id	sid	tid	token	lemma	pos
ejpam-3248	1	1	european	european	PROPN
ejpam-3248	1	2	journal	journal	PROPN
ejpam-3248	1	3	of	of	ADP
ejpam-3248	1	4	pure	pure	ADJ
ejpam-3248	1	5	and	and	CCONJ
ejpam-3248	1	6	applied	apply	VERB
ejpam-3248	1	7	mathematics	mathematic	NOUN
ejpam-3248	1	8	vol	vol	NOUN
ejpam-3248	1	9	.	.	PUNCT
ejpam-3248	2	1	11	11	NUM
ejpam-3248	2	2	,	,	PUNCT
ejpam-3248	2	3	no	no	INTJ
ejpam-3248	2	4	.	.	NOUN
ejpam-3248	2	5	3	3	NUM
ejpam-3248	2	6	,	,	PUNCT
ejpam-3248	2	7	2018	2018	NUM
ejpam-3248	2	8	,	,	PUNCT
ejpam-3248	2	9	717	717	NUM
ejpam-3248	2	10	-	-	SYM
ejpam-3248	2	11	729	729	NUM
ejpam-3248	2	12	issn	issn	PROPN
ejpam-3248	2	13	1307	1307	NUM
ejpam-3248	2	14	-	-	SYM
ejpam-3248	2	15	5543	5543	NUM
ejpam-3248	2	16	–	–	PUNCT
ejpam-3248	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3248	2	18	published	publish	VERB
ejpam-3248	2	19	by	by	ADP
ejpam-3248	2	20	new	new	PROPN
ejpam-3248	2	21	york	york	PROPN
ejpam-3248	2	22	business	business	PROPN
ejpam-3248	2	23	global	global	PROPN
ejpam-3248	2	24	multiplicative	multiplicative	ADJ
ejpam-3248	2	25	(	(	PUNCT
ejpam-3248	2	26	generalized	generalized	ADJ
ejpam-3248	2	27	)	)	PUNCT
ejpam-3248	2	28	reverse	reverse	ADJ
ejpam-3248	2	29	derivations	derivation	NOUN
ejpam-3248	2	30	on	on	ADP
ejpam-3248	2	31	semiprime	semiprime	NOUN
ejpam-3248	2	32	ring	ring	PROPN
ejpam-3248	2	33	asma	asma	PROPN
ejpam-3248	2	34	ali1,∗	ali1,∗	PROPN
ejpam-3248	2	35	,	,	PUNCT
ejpam-3248	2	36	ambreen	ambreen	ADJ
ejpam-3248	2	37	bano1	bano1	NOUN
ejpam-3248	2	38	1	1	NUM
ejpam-3248	2	39	department	department	NOUN
ejpam-3248	2	40	of	of	ADP
ejpam-3248	2	41	mathematics	mathematics	PROPN
ejpam-3248	2	42	,	,	PUNCT
ejpam-3248	2	43	aligarh	aligarh	PROPN
ejpam-3248	2	44	muslim	muslim	PROPN
ejpam-3248	2	45	university	university	PROPN
ejpam-3248	2	46	,	,	PUNCT
ejpam-3248	2	47	aligarh	aligarh	PROPN
ejpam-3248	2	48	,	,	PUNCT
ejpam-3248	2	49	india	india	PROPN
ejpam-3248	2	50	abstract	abstract	NOUN
ejpam-3248	2	51	.	.	PUNCT
ejpam-3248	3	1	let	let	VERB
ejpam-3248	3	2	r	r	PRON
ejpam-3248	3	3	be	be	AUX
ejpam-3248	3	4	a	a	DET
ejpam-3248	3	5	semiprime	semiprime	NOUN
ejpam-3248	3	6	ring	ring	NOUN
ejpam-3248	3	7	.	.	PUNCT
ejpam-3248	4	1	a	a	DET
ejpam-3248	4	2	mapping	mapping	NOUN
ejpam-3248	4	3	f	f	NOUN
ejpam-3248	4	4	:	:	PUNCT
ejpam-3248	5	1	r→	r→	PROPN
ejpam-3248	5	2	r	r	NOUN
ejpam-3248	5	3	(	(	PUNCT
ejpam-3248	5	4	not	not	PART
ejpam-3248	5	5	necessarily	necessarily	ADV
ejpam-3248	5	6	additive	additive	VERB
ejpam-3248	5	7	)	)	PUNCT
ejpam-3248	5	8	is	be	AUX
ejpam-3248	5	9	called	call	VERB
ejpam-3248	5	10	a	a	DET
ejpam-3248	5	11	multiplicative	multiplicative	ADJ
ejpam-3248	5	12	(	(	PUNCT
ejpam-3248	5	13	generalized	generalized	ADJ
ejpam-3248	5	14	)	)	PUNCT
ejpam-3248	5	15	reverse	reverse	ADJ
ejpam-3248	5	16	derivation	derivation	NOUN
ejpam-3248	5	17	if	if	SCONJ
ejpam-3248	5	18	there	there	PRON
ejpam-3248	5	19	exists	exist	VERB
ejpam-3248	5	20	a	a	DET
ejpam-3248	5	21	map	map	NOUN
ejpam-3248	6	1	d	d	X
ejpam-3248	6	2	:	:	PUNCT
ejpam-3248	6	3	r→	r→	PROPN
ejpam-3248	6	4	r	r	NOUN
ejpam-3248	6	5	(	(	PUNCT
ejpam-3248	6	6	not	not	PART
ejpam-3248	6	7	necessarily	necessarily	ADV
ejpam-3248	6	8	a	a	DET
ejpam-3248	6	9	derivation	derivation	NOUN
ejpam-3248	6	10	nor	nor	CCONJ
ejpam-3248	6	11	an	an	DET
ejpam-3248	6	12	additive	additive	ADJ
ejpam-3248	6	13	map	map	NOUN
ejpam-3248	6	14	)	)	PUNCT
ejpam-3248	6	15	such	such	ADJ
ejpam-3248	6	16	that	that	SCONJ
ejpam-3248	6	17	f	f	PROPN
ejpam-3248	6	18	(	(	PUNCT
ejpam-3248	6	19	xy	xy	PROPN
ejpam-3248	6	20	)	)	PUNCT
ejpam-3248	6	21	=	=	SYM
ejpam-3248	6	22	f	f	PROPN
ejpam-3248	6	23	(	(	PUNCT
ejpam-3248	6	24	y)x	y)x	X
ejpam-3248	6	25	+	+	NOUN
ejpam-3248	6	26	yd(x	yd(x	NOUN
ejpam-3248	6	27	)	)	PUNCT
ejpam-3248	6	28	for	for	ADP
ejpam-3248	6	29	all	all	DET
ejpam-3248	6	30	x	x	NOUN
ejpam-3248	6	31	,	,	PUNCT
ejpam-3248	6	32	y	y	PROPN
ejpam-3248	6	33	∈	∈	PROPN
ejpam-3248	6	34	r.	r.	PROPN
ejpam-3248	6	35	in	in	ADP
ejpam-3248	6	36	this	this	DET
ejpam-3248	6	37	paper	paper	NOUN
ejpam-3248	6	38	we	we	PRON
ejpam-3248	6	39	investigate	investigate	VERB
ejpam-3248	6	40	some	some	DET
ejpam-3248	6	41	identities	identity	NOUN
ejpam-3248	6	42	involving	involve	VERB
ejpam-3248	6	43	multiplicative	multiplicative	ADJ
ejpam-3248	6	44	(	(	PUNCT
ejpam-3248	6	45	generalized	generalized	ADJ
ejpam-3248	6	46	)	)	PUNCT
ejpam-3248	6	47	reverse	reverse	ADJ
ejpam-3248	6	48	derivation	derivation	NOUN
ejpam-3248	6	49	and	and	CCONJ
ejpam-3248	6	50	prove	prove	VERB
ejpam-3248	6	51	some	some	DET
ejpam-3248	6	52	theorems	theorem	NOUN
ejpam-3248	6	53	in	in	ADP
ejpam-3248	6	54	which	which	PRON
ejpam-3248	6	55	we	we	PRON
ejpam-3248	6	56	characterize	characterize	VERB
ejpam-3248	6	57	these	these	DET
ejpam-3248	6	58	mappings	mapping	NOUN
ejpam-3248	6	59	.	.	PUNCT
ejpam-3248	7	1	2010	2010	NUM
ejpam-3248	7	2	mathematics	mathematic	NOUN
ejpam-3248	7	3	subject	subject	NOUN
ejpam-3248	7	4	classifications	classification	NOUN
ejpam-3248	7	5	:	:	PUNCT
ejpam-3248	7	6	16u80	16u80	NUM
ejpam-3248	7	7	,	,	PUNCT
ejpam-3248	7	8	16n60	16n60	NUM
ejpam-3248	7	9	,	,	PUNCT
ejpam-3248	7	10	16w25	16w25	NUM
ejpam-3248	7	11	key	key	ADJ
ejpam-3248	7	12	words	word	NOUN
ejpam-3248	7	13	and	and	CCONJ
ejpam-3248	7	14	phrases	phrase	NOUN
ejpam-3248	7	15	:	:	PUNCT
ejpam-3248	7	16	semiprime	semiprime	NOUN
ejpam-3248	7	17	ring	ring	NOUN
ejpam-3248	7	18	,	,	PUNCT
ejpam-3248	7	19	ideal	ideal	ADJ
ejpam-3248	7	20	,	,	PUNCT
ejpam-3248	7	21	multiplicative	multiplicative	ADJ
ejpam-3248	7	22	(	(	PUNCT
ejpam-3248	7	23	generalized	generalized	ADJ
ejpam-3248	7	24	)	)	PUNCT
ejpam-3248	7	25	reverse	reverse	ADJ
ejpam-3248	7	26	derivation	derivation	NOUN
ejpam-3248	7	27	.	.	PUNCT
ejpam-3248	8	1	1	1	X
ejpam-3248	8	2	.	.	X
ejpam-3248	8	3	introduction	introduction	NOUN
ejpam-3248	8	4	let	let	VERB
ejpam-3248	8	5	r	r	PRON
ejpam-3248	8	6	be	be	AUX
ejpam-3248	8	7	an	an	DET
ejpam-3248	8	8	associative	associative	ADJ
ejpam-3248	8	9	ring	ring	NOUN
ejpam-3248	8	10	.	.	PUNCT
ejpam-3248	9	1	the	the	DET
ejpam-3248	9	2	centre	centre	NOUN
ejpam-3248	9	3	of	of	ADP
ejpam-3248	9	4	r	r	NOUN
ejpam-3248	9	5	is	be	AUX
ejpam-3248	9	6	denoted	denote	VERB
ejpam-3248	9	7	by	by	ADP
ejpam-3248	9	8	z(r	z(r	NOUN
ejpam-3248	9	9	)	)	PUNCT
ejpam-3248	9	10	.	.	PUNCT
ejpam-3248	10	1	for	for	ADP
ejpam-3248	10	2	x	x	SYM
ejpam-3248	10	3	,	,	PUNCT
ejpam-3248	10	4	y	y	PROPN
ejpam-3248	10	5	∈	∈	PROPN
