	2010	2010	NUM
ejpam-3142	407	10	)	)	PUNCT
ejpam-3142	407	11	.	.	PUNCT
ejpam-3142	408	1	references	reference	NOUN
ejpam-3142	408	2	89	89	NUM
ejpam-3142	408	3	[	[	SYM
ejpam-3142	408	4	13	13	NUM
ejpam-3142	408	5	]	]	X
ejpam-3142	408	6	n.	n.	PROPN
ejpam-3142	408	7	rehman	rehman	PROPN
ejpam-3142	408	8	,	,	PUNCT
ejpam-3142	408	9	s.	s.	PROPN
ejpam-3142	408	10	mallikarjuna	mallikarjuna	PROPN
ejpam-3142	408	11	and	and	CCONJ
ejpam-3142	408	12	v.	v.	ADP
ejpam-3142	408	13	v.	v.	CCONJ
ejpam-3142	408	14	kumar	kumar	PROPN
ejpam-3142	408	15	.	.	PUNCT
ejpam-3142	409	1	on	on	ADP
ejpam-3142	409	2	commutativity	commutativity	NOUN
ejpam-3142	409	3	of	of	ADP
ejpam-3142	409	4	rings	ring	NOUN
ejpam-3142	409	5	with	with	ADP
ejpam-3142	409	6	generalized	generalized	ADJ
ejpam-3142	409	7	derivations	derivation	NOUN
ejpam-3142	409	8	.	.	PUNCT
ejpam-3142	410	1	math	math	NOUN
ejpam-3142	410	2	.	.	PUNCT
ejpam-3142	411	1	j.	j.	PROPN
ejpam-3142	411	2	okayama	okayama	PROPN
ejpam-3142	411	3	univ	univ	PROPN
ejpam-3142	411	4	.	.	PROPN
ejpam-3142	411	5	,	,	PUNCT
ejpam-3142	411	6	44:43	44:43	NUM
ejpam-3142	411	7	-	-	SYM
ejpam-3142	411	8	49	49	NUM
ejpam-3142	411	9	,	,	PUNCT
ejpam-3142	411	10	(	(	PUNCT
ejpam-3142	411	11	2002	2002	NUM
ejpam-3142	411	12	)	)	PUNCT
ejpam-3142	411	13	.	.	PUNCT
ejpam-3142	412	1	[	[	X
ejpam-3142	412	2	14	14	NUM
ejpam-3142	412	3	]	]	X
ejpam-3142	412	4	n.	n.	PROPN
ejpam-3142	412	5	rehman	rehman	PROPN
ejpam-3142	412	6	,	,	PUNCT
ejpam-3142	412	7	r.	r.	PROPN
ejpam-3142	412	8	m.	m.	PROPN
ejpam-3142	412	9	al	al	PROPN
ejpam-3142	412	10	-	-	PUNCT
ejpam-3142	412	11	omary	omary	NOUN
ejpam-3142	412	12	and	and	CCONJ
ejpam-3142	412	13	c.	c.	PROPN
ejpam-3142	412	14	haetinger	haetinger	NOUN
ejpam-3142	412	15	.	.	PUNCT
ejpam-3142	413	1	on	on	ADP
ejpam-3142	413	2	lie	lie	NOUN
ejpam-3142	413	3	structrue	structrue	NOUN
ejpam-3142	413	4	of	of	ADP
ejpam-3142	413	5	prime	prime	ADJ
ejpam-3142	413	6	ring	ring	NOUN
ejpam-3142	413	7	with	with	ADP
ejpam-3142	413	8	generalized	generalized	ADJ
ejpam-3142	413	9	(	(	PUNCT
ejpam-3142	413	10	α	α	NOUN
ejpam-3142	413	11	,	,	PUNCT
ejpam-3142	413	12	β)−derivations	β)−derivation	NOUN
ejpam-3142	413	13	.	.	PUNCT
ejpam-3142	413	14	bol	bol	NOUN
ejpam-3142	413	15	.	.	PUNCT
ejpam-3142	414	1	soc	soc	PROPN
ejpam-3142	414	2	.	.	PUNCT
ejpam-3142	415	1	paranaense	paranaense	PROPN
ejpam-3142	415	2	de	de	PROPN
ejpam-3142	415	3	mat	mat	PROPN
ejpam-3142	415	4	.	.	PROPN
ejpam-3142	415	5	,	,	PUNCT
ejpam-3142	415	6	27(2):4352	27(2):4352	NUM