ejpam-3248	10	6	r	r	NOUN
ejpam-3248	10	7	,	,	PUNCT
ejpam-3248	10	8	the	the	DET
ejpam-3248	10	9	symbol	symbol	NOUN
ejpam-3248	10	10	[	[	X
ejpam-3248	10	11	x	x	X
ejpam-3248	10	12	,	,	PUNCT
ejpam-3248	10	13	y	y	PROPN
ejpam-3248	10	14	]	]	PUNCT
ejpam-3248	10	15	will	will	AUX
ejpam-3248	10	16	denote	denote	VERB
ejpam-3248	10	17	the	the	DET
ejpam-3248	10	18	commutator	commutator	NOUN
ejpam-3248	10	19	xy	xy	PROPN
ejpam-3248	10	20	−	−	PROPN
ejpam-3248	11	1	yx	yx	PROPN
ejpam-3248	11	2	and	and	CCONJ
ejpam-3248	11	3	the	the	DET
ejpam-3248	11	4	symbol	symbol	NOUN
ejpam-3248	11	5	x	x	PUNCT
ejpam-3248	11	6	◦	◦	NOUN
ejpam-3248	11	7	y	y	PROPN
ejpam-3248	11	8	will	will	AUX
ejpam-3248	11	9	denote	denote	VERB
ejpam-3248	11	10	the	the	DET
ejpam-3248	11	11	anticommutator	anticommutator	NOUN
ejpam-3248	11	12	xy	xy	PROPN
ejpam-3248	12	1	+	+	PROPN
ejpam-3248	12	2	yx	yx	PROPN
ejpam-3248	12	3	.	.	PROPN
ejpam-3248	12	4	recall	recall	VERB
ejpam-3248	12	5	that	that	SCONJ
ejpam-3248	12	6	a	a	DET
ejpam-3248	12	7	ring	ring	NOUN
ejpam-3248	12	8	r	r	NOUN
ejpam-3248	12	9	is	be	AUX
ejpam-3248	12	10	prime	prime	ADJ
ejpam-3248	12	11	if	if	SCONJ
ejpam-3248	12	12	for	for	ADP
ejpam-3248	12	13	any	any	DET
ejpam-3248	12	14	a	a	NOUN
ejpam-3248	12	15	,	,	PUNCT
ejpam-3248	12	16	b	b	X
ejpam-3248	12	17	∈	∈	PROPN
ejpam-3248	12	18	r	r	NOUN
ejpam-3248	12	19	,	,	PUNCT
ejpam-3248	12	20	arb	arb	NOUN
ejpam-3248	12	21	=	=	SYM
ejpam-3248	12	22	0	0	NUM
ejpam-3248	12	23	implies	imply	VERB
ejpam-3248	12	24	a	a	DET
ejpam-3248	12	25	=	=	SYM
ejpam-3248	12	26	0	0	NUM
ejpam-3248	12	27	or	or	CCONJ
ejpam-3248	12	28	b	b	NOUN
ejpam-3248	12	29	=	=	SYM
ejpam-3248	12	30	0	0	PROPN
ejpam-3248	12	31	and	and	CCONJ
ejpam-3248	12	32	a	a	DET
ejpam-3248	12	33	ring	ring	NOUN
ejpam-3248	12	34	r	r	NOUN
ejpam-3248	12	35	is	be	AUX
ejpam-3248	12	36	semiprime	semiprime	NOUN
ejpam-3248	12	37	if	if	SCONJ
ejpam-3248	12	38	for	for	ADP
ejpam-3248	12	39	any	any	DET
ejpam-3248	12	40	a	a	DET
ejpam-3248	12	41	∈	∈	PROPN
ejpam-3248	12	42	r	r	NOUN
ejpam-3248	12	43	,	,	PUNCT
ejpam-3248	12	44	ara	ara	PROPN
ejpam-3248	12	45	=	=	SYM
ejpam-3248	12	46	0	0	NUM
ejpam-3248	12	47	implies	imply	VERB
ejpam-3248	12	48	a	a	DET
ejpam-3248	12	49	=	=	NOUN
ejpam-3248	12	50	0	0	NUM
ejpam-3248	12	51	.	.	PUNCT
ejpam-3248	13	1	an	an	DET
ejpam-3248	13	2	additive	additive	ADJ
ejpam-3248	13	3	map	map	NOUN
ejpam-3248	14	1	d	d	X
ejpam-3248	14	2	:	:	PUNCT
ejpam-3248	14	3	r	r	NOUN
ejpam-3248	14	4	→	→	SYM
ejpam-3248	14	5	r	r	NOUN
ejpam-3248	14	6	is	be	AUX
ejpam-3248	14	7	called	call	VERB
ejpam-3248	14	8	a	a	DET
ejpam-3248	14	9	derivation	derivation	NOUN
ejpam-3248	14	10	if	if	SCONJ
ejpam-3248	14	11	d(xy	d(xy	NUM
ejpam-3248	14	12	)	)	PUNCT
ejpam-3248	14	13	=	=	SYM
ejpam-3248	15	1	d(x)y	d(x)y	PROPN
ejpam-3248	15	2	+	+	CCONJ
ejpam-3248	15	3	xd(y	xd(y	NOUN
ejpam-3248	15	4	)	)	PUNCT
ejpam-3248	15	5	for	for	ADP
ejpam-3248	15	6	all	all	DET
ejpam-3248	15	7	x	x	NOUN
ejpam-3248	15	8	,	,	PUNCT
ejpam-3248	15	9	y	y	PROPN
ejpam-3248	15	10	∈	∈	PROPN
ejpam-3248	15	11	r.	r.	NOUN
ejpam-3248	15	12	the	the	DET
ejpam-3248	15	13	concept	concept	NOUN
ejpam-3248	15	14	of	of	ADP
ejpam-3248	15	15	derivation	derivation	NOUN
ejpam-3248	15	16	was	be	AUX
ejpam-3248	15	17	extended	extend	VERB
ejpam-3248	15	18	to	to	ADP
ejpam-3248	15	19	generalized	generalize	VERB
ejpam-3248	15	20	derivation	derivation	NOUN
ejpam-3248	15	21	by	by	ADP
ejpam-3248	15	22	bresar	bresar	VERB
ejpam-3248	15	23	[	[	X
ejpam-3248	15	24	2	2	NUM
ejpam-3248	15	25	]	]	PUNCT
ejpam-3248	15	26	.	.	PUNCT
ejpam-3248	16	1	an	an	DET
ejpam-3248	16	2	additive	additive	ADJ
ejpam-3248	16	3	map	map	NOUN
ejpam-3248	16	4	f	f	NOUN
ejpam-3248	16	5	:	:	PUNCT
ejpam-3248	16	6	r	r	NOUN
ejpam-3248	16	7	→	→	SYM
ejpam-3248	16	8	r	r	NOUN
ejpam-3248	16	9	is	be	AUX
ejpam-3248	16	10	said	say	VERB
ejpam-3248	16	11	to	to	PART
ejpam-3248	16	12	be	be	AUX
ejpam-3248	16	13	a	a	DET
ejpam-3248	16	14	generalized	generalized	ADJ
ejpam-3248	16	15	derivation	derivation	NOUN
ejpam-3248	16	16	if	if	SCONJ
ejpam-3248	16	17	there	there	PRON
ejpam-3248	16	18	exists	exist	VERB
ejpam-3248	16	19	a	a	DET
ejpam-3248	16	20	derivation	derivation	NOUN
ejpam-3248	17	1	d	d	NOUN
ejpam-3248	17	2	:	:	PUNCT
ejpam-3248	17	3	r	r	NOUN
ejpam-3248	17	4	→	→	SYM
ejpam-3248	17	5	r	r	NOUN
ejpam-3248	17	6	such	such	ADJ
ejpam-3248	17	7	that	that	SCONJ
ejpam-3248	17	8	f	f	PROPN
ejpam-3248	17	9	(	(	PUNCT
ejpam-3248	17	10	xy	xy	PROPN
ejpam-3248	17	11	)	)	PUNCT
ejpam-3248	17	12	=	=	SYM
ejpam-3248	17	13	f	f	PROPN
ejpam-3248	17	14	(	(	PUNCT
ejpam-3248	17	15	x)y	x)y	PUNCT
ejpam-3248	17	16	+	+	NUM
ejpam-3248	17	17	xd(y	xd(y	NOUN
ejpam-3248	17	18	)	)	PUNCT
ejpam-3248	17	19	for	for	ADP
ejpam-3248	17	20	all	all	DET
ejpam-3248	17	21	x	x	NOUN
ejpam-3248	17	22	,	,	PUNCT
ejpam-3248	17	23	y	y	PROPN
ejpam-3248	17	24	∈	∈	PROPN
ejpam-3248	17	25	r.	r.	PROPN
ejpam-3248	17	26	daif	daif	PROPN
ejpam-3248	17	27	[	[	X
ejpam-3248	17	28	4	4	X
ejpam-3248	17	29	]	]	PUNCT
ejpam-3248	17	30	introduced	introduce	VERB
ejpam-3248	17	31	the	the	DET
ejpam-3248	17	32	concept	concept	NOUN
ejpam-3248	17	33	of	of	ADP
ejpam-3248	17	34	multiplicative	multiplicative	ADJ
ejpam-3248	17	35	derivation	derivation	NOUN
ejpam-3248	17	36	.	.	PUNCT
ejpam-3248	18	1	a	a	DET
ejpam-3248	18	2	map	map	NOUN
ejpam-3248	18	3	d	d	X
ejpam-3248	18	4	:	:	PUNCT
ejpam-3248	18	5	r	r	NOUN
ejpam-3248	18	6	→	→	SYM
ejpam-3248	18	7	r	r	NOUN
ejpam-3248	18	8	is	be	AUX
ejpam-3248	18	9	said	say	VERB
ejpam-3248	18	10	to	to	PART
ejpam-3248	18	11	be	be	AUX
ejpam-3248	18	12	a	a	DET
ejpam-3248	18	13	multiplicative	multiplicative	ADJ
ejpam-3248	18	14	derivation	derivation	NOUN
ejpam-3248	18	15	if	if	SCONJ
ejpam-3248	18	16	it	it	PRON
ejpam-3248	18	17	satisfies	satisfy	VERB
ejpam-3248	18	18	d(xy	d(xy	NUM
ejpam-3248	18	19	)	)	PUNCT
ejpam-3248	18	20	=	=	SYM
ejpam-3248	19	1	d(x)y	d(x)y	PROPN
ejpam-3248	19	2	+	+	CCONJ
ejpam-3248	19	3	xd(y	xd(y	NOUN
ejpam-3248	19	4	)	)	PUNCT
ejpam-3248	19	5	for	for	ADP
ejpam-3248	19	6	all	all	DET
ejpam-3248	19	7	x	x	NOUN
ejpam-3248	19	8	,	,	PUNCT
ejpam-3248	19	9	y	y	PROPN
ejpam-3248	19	10	∈	∈	PROPN
ejpam-3248	19	11	r.	r.	PROPN
ejpam-3248	19	12	daif	daif	PROPN
ejpam-3248	19	13	and	and	CCONJ
ejpam-3248	19	14	tammam	tammam	PROPN
ejpam-3248	19	15	el	el	PROPN
ejpam-3248	19	16	-	-	PROPN
ejpam-3248	19	17	sayiad	sayiad	PROPN
ejpam-3248	19	18	[	[	X
ejpam-3248	19	19	5	5	NUM
ejpam-3248	19	20	]	]	PUNCT
ejpam-3248	19	21	extended	extend	VERB
ejpam-3248	19	22	the	the	DET
ejpam-3248	19	23	concept	concept	NOUN
ejpam-3248	19	24	of	of	ADP
ejpam-3248	19	25	multiplicative	multiplicative	ADJ
ejpam-3248	19	26	derivation	derivation	NOUN
ejpam-3248	19	27	to	to	ADP
ejpam-3248	19	28	multiplicative	multiplicative	ADJ
ejpam-3248	19	29	generalized	generalized	ADJ
ejpam-3248	19	30	derivation	derivation	NOUN
ejpam-3248	19	31	.	.	PUNCT
ejpam-3248	20	1	a	a	DET
ejpam-3248	20	2	mapping	mapping	NOUN
ejpam-3248	20	3	f	f	NOUN
ejpam-3248	20	4	:	:	PUNCT
ejpam-3248	20	5	r	r	NOUN
ejpam-3248	20	6	→	→	SYM
ejpam-3248	20	7	r	r	NOUN
ejpam-3248	20	8	is	be	AUX
ejpam-3248	20	9	said	say	VERB
ejpam-3248	20	10	to	to	PART
ejpam-3248	20	11	be	be	AUX
ejpam-3248	20	12	a	a	DET
ejpam-3248	20	13	multiplicative	multiplicative	ADJ
ejpam-3248	20	14	generalized	generalized	ADJ
ejpam-3248	20	15	derivation	derivation	NOUN
ejpam-3248	20	16	if	if	SCONJ
ejpam-3248	20	17	there	there	PRON
ejpam-3248	20	18	exists	exist	VERB
ejpam-3248	20	19	a	a	DET
ejpam-3248	20	20	derivation	derivation	NOUN
ejpam-3248	20	21	d	d	NOUN
ejpam-3248	20	22	on	on	ADP
ejpam-3248	20	23	r	r	NOUN
ejpam-3248	21	1	such	such	ADJ
ejpam-3248	21	2	that	that	SCONJ
ejpam-3248	21	3	f	f	PROPN
ejpam-3248	21	4	(	(	PUNCT
ejpam-3248	21	5	xy	xy	PROPN
ejpam-3248	21	6	)	)	PUNCT
ejpam-3248	21	7	=	=	SYM
ejpam-3248	21	8	f	f	PROPN
ejpam-3248	21	9	(	(	PUNCT
ejpam-3248	21	10	x)y	x)y	PUNCT
ejpam-3248	21	11	+	+	NUM
ejpam-3248	21	12	xd(y	xd(y	NOUN
ejpam-3248	21	13	)	)	PUNCT
ejpam-3248	21	14	for	for	ADP
ejpam-3248	21	15	all	all	DET
ejpam-3248	21	16	x	x	NOUN
ejpam-3248	21	17	,	,	PUNCT
ejpam-3248	21	18	y	y	PROPN
ejpam-3248	21	19	∈	∈	PROPN
ejpam-3248	21	20	r.	r.	PROPN
ejpam-3248	21	21	in	in	ADP
ejpam-3248	21	22	this	this	DET
ejpam-3248	21	23	definition	definition	NOUN
ejpam-3248	21	24	if	if	SCONJ
ejpam-3248	21	25	we	we	PRON
ejpam-3248	21	26	take	take	VERB
ejpam-3248	21	27	d	d	NOUN
ejpam-3248	21	28	to	to	PART
ejpam-3248	21	29	be	be	AUX
ejpam-3248	21	30	a	a	DET
ejpam-3248	21	31	mapping	mapping	NOUN
ejpam-3248	21	32	not	not	PART
ejpam-3248	21	33	necessarily	necessarily	ADV
ejpam-3248	21	34	a	a	DET
ejpam-3248	21	35	derivation	derivation	NOUN
ejpam-3248	21	36	nor	nor	CCONJ
ejpam-3248	21	37	an	an	DET
ejpam-3248	21	38	additive	additive	ADJ
ejpam-3248	21	39	map	map	NOUN
ejpam-3248	21	40	,	,	PUNCT
ejpam-3248	21	41	then	then	ADV
ejpam-3248	21	42	f	f	PROPN
ejpam-3248	21	43	is	be	AUX
ejpam-3248	21	44	said	say	VERB
ejpam-3248	21	45	to	to	PART
ejpam-3248	21	46	be	be	AUX
ejpam-3248	21	47	a	a	DET
ejpam-3248	21	48	multiplicative	multiplicative	ADJ
ejpam-3248	21	49	(	(	PUNCT
ejpam-3248	21	50	generalized)-derivation	generalized)-derivation	NOUN
ejpam-3248	21	51	which	which	PRON
ejpam-3248	21	52	was	be	AUX
ejpam-3248	21	53	introduced	introduce	VERB
ejpam-3248	21	54	by	by	ADP
ejpam-3248	21	55	dhara	dhara	PROPN
ejpam-3248	21	56	and	and	CCONJ
ejpam-3248	21	57	ali	ali	PROPN
ejpam-3248	22	1	[	[	X
ejpam-3248	22	2	7	7	NUM
ejpam-3248	22	3	]	]	PUNCT
ejpam-3248	22	4	.	.	PUNCT
ejpam-3248	23	1	dhara	dhara	PROPN
ejpam-3248	23	2	and	and	CCONJ
ejpam-3248	23	3	ali	ali	PROPN
ejpam-3248	23	4	[	[	X
ejpam-3248	23	5	7	7	NUM
ejpam-3248	23	6	]	]	PUNCT
ejpam-3248	23	7	studied	study	VERB
ejpam-3248	23	8	the	the	DET
ejpam-3248	23	9	following	follow	VERB
ejpam-3248	23	10	identities	identity	NOUN
ejpam-3248	23	11	related	relate	VERB
ejpam-3248	23	12	∗corresponding	∗corresponde	VERB
ejpam-3248	23	13	author	author	NOUN
ejpam-3248	23	14	.	.	PUNCT
ejpam-3248	24	1	doi	doi	NOUN
ejpam-3248	24	2	:	:	PUNCT
ejpam-3248	24	3	https://doi.org/10.29020/nybg.ejpam.v11i3.3248	https://doi.org/10.29020/nybg.ejpam.v11i3.3248	PROPN
ejpam-3248	24	4	email	email	NOUN
ejpam-3248	24	5	addresses	address	NOUN
ejpam-3248	24	6	:	:	PUNCT
ejpam-3248	24	7	asma	asma	PROPN
ejpam-3248	24	8	ali2@rediffmail.com	ali2@rediffmail.com	PROPN
ejpam-3248	24	9	(	(	PUNCT
ejpam-3248	24	10	asma	asma	PROPN
ejpam-3248	24	11	ali	ali	PROPN
ejpam-3248	24	12	)	)	PUNCT
ejpam-3248	24	13	,	,	PUNCT
ejpam-3248	24	14	ambreenbn9@gmail.com	ambreenbn9@gmail.com	X
ejpam-3248	24	15	(	(	PUNCT
ejpam-3248	24	16	ambreen	ambreen	PROPN
ejpam-3248	24	17	bano	bano	PROPN
ejpam-3248	24	18	)	)	PUNCT
ejpam-3248	24	19	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3248	25	1	717	717	NUM
ejpam-3248	25	2	c	c	NOUN
ejpam-3248	25	3	©	©	PROPN
ejpam-3248	25	4	2018	2018	NUM
ejpam-3248	25	5	ejpam	ejpam	VERB
ejpam-3248	25	6	all	all	DET
ejpam-3248	25	7	rights	right	NOUN
ejpam-3248	25	8	reserved	reserve	VERB
ejpam-3248	25	9	.	.	PUNCT
ejpam-3248	26	1	a.	a.	PROPN
ejpam-3248	26	2	ali	ali	PROPN
ejpam-3248	26	3	,	,	PUNCT
ejpam-3248	26	4	a.	a.	PROPN
ejpam-3248	26	5	bano	bano	PROPN
ejpam-3248	26	6	/	/	SYM
ejpam-3248	26	7	eur	eur	PROPN
ejpam-3248	26	8	.	.	PUNCT
ejpam-3248	27	1	j.	j.	PROPN
ejpam-3248	27	2	pure	pure	PROPN
ejpam-3248	27	3	appl	appl	PROPN
ejpam-3248	27	4	.	.	PROPN
ejpam-3248	27	5	math	math	PROPN
ejpam-3248	27	6	,	,	PUNCT
ejpam-3248	27	7	11	11	NUM
ejpam-3248	27	8	(	(	PUNCT
ejpam-3248	27	9	3	3	NUM
ejpam-3248	27	10	)	)	PUNCT
ejpam-3248	27	11	(	(	PUNCT
ejpam-3248	27	12	2018	2018	NUM
ejpam-3248	27	13	)	)	PUNCT
ejpam-3248	27	14	,	,	PUNCT
ejpam-3248	27	15	717	717	NUM
ejpam-3248	27	16	-	-	SYM
ejpam-3248	27	17	729	729	NUM
ejpam-3248	27	18	718	718	NUM
ejpam-3248	27	19	on	on	ADP
ejpam-3248	27	20	multiplicative	multiplicative	ADJ
ejpam-3248	27	21	(	(	PUNCT
ejpam-3248	27	22	generalized	generalized	ADJ
ejpam-3248	27	23	)	)	PUNCT
ejpam-3248	27	24	derivation	derivation	NOUN
ejpam-3248	27	25	on	on	ADP
ejpam-3248	27	26	a	a	DET
ejpam-3248	27	27	semiprime	semiprime	NOUN
ejpam-3248	27	28	ring	ring	NOUN
ejpam-3248	27	29	:	:	PUNCT
ejpam-3248	27	30	(	(	PUNCT
ejpam-3248	27	31	i)f	i)f	X
ejpam-3248	27	32	(	(	PUNCT
ejpam-3248	27	33	xy	xy	NOUN
ejpam-3248	27	34	)	)	PUNCT
ejpam-3248	27	35	±	±	NOUN
ejpam-3248	27	36	xy	xy	PROPN
ejpam-3248	27	37	∈	∈	PROPN
ejpam-3248	27	38	z(r	z(r	PROPN
ejpam-3248	27	39	)	)	PUNCT
ejpam-3248	27	40	,	,	PUNCT
ejpam-3248	27	41	(	(	PUNCT
ejpam-3248	27	42	ii)f	ii)f	PROPN
ejpam-3248	27	43	(	(	PUNCT
ejpam-3248	27	44	xy)±	xy)±	VERB
ejpam-3248	27	45	yx	yx	PROPN
ejpam-3248	27	46	∈	∈	PROPN
ejpam-3248	27	47	z(r	z(r	PROPN
ejpam-3248	27	48	)	)	PUNCT
ejpam-3248	27	49	,	,	PUNCT
ejpam-3248	27	50	(	(	PUNCT
ejpam-3248	27	51	iii)f	iii)f	PROPN
ejpam-3248	27	52	(	(	PUNCT
ejpam-3248	27	53	x)f	x)f	X
ejpam-3248	27	54	(	(	PUNCT
ejpam-3248	27	55	y)±	y)±	VERB