ejpam-3142	415	7	,	,	PUNCT
ejpam-3142	415	8	(	(	PUNCT
ejpam-3142	415	9	2009	2009	NUM
ejpam-3142	415	10	)	)	PUNCT
ejpam-3142	415	11	.	.	PUNCT
ejpam-3142	416	1	[	[	X
ejpam-3142	416	2	15	15	NUM
ejpam-3142	416	3	]	]	X
ejpam-3142	416	4	n.	n.	PROPN
ejpam-3142	416	5	rehman	rehman	PROPN
ejpam-3142	416	6	and	and	CCONJ
ejpam-3142	416	7	r.	r.	PROPN
ejpam-3142	416	8	m.	m.	PROPN
ejpam-3142	416	9	al	al	PROPN
ejpam-3142	416	10	-	-	PUNCT
ejpam-3142	416	11	omary	omary	NOUN
ejpam-3142	416	12	.	.	PUNCT
ejpam-3142	417	1	on	on	ADP
ejpam-3142	417	2	commutativity	commutativity	NOUN
ejpam-3142	417	3	of	of	ADP
ejpam-3142	417	4	2−torsion	2−torsion	NUM
ejpam-3142	417	5	free	free	VERB
ejpam-3142	417	6	∗−prime	∗−prime	PRON
ejpam-3142	417	7	rings	ring	NOUN
ejpam-3142	417	8	with	with	ADP
ejpam-3142	417	9	generalized	generalized	ADJ
ejpam-3142	417	10	derivations	derivation	NOUN
ejpam-3142	417	11	.	.	PUNCT
ejpam-3142	418	1	mathematica	mathematica	PROPN
ejpam-3142	418	2	,	,	PUNCT
ejpam-3142	418	3	53	53	NUM
ejpam-3142	418	4	(	(	PUNCT
ejpam-3142	418	5	76):171	76):171	NUM
ejpam-3142	418	6	-	-	PUNCT
ejpam-3142	418	7	180	180	NUM
ejpam-3142	418	8	,	,	PUNCT
ejpam-3142	418	9	(	(	PUNCT
ejpam-3142	418	10	2011	2011	NUM
ejpam-3142	418	11	)	)	PUNCT
ejpam-3142	418	12	.	.	PUNCT
ejpam-3142	419	1	[	[	X
ejpam-3142	419	2	16	16	NUM
ejpam-3142	419	3	]	]	X
ejpam-3142	419	4	n.	n.	PROPN
ejpam-3142	419	5	rehman	rehman	PROPN
ejpam-3142	419	6	,	,	PUNCT
ejpam-3142	419	7	r.	r.	PROPN
ejpam-3142	419	8	m.	m.	PROPN
ejpam-3142	419	9	al	al	PROPN
ejpam-3142	419	10	-	-	PUNCT
ejpam-3142	419	11	omary	omary	PROPN
ejpam-3142	419	12	and	and	CCONJ
ejpam-3142	419	13	h.	h.	PROPN
ejpam-3142	419	14	shuliang	shuliang	PROPN
ejpam-3142	419	15	.	.	PUNCT
ejpam-3142	420	1	lie	lie	VERB
ejpam-3142	420	2	ideals	ideal	NOUN
ejpam-3142	420	3	and	and	CCONJ
ejpam-3142	420	4	generalized	generalize	VERB
ejpam-3142	420	5	(	(	PUNCT
ejpam-3142	420	6	α	α	NOUN
ejpam-3142	420	7	,	,	PUNCT
ejpam-3142	420	8	β)-derivations	β)-derivation	NOUN
ejpam-3142	420	9	of	of	ADP
ejpam-3142	420	10	∗−prime	∗−prime	DET
ejpam-3142	420	11	rings	ring	NOUN
ejpam-3142	420	12	.	.	PUNCT
ejpam-3142	421	1	africa	africa	PROPN
ejpam-3142	421	2	mathematica	mathematica	PROPN
ejpam-3142	421	3	,	,	PUNCT
ejpam-3142	421	4	24	24	NUM
ejpam-3142	421	5	(	(	PUNCT
ejpam-3142	421	6	4):503510	4):503510	NUM
ejpam-3142	421	7	,	,	PUNCT
ejpam-3142	421	8	(	(	PUNCT
ejpam-3142	421	9	2013	2013	NUM
ejpam-3142	421	10	)	)	PUNCT
ejpam-3142	421	11	.	.	PUNCT