ejpam-3248	27	56	xy	xy	PROPN
ejpam-3248	27	57	∈	∈	PROPN
ejpam-3248	27	58	z(r	z(r	PROPN
ejpam-3248	27	59	)	)	PUNCT
ejpam-3248	27	60	and	and	CCONJ
ejpam-3248	27	61	(	(	PUNCT
ejpam-3248	27	62	iv)f	iv)f	PROPN
ejpam-3248	27	63	(	(	PUNCT
ejpam-3248	27	64	x)f	x)f	X
ejpam-3248	27	65	(	(	PUNCT
ejpam-3248	27	66	y)±	y)±	VERB
ejpam-3248	27	67	yx	yx	NOUN
ejpam-3248	27	68	∈	∈	PROPN
ejpam-3248	27	69	z(r	z(r	PROPN
ejpam-3248	27	70	)	)	PUNCT
ejpam-3248	27	71	for	for	ADP
ejpam-3248	27	72	all	all	DET
ejpam-3248	27	73	x	x	NOUN
ejpam-3248	27	74	,	,	PUNCT
ejpam-3248	27	75	y	y	PROPN
ejpam-3248	27	76	in	in	ADP
ejpam-3248	27	77	some	some	DET
ejpam-3248	27	78	suitable	suitable	ADJ
ejpam-3248	27	79	subset	subset	NOUN
ejpam-3248	27	80	of	of	ADP
ejpam-3248	27	81	a	a	DET
ejpam-3248	27	82	semiprime	semiprime	NOUN
ejpam-3248	27	83	ring	ring	NOUN
ejpam-3248	27	84	r.	r.	PROPN
ejpam-3248	27	85	the	the	DET
ejpam-3248	27	86	concept	concept	NOUN
ejpam-3248	27	87	of	of	ADP
ejpam-3248	27	88	reverse	reverse	ADJ
ejpam-3248	27	89	derivation	derivation	NOUN
ejpam-3248	27	90	was	be	AUX
ejpam-3248	27	91	first	first	ADJ
ejpam-3248	27	92	time	time	NOUN
ejpam-3248	27	93	introduced	introduce	VERB
ejpam-3248	27	94	by	by	ADP
ejpam-3248	27	95	herstein	herstein	NOUN
ejpam-3248	27	96	[	[	X
ejpam-3248	27	97	8	8	NUM
ejpam-3248	27	98	]	]	PUNCT
ejpam-3248	27	99	.	.	PUNCT
ejpam-3248	28	1	a	a	DET
ejpam-3248	28	2	mapping	mapping	NOUN
ejpam-3248	28	3	d	d	NOUN
ejpam-3248	28	4	:	:	PUNCT
ejpam-3248	28	5	r	r	NOUN
ejpam-3248	28	6	→	→	SYM
ejpam-3248	28	7	r	r	NOUN
ejpam-3248	28	8	which	which	PRON
ejpam-3248	28	9	satisfies	satisfy	VERB
ejpam-3248	28	10	d(xy	d(xy	NUM
ejpam-3248	28	11	)	)	PUNCT
ejpam-3248	28	12	=	=	SYM
ejpam-3248	28	13	d(y)x	d(y)x	PROPN
ejpam-3248	28	14	+	+	CCONJ
ejpam-3248	28	15	yd(x	yd(x	NOUN
ejpam-3248	28	16	)	)	PUNCT
ejpam-3248	28	17	for	for	ADP
ejpam-3248	28	18	all	all	DET
ejpam-3248	28	19	x	x	NOUN
ejpam-3248	28	20	,	,	PUNCT
ejpam-3248	28	21	y	y	PROPN
ejpam-3248	28	22	∈	∈	PROPN
ejpam-3248	28	23	r	r	NOUN
ejpam-3248	28	24	is	be	AUX
ejpam-3248	28	25	called	call	VERB
ejpam-3248	28	26	a	a	DET
ejpam-3248	28	27	reverse	reverse	ADJ
ejpam-3248	28	28	derivation	derivation	NOUN
ejpam-3248	28	29	.	.	PUNCT
ejpam-3248	29	1	further	far	ADV
ejpam-3248	29	2	bresar	bresar	VERB
ejpam-3248	29	3	and	and	CCONJ
ejpam-3248	29	4	vukman	vukman	VERB
ejpam-3248	30	1	[	[	X
ejpam-3248	30	2	3	3	NUM
ejpam-3248	30	3	]	]	PUNCT
ejpam-3248	30	4	studied	study	VERB
ejpam-3248	30	5	the	the	DET
ejpam-3248	30	6	reverse	reverse	ADJ
ejpam-3248	30	7	derivation	derivation	NOUN
ejpam-3248	30	8	.	.	PUNCT
ejpam-3248	31	1	aboubakr	aboubakr	PROPN
ejpam-3248	31	2	and	and	CCONJ
ejpam-3248	31	3	gonzalez	gonzalez	PROPN
ejpam-3248	32	1	[	[	X
ejpam-3248	32	2	1	1	X
ejpam-3248	32	3	]	]	PUNCT
ejpam-3248	32	4	generalized	generalize	VERB
ejpam-3248	32	5	the	the	DET
ejpam-3248	32	6	notion	notion	NOUN
ejpam-3248	32	7	of	of	ADP
ejpam-3248	32	8	reverse	reverse	ADJ
ejpam-3248	32	9	derivation	derivation	NOUN
ejpam-3248	32	10	by	by	ADP
ejpam-3248	32	11	introducing	introduce	VERB
ejpam-3248	32	12	generalized	generalized	ADJ
ejpam-3248	32	13	reverse	reverse	ADJ
ejpam-3248	32	14	derivation	derivation	NOUN
ejpam-3248	32	15	.	.	PUNCT
ejpam-3248	33	1	an	an	DET
ejpam-3248	33	2	additive	additive	ADJ
ejpam-3248	33	3	map	map	NOUN
ejpam-3248	33	4	f	f	NOUN
ejpam-3248	33	5	:	:	PUNCT
ejpam-3248	33	6	r	r	NOUN
ejpam-3248	33	7	→	→	SYM
ejpam-3248	33	8	r	r	NOUN
ejpam-3248	33	9	is	be	AUX
ejpam-3248	33	10	said	say	VERB
ejpam-3248	33	11	to	to	PART
ejpam-3248	33	12	be	be	AUX
ejpam-3248	33	13	a	a	DET
ejpam-3248	33	14	generalized	generalized	ADJ
ejpam-3248	33	15	reverse	reverse	ADJ
ejpam-3248	33	16	derivation	derivation	NOUN
ejpam-3248	33	17	if	if	SCONJ
ejpam-3248	33	18	f	f	PROPN
ejpam-3248	33	19	(	(	PUNCT
ejpam-3248	33	20	xy	xy	PROPN
ejpam-3248	33	21	)	)	PUNCT
ejpam-3248	33	22	=	=	SYM
ejpam-3248	33	23	f	f	PROPN
ejpam-3248	33	24	(	(	PUNCT
ejpam-3248	33	25	y)x	y)x	X
ejpam-3248	33	26	+	+	NOUN
ejpam-3248	33	27	yd(x	yd(x	NOUN
ejpam-3248	33	28	)	)	PUNCT
ejpam-3248	33	29	holds	hold	VERB
ejpam-3248	33	30	for	for	ADP
ejpam-3248	33	31	all	all	DET
ejpam-3248	33	32	x	x	NOUN
ejpam-3248	33	33	,	,	PUNCT
ejpam-3248	33	34	y	y	PROPN
ejpam-3248	33	35	∈	∈	PROPN
ejpam-3248	33	36	r	r	NOUN
ejpam-3248	33	37	,	,	PUNCT
ejpam-3248	33	38	where	where	SCONJ
ejpam-3248	33	39	d	d	NOUN
ejpam-3248	33	40	is	be	AUX
ejpam-3248	33	41	a	a	DET
ejpam-3248	33	42	reverse	reverse	ADJ
ejpam-3248	33	43	derivation	derivation	NOUN
ejpam-3248	33	44	of	of	ADP
ejpam-3248	33	45	r.	r.	PROPN
ejpam-3248	33	46	very	very	ADV
ejpam-3248	33	47	recently	recently	ADV
ejpam-3248	33	48	tiwari	tiwari	ADJ
ejpam-3248	33	49	et	et	PROPN
ejpam-3248	33	50	al	al	PROPN
ejpam-3248	34	1	[	[	X
ejpam-3248	34	2	11	11	NUM
ejpam-3248	34	3	]	]	SYM
ejpam-3248	34	4	defined	define	VERB
ejpam-3248	34	5	multiplicative	multiplicative	ADJ
ejpam-3248	34	6	(	(	PUNCT
ejpam-3248	34	7	generalized	generalized	ADJ
ejpam-3248	34	8	)	)	PUNCT
ejpam-3248	34	9	reverse	reverse	ADJ
ejpam-3248	34	10	derivation	derivation	NOUN
ejpam-3248	34	11	.	.	PUNCT
ejpam-3248	35	1	a	a	DET
ejpam-3248	35	2	map	map	NOUN
ejpam-3248	35	3	f	f	X
ejpam-3248	35	4	:	:	PUNCT
ejpam-3248	35	5	r	r	NOUN
ejpam-3248	35	6	→	→	SYM
ejpam-3248	35	7	r	r	NOUN
ejpam-3248	35	8	is	be	AUX
ejpam-3248	35	9	said	say	VERB
ejpam-3248	35	10	to	to	PART
ejpam-3248	35	11	be	be	AUX
ejpam-3248	35	12	a	a	DET
ejpam-3248	35	13	multiplicative	multiplicative	ADJ
ejpam-3248	35	14	(	(	PUNCT
ejpam-3248	35	15	generalized	generalized	ADJ
ejpam-3248	35	16	)	)	PUNCT
ejpam-3248	35	17	reverse	reverse	ADJ
ejpam-3248	35	18	derivation	derivation	NOUN
ejpam-3248	35	19	if	if	SCONJ
ejpam-3248	35	20	f	f	PROPN
ejpam-3248	35	21	(	(	PUNCT
ejpam-3248	35	22	xy	xy	PROPN
ejpam-3248	35	23	)	)	PUNCT
ejpam-3248	35	24	=	=	SYM
ejpam-3248	35	25	f	f	PROPN
ejpam-3248	35	26	(	(	PUNCT
ejpam-3248	35	27	y)x	y)x	X
ejpam-3248	35	28	+	+	NOUN
ejpam-3248	35	29	yd(x	yd(x	NOUN
ejpam-3248	35	30	)	)	PUNCT
ejpam-3248	35	31	holds	hold	VERB
ejpam-3248	35	32	for	for	ADP
ejpam-3248	35	33	all	all	DET
ejpam-3248	35	34	x	x	NOUN
ejpam-3248	35	35	,	,	PUNCT
ejpam-3248	35	36	y	y	PROPN
ejpam-3248	35	37	∈	∈	PROPN
ejpam-3248	35	38	r	r	NOUN
ejpam-3248	35	39	,	,	PUNCT
ejpam-3248	35	40	where	where	SCONJ
ejpam-3248	35	41	d	d	NOUN
ejpam-3248	35	42	is	be	AUX
ejpam-3248	35	43	any	any	DET
ejpam-3248	35	44	map	map	NOUN
ejpam-3248	35	45	on	on	ADP
ejpam-3248	35	46	r.	r.	PROPN
ejpam-3248	35	47	in	in	ADP
ejpam-3248	35	48	the	the	DET
ejpam-3248	35	49	mentioned	mention	VERB
ejpam-3248	35	50	paper	paper	NOUN
ejpam-3248	35	51	they	they	PRON
ejpam-3248	35	52	proved	prove	VERB
ejpam-3248	35	53	commutativity	commutativity	NOUN
ejpam-3248	35	54	of	of	ADP
ejpam-3248	35	55	semiprime	semiprime	NOUN
ejpam-3248	35	56	ring	ring	NOUN
ejpam-3248	35	57	admitting	admit	VERB
ejpam-3248	35	58	a	a	DET
ejpam-3248	35	59	multiplicative	multiplicative	ADJ
ejpam-3248	35	60	(	(	PUNCT
ejpam-3248	35	61	generalized	generalized	ADJ
ejpam-3248	35	62	)	)	PUNCT
ejpam-3248	35	63	reverse	reverse	ADJ
ejpam-3248	35	64	derivation	derivation	NOUN
ejpam-3248	35	65	satisfying	satisfy	VERB
ejpam-3248	35	66	one	one	NUM
ejpam-3248	35	67	of	of	ADP
ejpam-3248	35	68	the	the	DET
ejpam-3248	35	69	following	following	ADJ
ejpam-3248	35	70	conditions	condition	NOUN
ejpam-3248	35	71	:	:	PUNCT
ejpam-3248	35	72	(	(	PUNCT
ejpam-3248	35	73	i)f	i)f	X
ejpam-3248	35	74	(	(	PUNCT
ejpam-3248	35	75	x)f	x)f	X
ejpam-3248	35	76	(	(	PUNCT
ejpam-3248	36	1	y)±	y)±	VERB
ejpam-3248	36	2	xy	xy	X
ejpam-3248	36	3	=	=	PUNCT
ejpam-3248	36	4	0	0	PROPN
ejpam-3248	36	5	,	,	PUNCT
ejpam-3248	36	6	(	(	PUNCT
ejpam-3248	36	7	ii)f	ii)f	PROPN
ejpam-3248	36	8	(	(	PUNCT
ejpam-3248	36	9	x)f	x)f	X
ejpam-3248	36	10	(	(	PUNCT
ejpam-3248	36	11	y)±	y)±	ADJ
ejpam-3248	36	12	yx	yx	NOUN
ejpam-3248	36	13	=	=	SYM
ejpam-3248	36	14	0	0	PROPN
ejpam-3248	36	15	,	,	PUNCT
ejpam-3248	36	16	(	(	PUNCT
ejpam-3248	36	17	iii)f	iii)f	PROPN
ejpam-3248	36	18	(	(	PUNCT
ejpam-3248	36	19	xy)±	xy)±	VERB
ejpam-3248	37	1	[	[	X
ejpam-3248	37	2	x	x	X
ejpam-3248	37	3	,	,	PUNCT
ejpam-3248	37	4	y	y	PROPN
ejpam-3248	37	5	]	]	X
ejpam-3248	37	6	=	=	SYM
ejpam-3248	37	7	0	0	NUM
ejpam-3248	37	8	,	,	PUNCT
ejpam-3248	37	9	(	(	PUNCT
ejpam-3248	37	10	iv)f	iv)f	PROPN
ejpam-3248	37	11	(	(	PUNCT
ejpam-3248	37	12	xy)±	xy)±	VERB
ejpam-3248	37	13	(	(	PUNCT
ejpam-3248	37	14	x	x	SYM
ejpam-3248	37	15	◦	◦	VERB
ejpam-3248	37	16	y	y	NOUN
ejpam-3248	37	17	)	)	PUNCT
ejpam-3248	37	18	=	=	SYM
ejpam-3248	37	19	0	0	NUM
ejpam-3248	37	20	,	,	PUNCT
ejpam-3248	37	21	(	(	PUNCT
ejpam-3248	37	22	v)f	v)f	X
ejpam-3248	37	23	(	(	PUNCT
ejpam-3248	37	24	xy)±	xy)±	VERB
ejpam-3248	37	25	f	f	X
ejpam-3248	37	26	(	(	PUNCT
ejpam-3248	37	27	x)f	x)f	X
ejpam-3248	37	28	(	(	PUNCT
ejpam-3248	37	29	y	y	NOUN
ejpam-3248	37	30	)	)	PUNCT
ejpam-3248	37	31	=	=	SYM
ejpam-3248	37	32	0	0	NUM
ejpam-3248	37	33	,	,	PUNCT
ejpam-3248	37	34	for	for	ADP
ejpam-3248	37	35	all	all	DET
ejpam-3248	37	36	x	x	NOUN
ejpam-3248	37	37	,	,	PUNCT
ejpam-3248	37	38	y	y	PROPN
ejpam-3248	37	39	∈	∈	PROPN
ejpam-3248	38	1	i	i	PRON
ejpam-3248	38	2	,	,	PUNCT
ejpam-3248	38	3	a	a	DET
ejpam-3248	38	4	two	two	NUM
ejpam-3248	38	5	sided	sided	ADJ
ejpam-3248	38	6	ideal	ideal	NOUN
ejpam-3248	38	7	in	in	ADP
ejpam-3248	38	8	a	a	DET
ejpam-3248	38	9	semiprime	semiprime	NOUN
ejpam-3248	38	10	ring	ring	NOUN
ejpam-3248	38	11	r.	r.	PROPN
ejpam-3248	38	12	as	as	ADP
ejpam-3248	38	13	a	a	DET
ejpam-3248	38	14	line	line	NOUN
ejpam-3248	38	15	of	of	ADP
ejpam-3248	38	16	investigation	investigation	NOUN
ejpam-3248	38	17	we	we	PRON
ejpam-3248	38	18	study	study	VERB
ejpam-3248	38	19	the	the	DET
ejpam-3248	38	20	following	follow	VERB
ejpam-3248	38	21	situations	situation	NOUN
ejpam-3248	38	22	:	:	PUNCT
ejpam-3248	38	23	(	(	PUNCT
ejpam-3248	38	24	i)f	i)f	X
ejpam-3248	38	25	(	(	PUNCT
ejpam-3248	38	26	x)f	x)f	X
ejpam-3248	38	27	(	(	PUNCT
ejpam-3248	38	28	y)±	y)±	VERB
ejpam-3248	38	29	xy	xy	PROPN
ejpam-3248	38	30	∈	∈	PROPN
ejpam-3248	38	31	z(r	z(r	NOUN
ejpam-3248	38	32	)	)	PUNCT
ejpam-3248	38	33	for	for	ADP
ejpam-3248	38	34	all	all	DET
ejpam-3248	38	35	x	x	NOUN
ejpam-3248	38	36	,	,	PUNCT
ejpam-3248	38	37	y	y	PROPN
ejpam-3248	38	38	∈	∈	PROPN
ejpam-3248	39	1	i	i	PRON
ejpam-3248	39	2	,	,	PUNCT
ejpam-3248	39	3	(	(	PUNCT
ejpam-3248	39	4	ii)f	ii)f	PROPN
ejpam-3248	39	5	(	(	PUNCT
ejpam-3248	39	6	x)f	x)f	X
ejpam-3248	39	7	(	(	PUNCT
ejpam-3248	39	8	y)±	y)±	VERB
ejpam-3248	39	9	yx	yx	NOUN
ejpam-3248	39	10	∈	∈	PROPN
ejpam-3248	39	11	z(r	z(r	PROPN
ejpam-3248	39	12	)	)	PUNCT
ejpam-3248	39	13	for	for	ADP
ejpam-3248	39	14	all	all	DET
ejpam-3248	39	15	x	x	NOUN
ejpam-3248	39	16	,	,	PUNCT
ejpam-3248	39	17	y	y	PROPN
ejpam-3248	39	18	∈	∈	PROPN
ejpam-3248	40	1	i	i	PRON
ejpam-3248	40	2	,	,	PUNCT
ejpam-3248	40	3	(	(	PUNCT
ejpam-3248	40	4	iii)f	iii)f	PROPN
ejpam-3248	40	5	(	(	PUNCT
ejpam-3248	40	6	xy)±	xy)±	VERB
ejpam-3248	40	7	[	[	X
ejpam-3248	40	8	x	x	X
ejpam-3248	40	9	,	,	PUNCT
ejpam-3248	40	10	y	y	PROPN
ejpam-3248	40	11	]	]	X
ejpam-3248	40	12	∈	∈	PROPN
ejpam-3248	40	13	z(r	z(r	PROPN
ejpam-3248	40	14	)	)	PUNCT
ejpam-3248	40	15	for	for	ADP
ejpam-3248	40	16	all	all	DET
ejpam-3248	40	17	x	x	NOUN
ejpam-3248	40	18	,	,	PUNCT
ejpam-3248	40	19	y	y	PROPN
ejpam-3248	40	20	∈	∈	PROPN
ejpam-3248	41	1	i	i	PRON
ejpam-3248	41	2	,	,	PUNCT
ejpam-3248	41	3	(	(	PUNCT
ejpam-3248	41	4	iv)f	iv)f	PROPN
ejpam-3248	41	5	(	(	PUNCT
ejpam-3248	41	6	xy)±	xy)±	VERB
ejpam-3248	41	7	x	x	PUNCT
ejpam-3248	41	8	◦	◦	VERB
ejpam-3248	41	9	y	y	PROPN
ejpam-3248	41	10	∈	∈	PROPN
ejpam-3248	41	11	z(r	z(r	PROPN
ejpam-3248	41	12	)	)	PUNCT
ejpam-3248	41	13	for	for	ADP
ejpam-3248	41	14	all	all	DET
ejpam-3248	41	15	x	x	NOUN
ejpam-3248	41	16	,	,	PUNCT
ejpam-3248	41	17	y	y	PROPN
ejpam-3248	41	18	∈	∈	PROPN
ejpam-3248	42	1	i	i	PRON
ejpam-3248	42	2	,	,	PUNCT
ejpam-3248	42	3	(	(	PUNCT
ejpam-3248	42	4	v)f	v)f	X
ejpam-3248	42	5	(	(	PUNCT
ejpam-3248	42	6	xy)±	xy)±	VERB
ejpam-3248	42	7	f	f	PROPN
ejpam-3248	42	8	(	(	PUNCT
ejpam-3248	42	9	y)f	y)f	NOUN
ejpam-3248	42	10	(	(	PUNCT
ejpam-3248	42	11	x	x	X
ejpam-3248	42	12	)	)	PUNCT
ejpam-3248	42	13	∈	∈	PROPN
ejpam-3248	42	14	z(r	z(r	PROPN
ejpam-3248	42	15	)	)	PUNCT
ejpam-3248	42	16	for	for	ADP
ejpam-3248	42	17	all	all	DET
ejpam-3248	42	18	x	x	NOUN
ejpam-3248	42	19	,	,	PUNCT
ejpam-3248	42	20	y	y	PROPN
ejpam-3248	42	21	∈	∈	PROPN
ejpam-3248	43	1	i	i	PRON
ejpam-3248	43	2	,	,	PUNCT
ejpam-3248	43	3	(	(	PUNCT
ejpam-3248	43	4	vi)[f	vi)[f	VERB
ejpam-3248	43	5	(	(	PUNCT
ejpam-3248	43	6	x	x	NOUN
ejpam-3248	43	7	)	)	PUNCT
ejpam-3248	43	8	,	,	PUNCT
ejpam-3248	43	9	y]±	y]±	PROPN
ejpam-3248	43	10	xy	xy	PROPN
ejpam-3248	43	11	∈	∈	PROPN
ejpam-3248	43	12	z(r	z(r	PROPN
ejpam-3248	43	13	)	)	PUNCT
ejpam-3248	43	14	for	for	ADP
ejpam-3248	43	15	all	all	DET
ejpam-3248	43	16	x	x	NOUN
ejpam-3248	43	17	,	,	PUNCT
ejpam-3248	43	18	y	y	PROPN
ejpam-3248	43	19	∈	∈	PROPN
ejpam-3248	44	1	i	i	PRON
ejpam-3248	44	2	,	,	PUNCT
ejpam-3248	44	3	(	(	PUNCT
ejpam-3248	44	4	vii)f	vii)f	PROPN
ejpam-3248	44	5	(	(	PUNCT
ejpam-3248	44	6	x	x	X
ejpam-3248	44	7	)	)	PUNCT
ejpam-3248	44	8	◦	◦	NOUN
ejpam-3248	44	9	y	y	PROPN
ejpam-3248	44	10	±	±	NUM
ejpam-3248	44	11	xy	xy	PROPN
ejpam-3248	44	12	∈	∈	PROPN
ejpam-3248	44	13	z(r	z(r	PROPN
ejpam-3248	44	14	)	)	PUNCT
ejpam-3248	44	15	for	for	ADP
ejpam-3248	44	16	all	all	DET
ejpam-3248	44	17	x	x	NOUN
ejpam-3248	44	18	,	,	PUNCT
ejpam-3248	44	19	y	y	PROPN
ejpam-3248	44	20	∈	∈	PROPN
ejpam-3248	45	1	i	i	PRON
ejpam-3248	45	2	,	,	PUNCT
ejpam-3248	45	3	(	(	PUNCT
ejpam-3248	45	4	viii)[f	viii)[f	X
ejpam-3248	45	5	(	(	PUNCT
ejpam-3248	45	6	x	x	NOUN
ejpam-3248	45	7	)	)	PUNCT
ejpam-3248	45	8	,	,	PUNCT
ejpam-3248	45	9	y]±	y]±	PROPN
ejpam-3248	45	10	yx	yx	PROPN
ejpam-3248	45	11	∈	∈	PROPN
ejpam-3248	45	12	z(r	z(r	PROPN
ejpam-3248	45	13	)	)	PUNCT
ejpam-3248	45	14	for	for	ADP
ejpam-3248	45	15	all	all	DET
ejpam-3248	45	16	x	x	NOUN
ejpam-3248	45	17	,	,	PUNCT
ejpam-3248	45	18	y	y	PROPN
ejpam-3248	45	19	∈	∈	PROPN
ejpam-3248	45	20	i	i	PRON
ejpam-3248	45	21	,	,	PUNCT
ejpam-3248	45	22	(	(	PUNCT
ejpam-3248	45	23	ix)f	ix)f	NOUN
ejpam-3248	45	24	(	(	PUNCT
ejpam-3248	45	25	x	x	X
ejpam-3248	45	26	)	)	PUNCT
ejpam-3248	45	27	◦	◦	NOUN
ejpam-3248	45	28	y	y	PROPN
ejpam-3248	45	29	±	±	NUM
ejpam-3248	45	30	yx	yx	PROPN
ejpam-3248	45	31	∈	∈	PROPN
ejpam-3248	45	32	z(r	z(r	PROPN
ejpam-3248	45	33	)	)	PUNCT
ejpam-3248	45	34	for	for	ADP
ejpam-3248	45	35	all	all	DET
ejpam-3248	45	36	x	x	NOUN
ejpam-3248	45	37	,	,	PUNCT
ejpam-3248	45	38	y	y	PROPN
ejpam-3248	45	39	∈	∈	PROPN
ejpam-3248	45	40	i.	i.	NOUN
ejpam-3248	45	41	where	where	SCONJ
ejpam-3248	45	42	i	i	PRON
ejpam-3248	45	43	is	be	AUX
ejpam-3248	45	44	a	a	DET
ejpam-3248	45	45	non	non	ADJ
ejpam-3248	45	46	zero	zero	NUM
ejpam-3248	45	47	ideal	ideal	NOUN
ejpam-3248	45	48	in	in	ADP
ejpam-3248	45	49	a	a	DET
ejpam-3248	45	50	semiprime	semiprime	NOUN
ejpam-3248	45	51	ring	ring	NOUN
ejpam-3248	45	52	r.	r.	PROPN
ejpam-3248	45	53	2	2	NUM
ejpam-3248	45	54	.	.	PUNCT
ejpam-3248	45	55	preliminaries	preliminary	NOUN
ejpam-3248	45	56	let	let	VERB
ejpam-3248	45	57	r	r	PRON
ejpam-3248	45	58	be	be	AUX
ejpam-3248	45	59	a	a	DET
ejpam-3248	45	60	ring	ring	NOUN
ejpam-3248	45	61	,	,	PUNCT
ejpam-3248	45	62	we	we	PRON
ejpam-3248	45	63	need	need	VERB
ejpam-3248	45	64	the	the	DET
ejpam-3248	45	65	following	following	ADJ
ejpam-3248	45	66	basic	basic	ADJ
ejpam-3248	45	67	identities	identity	NOUN
ejpam-3248	45	68	which	which	PRON
ejpam-3248	45	69	will	will	AUX
ejpam-3248	45	70	be	be	AUX
ejpam-3248	45	71	used	use	VERB
ejpam-3248	45	72	in	in	ADP
ejpam-3248	45	73	the	the	DET
ejpam-3248	45	74	proof	proof	NOUN
ejpam-3248	45	75	of	of	ADP
ejpam-3248	45	76	our	our	PRON
ejpam-3248	45	77	results	result	NOUN
ejpam-3248	45	78	.	.	PUNCT
ejpam-3248	46	1	for	for	ADP
ejpam-3248	46	2	any	any	DET
ejpam-3248	46	3	x	x	NOUN
ejpam-3248	46	4	,	,	PUNCT
ejpam-3248	46	5	y	y	PROPN
ejpam-3248	46	6	,	,	PUNCT
ejpam-3248	46	7	z	z	NOUN
ejpam-3248	46	8	∈	∈	PROPN
ejpam-3248	46	9	r	r	NOUN
ejpam-3248	46	10	,	,	PUNCT
ejpam-3248	46	11	[	[	X
ejpam-3248	46	12	xy	xy	X
ejpam-3248	46	13	,	,	PUNCT
ejpam-3248	46	14	z	z	NOUN
ejpam-3248	46	15	]	]	X
ejpam-3248	46	16	=	=	SYM
ejpam-3248	46	17	x[y	x[y	PROPN
ejpam-3248	46	18	,	,	PUNCT
ejpam-3248	46	19	z	z	X
ejpam-3248	46	20	]	]	X
ejpam-3248	46	21	+	+	CCONJ
ejpam-3248	46	22	[	[	X
ejpam-3248	46	23	x	x	X
ejpam-3248	46	24	,	,	PUNCT
ejpam-3248	46	25	z]y	z]y	NOUN
ejpam-3248	46	26	and	and	CCONJ
ejpam-3248	46	27	[	[	X
ejpam-3248	46	28	x	x	X
ejpam-3248	46	29	,	,	PUNCT
ejpam-3248	46	30	yz	yz	PROPN
ejpam-3248	46	31	]	]	X
ejpam-3248	46	32	=	=	SYM
ejpam-3248	46	33	y[x	y[x	NOUN
ejpam-3248	46	34	,	,	PUNCT
ejpam-3248	46	35	z	z	X
ejpam-3248	46	36	]	]	X
ejpam-3248	46	37	+	+	CCONJ
ejpam-3248	46	38	[	[	X
ejpam-3248	46	39	x	x	X
ejpam-3248	46	40	,	,	PUNCT
ejpam-3248	46	41	y]z	y]z	NOUN
ejpam-3248	46	42	.	.	PUNCT
ejpam-3248	47	1	x	x	PUNCT
ejpam-3248	47	2	◦	◦	NOUN
ejpam-3248	47	3	(	(	PUNCT
ejpam-3248	47	4	yz	yz	NOUN
ejpam-3248	47	5	)	)	PUNCT
ejpam-3248	47	6	=	=	PRON
ejpam-3248	48	1	(	(	PUNCT
ejpam-3248	48	2	x	x	SYM
ejpam-3248	48	3	◦	◦	VERB
ejpam-3248	48	4	y)z	y)z	X
ejpam-3248	48	5	−	−	NOUN
ejpam-3248	48	6	y[x	y[x	NOUN
ejpam-3248	48	7	,	,	PUNCT
ejpam-3248	48	8	z	z	NOUN
ejpam-3248	48	9	]	]	X
ejpam-3248	48	10	=	=	SYM
ejpam-3248	48	11	y(x	y(x	PROPN
ejpam-3248	48	12	◦	◦	NOUN
ejpam-3248	48	13	z	z	NOUN
ejpam-3248	48	14	)	)	PUNCT
ejpam-3248	49	1	+	+	CCONJ
ejpam-3248	50	1	[	[	X
ejpam-3248	50	2	x	x	X
ejpam-3248	50	3	,	,	PUNCT
ejpam-3248	50	4	y]z	y]z	NOUN
ejpam-3248	50	5	.	.	PUNCT
ejpam-3248	51	1	(	(	PUNCT
ejpam-3248	51	2	xy	xy	NOUN
ejpam-3248	51	3	)	)	PUNCT
ejpam-3248	51	4	◦	◦	NOUN
ejpam-3248	51	5	z	z	NOUN
ejpam-3248	52	1	=	=	SYM
ejpam-3248	53	1	x(y	x(y	PUNCT
ejpam-3248	54	1	◦	◦	NOUN
ejpam-3248	54	2	z)−	z)−	PUNCT
ejpam-3248	55	1	[	[	X
ejpam-3248	55	2	x	x	X
ejpam-3248	55	3	,	,	PUNCT
ejpam-3248	55	4	z]y	z]y	NUM
ejpam-3248	55	5	=	=	SYM
ejpam-3248	55	6	(	(	PUNCT
ejpam-3248	55	7	x	x	PART
ejpam-3248	55	8	◦	◦	NOUN
ejpam-3248	55	9	z)y	z)y	NOUN
ejpam-3248	55	10	+	+	CCONJ
ejpam-3248	55	11	x[y	x[y	PROPN
ejpam-3248	55	12	,	,	PUNCT
ejpam-3248	55	13	z	z	NOUN
ejpam-3248	55	14	]	]	X
ejpam-3248	55	15	.	.	PUNCT
ejpam-3248	56	1	for	for	ADP
ejpam-3248	56	2	any	any	DET
ejpam-3248	56	3	subset	subset	NOUN
ejpam-3248	56	4	s	s	NOUN
ejpam-3248	56	5	of	of	ADP
ejpam-3248	56	6	r	r	NOUN
ejpam-3248	56	7	,	,	PUNCT
ejpam-3248	56	8	we	we	PRON
ejpam-3248	56	9	will	will	AUX
ejpam-3248	56	10	denote	denote	VERB
ejpam-3248	56	11	rr(s	rr(s	NOUN
ejpam-3248	56	12	)	)	PUNCT
ejpam-3248	56	13	the	the	DET
ejpam-3248	56	14	right	right	ADJ
ejpam-3248	56	15	annihilator	annihilator	NOUN
ejpam-3248	56	16	of	of	ADP
ejpam-3248	56	17	s	s	PROPN
ejpam-3248	56	18	in	in	ADP
ejpam-3248	56	19	r	r	NOUN
ejpam-3248	56	20	,	,	PUNCT
ejpam-3248	56	21	that	that	PRON
ejpam-3248	56	22	is	is	ADV
ejpam-3248	56	23	rr(s	rr(s	NOUN
ejpam-3248	56	24	)	)	PUNCT
ejpam-3248	57	1	=	=	PRON
ejpam-3248	57	2	{	{	PUNCT
ejpam-3248	57	3	x	x	PUNCT
ejpam-3248	57	4	∈	∈	PROPN
ejpam-3248	57	5	r|sx	r|sx	X
ejpam-3248	57	6	=	=	PUNCT
ejpam-3248	57	7	0	0	PUNCT
ejpam-3248	57	8	}	}	PUNCT
ejpam-3248	57	9	and	and	CCONJ
ejpam-3248	57	10	by	by	ADP
ejpam-3248	57	11	lr(s	lr(s	NOUN
ejpam-3248	57	12	)	)	PUNCT
ejpam-3248	57	13	the	the	DET
ejpam-3248	57	14	left	left	ADJ
ejpam-3248	57	15	annihilator	annihilator	NOUN
ejpam-3248	57	16	of	of	ADP
ejpam-3248	57	17	s	s	PRON
ejpam-3248	57	18	in	in	ADP
ejpam-3248	57	19	r	r	NOUN
ejpam-3248	57	20	,	,	PUNCT
ejpam-3248	57	21	that	that	ADV
ejpam-3248	57	22	is	is	ADV
ejpam-3248	57	23	,	,	PUNCT
ejpam-3248	57	24	lr(s	lr(s	ADJ
ejpam-3248	57	25	)	)	PUNCT
ejpam-3248	57	26	=	=	SYM
ejpam-3248	57	27	{	{	PUNCT
ejpam-3248	57	28	x	x	PUNCT
ejpam-3248	57	29	∈	∈	NOUN
ejpam-3248	57	30	r|xs	r|xs	NOUN
ejpam-3248	57	31	=	=	PUNCT
ejpam-3248	57	32	0	0	NUM
ejpam-3248	57	33	}	}	PUNCT
ejpam-3248	57	34	.	.	PUNCT
ejpam-3248	58	1	if	if	SCONJ
ejpam-3248	58	2	rr(s	rr(s	NOUN
ejpam-3248	58	3	)	)	PUNCT
ejpam-3248	58	4	=	=	SYM
ejpam-3248	59	1	lr(s	lr(s	PROPN
ejpam-3248	59	2	)	)	PUNCT
ejpam-3248	59	3	,	,	PUNCT
ejpam-3248	59	4	then	then	ADV
ejpam-3248	59	5	rr(s	rr(s	PUNCT
ejpam-3248	59	6	)	)	PUNCT
ejpam-3248	59	7	is	be	AUX
ejpam-3248	59	8	called	call	VERB
ejpam-3248	59	9	an	an	DET
ejpam-3248	59	10	annihilator	annihilator	NOUN
ejpam-3248	59	11	of	of	ADP
ejpam-3248	59	12	r	r	NOUN
ejpam-3248	59	13	and	and	CCONJ
ejpam-3248	59	14	is	be	AUX
ejpam-3248	59	15	written	write	VERB
ejpam-3248	59	16	as	as	ADP
ejpam-3248	59	17	annr(s	annr(s	NOUN
ejpam-3248	59	18	)	)	PUNCT
ejpam-3248	59	19	.	.	PUNCT
ejpam-3248	60	1	for	for	ADP
ejpam-3248	60	2	given	give	VERB
ejpam-3248	60	3	x	x	PRON
ejpam-3248	60	4	,	,	PUNCT
ejpam-3248	60	5	y	y	PROPN
ejpam-3248	60	6	∈	∈	PROPN
ejpam-3248	60	7	r	r	NOUN
ejpam-3248	60	8	,	,	PUNCT
ejpam-3248	60	9	set	set	VERB
ejpam-3248	60	10	[	[	X
ejpam-3248	60	11	x	x	NOUN
ejpam-3248	60	12	,	,	PUNCT
ejpam-3248	60	13	y]0	y]0	X
ejpam-3248	60	14	=	=	SYM
ejpam-3248	60	15	x	x	NOUN
ejpam-3248	60	16	,	,	PUNCT
ejpam-3248	60	17	[	[	X
ejpam-3248	60	18	x	x	X
ejpam-3248	60	19	,	,	PUNCT
ejpam-3248	60	20	y]1	y]1	X
ejpam-3248	60	21	=	=	PUNCT
ejpam-3248	61	1	[	[	X
ejpam-3248	61	2	x	x	X
ejpam-3248	61	3	,	,	PUNCT
ejpam-3248	61	4	y	y	PROPN
ejpam-3248	61	5	]	]	X
ejpam-3248	61	6	=	=	PUNCT
ejpam-3248	61	7	xy	xy	PROPN
ejpam-3248	61	8	−	−	PROPN
ejpam-3248	62	1	yx	yx	PROPN
ejpam-3248	62	2	and	and	CCONJ
ejpam-3248	62	3	[	[	X
ejpam-3248	62	4	x	x	X
ejpam-3248	62	5	,	,	PUNCT
ejpam-3248	62	6	y]k	y]k	PROPN
ejpam-3248	62	7	=	=	PUNCT
ejpam-3248	63	1	[	[	X
ejpam-3248	63	2	[	[	X
ejpam-3248	63	3	x	x	X
ejpam-3248	63	4	,	,	PUNCT
ejpam-3248	63	5	y]k−1	y]k−1	PROPN
ejpam-3248	63	6	,	,	PUNCT
ejpam-3248	63	7	y	y	PROPN
ejpam-3248	63	8	]	]	PUNCT
ejpam-3248	63	9	for	for	ADP
ejpam-3248	63	10	k	k	PROPN
ejpam-3248	63	11	>	>	X
ejpam-3248	63	12	1	1	X
ejpam-3248	63	13	.	.	PUNCT
ejpam-3248	63	14	a.	a.	PROPN
ejpam-3248	63	15	ali	ali	PROPN
ejpam-3248	63	16	,	,	PUNCT
ejpam-3248	63	17	a.	a.	PROPN
ejpam-3248	63	18	bano	bano	PROPN
ejpam-3248	63	19	/	/	SYM
ejpam-3248	63	20	eur	eur	PROPN
ejpam-3248	63	21	.	.	PUNCT
ejpam-3248	64	1	j.	j.	PROPN
ejpam-3248	64	2	pure	pure	PROPN
ejpam-3248	64	3	appl	appl	PROPN
ejpam-3248	64	4	.	.	PROPN
ejpam-3248	64	5	math	math	PROPN
ejpam-3248	64	6	,	,	PUNCT
ejpam-3248	64	7	11	11	NUM
ejpam-3248	64	8	(	(	PUNCT
ejpam-3248	64	9	3	3	NUM
ejpam-3248	64	10	)	)	PUNCT
ejpam-3248	64	11	(	(	PUNCT
ejpam-3248	64	12	2018	2018	NUM
ejpam-3248	64	13	)	)	PUNCT
ejpam-3248	64	14	,	,	PUNCT
ejpam-3248	64	15	717	717	NUM
ejpam-3248	64	16	-	-	SYM
ejpam-3248	64	17	729	729	NUM
ejpam-3248	64	18	719	719	NUM
ejpam-3248	64	19	moreover	moreover	ADV
ejpam-3248	64	20	,	,	PUNCT
ejpam-3248	64	21	we	we	PRON
ejpam-3248	64	22	shall	shall	AUX
ejpam-3248	64	23	require	require	VERB
ejpam-3248	64	24	the	the	DET
ejpam-3248	64	25	following	follow	VERB
ejpam-3248	64	26	known	know	VERB
ejpam-3248	64	27	results	result	NOUN
ejpam-3248	64	28	.	.	PUNCT
ejpam-3248	65	1	lemma	lemma	PROPN
ejpam-3248	65	2	2.1	2.1	NUM
ejpam-3248	65	3	.	.	PUNCT
ejpam-3248	66	1	[	[	X
ejpam-3248	66	2	9	9	NUM
ejpam-3248	66	3	,	,	PUNCT
ejpam-3248	66	4	corollary	corollary	ADJ
ejpam-3248	66	5	1	1	NUM
ejpam-3248	66	6	]	]	PUNCT
ejpam-3248	66	7	if	if	SCONJ
ejpam-3248	66	8	r	r	NOUN
ejpam-3248	66	9	is	be	AUX
ejpam-3248	66	10	a	a	DET
ejpam-3248	66	11	semiprime	semiprime	NOUN
ejpam-3248	66	12	ring	ring	NOUN
ejpam-3248	66	13	and	and	CCONJ
ejpam-3248	66	14	i	i	PRON
ejpam-3248	66	15	is	be	AUX
ejpam-3248	66	16	an	an	DET
ejpam-3248	66	17	ideal	ideal	NOUN
ejpam-3248	66	18	of	of	ADP
ejpam-3248	66	19	r	r	NOUN
ejpam-3248	66	20	,	,	PUNCT
ejpam-3248	66	21	then	then	ADV
ejpam-3248	66	22	rr(i	rr(i	NOUN
ejpam-3248	66	23	)	)	PUNCT
ejpam-3248	66	24	=	=	SYM
ejpam-3248	66	25	lr(i	lr(i	NOUN
ejpam-3248	66	26	)	)	PUNCT
ejpam-3248	66	27	.	.	PUNCT
ejpam-3248	67	1	lemma	lemma	PROPN
ejpam-3248	67	2	2.2	2.2	NUM
ejpam-3248	67	3	.	.	PUNCT
ejpam-3248	68	1	[	[	X
ejpam-3248	68	2	9	9	NUM
ejpam-3248	68	3	,	,	PUNCT
ejpam-3248	68	4	corollary	corollary	NOUN
ejpam-3248	68	5	2	2	NUM
ejpam-3248	68	6	]	]	PUNCT
ejpam-3248	68	7	if	if	SCONJ
ejpam-3248	68	8	r	r	NOUN
ejpam-3248	68	9	is	be	AUX
ejpam-3248	68	10	a	a	DET
ejpam-3248	68	11	semiprime	semiprime	NOUN
ejpam-3248	68	12	ring	ring	NOUN
ejpam-3248	68	13	and	and	CCONJ
ejpam-3248	68	14	i	i	PRON
ejpam-3248	68	15	is	be	AUX
ejpam-3248	68	16	an	an	DET
ejpam-3248	68	17	ideal	ideal	NOUN
ejpam-3248	68	18	of	of	ADP
ejpam-3248	68	19	r	r	NOUN
ejpam-3248	68	20	,	,	PUNCT
ejpam-3248	68	21	then	then	ADV
ejpam-3248	68	22	i	i	PRON
ejpam-3248	68	23	∩	∩	ADJ
ejpam-3248	68	24	annr(i	annr(i	X
ejpam-3248	68	25	)	)	PUNCT
ejpam-3248	68	26	=	=	SYM
ejpam-3248	68	27	0	0	X
ejpam-3248	68	28	.	.	PUNCT
ejpam-3248	69	1	lemma	lemma	PROPN
ejpam-3248	69	2	2.3	2.3	NUM
ejpam-3248	69	3	.	.	PUNCT
ejpam-3248	70	1	[	[	X
ejpam-3248	70	2	6	6	NUM
ejpam-3248	70	3	,	,	PUNCT
ejpam-3248	70	4	fact-4	fact-4	PRON
ejpam-3248	70	5	]	]	PUNCT
ejpam-3248	70	6	let	let	VERB
ejpam-3248	70	7	r	r	PRON
ejpam-3248	70	8	be	be	AUX
ejpam-3248	70	9	a	a	DET
ejpam-3248	70	10	semiprime	semiprime	NOUN
ejpam-3248	70	11	ring	ring	NOUN
ejpam-3248	70	12	,	,	PUNCT
ejpam-3248	70	13	d	d	X
ejpam-3248	70	14	a	a	DET
ejpam-3248	70	15	nonzero	nonzero	ADJ
ejpam-3248	70	16	derivation	derivation	NOUN
ejpam-3248	70	17	of	of	ADP
ejpam-3248	70	18	r	r	NOUN
ejpam-3248	70	19	such	such	ADJ
ejpam-3248	70	20	that	that	DET
ejpam-3248	70	21	x[[d(x	x[[d(x	NOUN
ejpam-3248	70	22	)	)	PUNCT
ejpam-3248	70	23	,	,	PUNCT
ejpam-3248	70	24	x	x	X
ejpam-3248	70	25	]	]	X
ejpam-3248	70	26	,	,	PUNCT
ejpam-3248	70	27	x	x	X
ejpam-3248	70	28	]	]	X
ejpam-3248	70	29	=	=	SYM
ejpam-3248	70	30	0	0	NUM
ejpam-3248	70	31	for	for	ADP
ejpam-3248	70	32	all	all	DET
ejpam-3248	70	33	x	x	SYM
ejpam-3248	70	34	∈	∈	PROPN
ejpam-3248	70	35	r	r	NOUN
ejpam-3248	70	36	,	,	PUNCT
ejpam-3248	70	37	then	then	ADV
ejpam-3248	70	38	d	d	PROPN
ejpam-3248	70	39	maps	map	VERB
ejpam-3248	70	40	r	r	NOUN
ejpam-3248	70	41	into	into	ADP
ejpam-3248	70	42	its	its	PRON
ejpam-3248	70	43	centre	centre	NOUN
ejpam-3248	70	44	.	.	PUNCT
ejpam-3248	71	1	3	3	X
ejpam-3248	71	2	.	.	X
ejpam-3248	71	3	main	main	ADJ
ejpam-3248	71	4	results	result	NOUN
ejpam-3248	71	5	theorem	theorem	VERB
ejpam-3248	71	6	3.1	3.1	NUM
ejpam-3248	71	7	.	.	PUNCT
ejpam-3248	72	1	let	let	VERB
ejpam-3248	72	2	r	r	PRON
ejpam-3248	72	3	be	be	AUX
ejpam-3248	72	4	a	a	DET
ejpam-3248	72	5	semiprime	semiprime	NOUN
ejpam-3248	72	6	ring	ring	NOUN
ejpam-3248	72	7	and	and	CCONJ
ejpam-3248	72	8	f	f	PROPN
ejpam-3248	72	9	be	be	AUX
ejpam-3248	72	10	a	a	DET
ejpam-3248	72	11	non	non	ADJ
ejpam-3248	72	12	-	-	ADJ
ejpam-3248	72	13	zero	zero	ADJ
ejpam-3248	72	14	multiplicative	multiplicative	ADJ
ejpam-3248	72	15	(	(	PUNCT
ejpam-3248	72	16	generalized	generalized	ADJ
ejpam-3248	72	17	)	)	PUNCT
ejpam-3248	72	18	reverse	reverse	ADJ
ejpam-3248	72	19	derivation	derivation	NOUN
ejpam-3248	72	20	associated	associate	VERB
ejpam-3248	72	21	with	with	ADP
ejpam-3248	72	22	a	a	DET
ejpam-3248	72	23	map	map	NOUN
ejpam-3248	73	1	d	d	NOUN
ejpam-3248	73	2	,	,	PUNCT
ejpam-3248	73	3	i	i	PRON
ejpam-3248	73	4	be	be	VERB
ejpam-3248	73	5	a	a	DET
ejpam-3248	73	6	non	non	ADJ
ejpam-3248	73	7	-	-	ADJ
ejpam-3248	73	8	zero	zero	NUM
ejpam-3248	73	9	ideal	ideal	NOUN
ejpam-3248	73	10	of	of	ADP
ejpam-3248	73	11	r.	r.	PROPN
ejpam-3248	73	12	if	if	SCONJ
ejpam-3248	73	13	f	f	PROPN
ejpam-3248	73	14	(	(	PUNCT
ejpam-3248	73	15	x)f	x)f	X
ejpam-3248	73	16	(	(	PUNCT
ejpam-3248	73	17	y)±xy	y)±xy	PROPN
ejpam-3248	73	18	∈	∈	PROPN
ejpam-3248	73	19	z(r	z(r	PROPN
ejpam-3248	73	20	)	)	PUNCT
ejpam-3248	73	21	for	for	ADP
ejpam-3248	73	22	all	all	DET
ejpam-3248	73	23	x	x	NOUN
ejpam-3248	73	24	,	,	PUNCT
ejpam-3248	73	25	y	y	PROPN
ejpam-3248	73	26	∈	∈	PROPN
ejpam-3248	74	1	i	i	PRON
ejpam-3248	74	2	,	,	PUNCT
ejpam-3248	74	3	then	then	ADV
ejpam-3248	74	4	[	[	X
ejpam-3248	74	5	d(x	d(x	NOUN
ejpam-3248	74	6	)	)	PUNCT
ejpam-3248	74	7	,	,	PUNCT
ejpam-3248	74	8	x	x	X
ejpam-3248	74	9	]	]	X
ejpam-3248	74	10	=	=	SYM
ejpam-3248	74	11	0	0	NUM
ejpam-3248	74	12	for	for	ADP
ejpam-3248	74	13	all	all	DET
ejpam-3248	74	14	x	x	SYM
ejpam-3248	74	15	∈	∈	NOUN
ejpam-3248	74	16	i.	i.	NOUN
ejpam-3248	74	17	proof	proof	NOUN
ejpam-3248	74	18	by	by	ADP
ejpam-3248	74	19	the	the	DET
ejpam-3248	74	20	hypothesis	hypothesis	NOUN
ejpam-3248	74	21	,	,	PUNCT
ejpam-3248	74	22	we	we	PRON
ejpam-3248	74	23	have	have	VERB
ejpam-3248	74	24	f	f	PROPN
ejpam-3248	74	25	(	(	PUNCT
ejpam-3248	74	26	x)f	x)f	X
ejpam-3248	74	27	(	(	PUNCT
ejpam-3248	74	28	y	y	NOUN
ejpam-3248	74	29	)	)	PUNCT
ejpam-3248	75	1	+	+	CCONJ
ejpam-3248	75	2	xy	xy	PROPN
ejpam-3248	75	3	∈	∈	PROPN
ejpam-3248	75	4	z(r	z(r	PROPN
ejpam-3248	75	5	)	)	PUNCT
ejpam-3248	75	6	for	for	ADP
ejpam-3248	75	7	all	all	DET
ejpam-3248	75	8	x	x	NOUN
ejpam-3248	75	9	,	,	PUNCT
ejpam-3248	75	10	y	y	PROPN
ejpam-3248	75	11	∈	∈	PROPN
ejpam-3248	75	12	i.	i.	NOUN
ejpam-3248	75	13	(	(	PUNCT
ejpam-3248	75	14	3.1	3.1	NUM
ejpam-3248	75	15	)	)	PUNCT
ejpam-3248	75	16	substituting	substitute	VERB
ejpam-3248	75	17	zy	zy	NOUN
ejpam-3248	75	18	for	for	ADP
ejpam-3248	75	19	y	y	PROPN
ejpam-3248	75	20	in	in	ADP
ejpam-3248	75	21	(	(	PUNCT
ejpam-3248	75	22	3.1	3.1	NUM
ejpam-3248	75	23	)	)	PUNCT
ejpam-3248	75	24	and	and	CCONJ
ejpam-3248	75	25	using	use	VERB
ejpam-3248	75	26	the	the	DET
ejpam-3248	75	27	definition	definition	NOUN
ejpam-3248	75	28	of	of	ADP
ejpam-3248	75	29	multiplicative	multiplicative	ADJ
ejpam-3248	75	30	(	(	PUNCT
ejpam-3248	75	31	generalized	generalized	ADJ
ejpam-3248	75	32	)	)	PUNCT
ejpam-3248	75	33	reverse	reverse	ADJ
ejpam-3248	75	34	derivation	derivation	NOUN
ejpam-3248	75	35	,	,	PUNCT
ejpam-3248	75	36	we	we	PRON
ejpam-3248	75	37	find	find	VERB
ejpam-3248	75	38	f	f	PROPN
ejpam-3248	75	39	(	(	PUNCT
ejpam-3248	75	40	x)f	x)f	X
ejpam-3248	75	41	(	(	PUNCT
ejpam-3248	75	42	y)z	y)z	X
ejpam-3248	76	1	+	+	NUM
ejpam-3248	76	2	f	f	X
ejpam-3248	76	3	(	(	PUNCT
ejpam-3248	76	4	x)yd(z	x)yd(z	PROPN
ejpam-3248	76	5	)	)	PUNCT
ejpam-3248	76	6	+	+	CCONJ
ejpam-3248	76	7	xzy	xzy	NOUN
ejpam-3248	76	8	−	−	PROPN
ejpam-3248	76	9	xyz	xyz	PROPN
ejpam-3248	76	10	+	+	NUM
ejpam-3248	76	11	xyz	xyz	PROPN
ejpam-3248	76	12	∈	∈	PROPN
ejpam-3248	76	13	z(r	z(r	PROPN
ejpam-3248	76	14	)	)	PUNCT
ejpam-3248	76	15	for	for	ADP
ejpam-3248	76	16	all	all	DET
ejpam-3248	76	17	x	x	NOUN
ejpam-3248	76	18	,	,	PUNCT
ejpam-3248	76	19	y	y	PROPN
ejpam-3248	76	20	,	,	PUNCT
ejpam-3248	76	21	z	z	PROPN
ejpam-3248	76	22	∈	∈	PROPN
ejpam-3248	76	23	i.	i.	NOUN
ejpam-3248	76	24	this	this	PRON
ejpam-3248	76	25	implies	imply	VERB
ejpam-3248	76	26	that	that	SCONJ
ejpam-3248	76	27	(	(	PUNCT
ejpam-3248	76	28	f	f	X
ejpam-3248	76	29	(	(	PUNCT
ejpam-3248	76	30	x)f	x)f	X
ejpam-3248	76	31	(	(	PUNCT
ejpam-3248	76	32	y	y	NOUN
ejpam-3248	76	33	)	)	PUNCT
ejpam-3248	77	1	+	+	NUM
ejpam-3248	77	2	xy)z	xy)z	PROPN
ejpam-3248	78	1	+	+	NUM
ejpam-3248	78	2	f	f	X
ejpam-3248	78	3	(	(	PUNCT
ejpam-3248	78	4	x)yd(z	x)yd(z	PROPN
ejpam-3248	78	5	)	)	PUNCT
ejpam-3248	78	6	+	+	SYM
ejpam-3248	78	7	x[z	x[z	PROPN
ejpam-3248	78	8	,	,	PUNCT
ejpam-3248	78	9	y	y	X
ejpam-3248	78	10	]	]	X
ejpam-3248	78	11	∈	∈	PROPN
ejpam-3248	78	12	z(r	z(r	PROPN
ejpam-3248	78	13	)	)	PUNCT
ejpam-3248	78	14	.	.	PUNCT
ejpam-3248	79	1	(	(	PUNCT
ejpam-3248	79	2	3.2	3.2	NUM
ejpam-3248	79	3	)	)	PUNCT
ejpam-3248	79	4	commuting	commuting	NOUN
ejpam-3248	79	5	(	(	PUNCT
ejpam-3248	79	6	3.2	3.2	NUM
ejpam-3248	79	7	)	)	PUNCT
ejpam-3248	79	8	with	with	ADP
ejpam-3248	79	9	z	z	NOUN
ejpam-3248	79	10	and	and	CCONJ
ejpam-3248	79	11	using	use	VERB
ejpam-3248	79	12	(	(	PUNCT
ejpam-3248	79	13	3.1	3.1	NUM
ejpam-3248	79	14	)	)	PUNCT
ejpam-3248	79	15	,	,	PUNCT
ejpam-3248	79	16	we	we	PRON
ejpam-3248	79	17	get	get	VERB
ejpam-3248	79	18	[	[	X
ejpam-3248	79	19	f	f	X
ejpam-3248	79	20	(	(	PUNCT
ejpam-3248	79	21	x)yd(z	x)yd(z	PROPN
ejpam-3248	79	22	)	)	PUNCT
ejpam-3248	79	23	,	,	PUNCT
ejpam-3248	80	1	z	z	X
ejpam-3248	80	2	]	]	X
ejpam-3248	80	3	+	+	CCONJ
ejpam-3248	81	1	[	[	X
ejpam-3248	81	2	x[z	x[z	X
ejpam-3248	81	3	,	,	PUNCT
ejpam-3248	81	4	y	y	PROPN
ejpam-3248	81	5	]	]	X
ejpam-3248	81	6	,	,	PUNCT
ejpam-3248	81	7	z	z	X
ejpam-3248	81	8	]	]	X
ejpam-3248	81	9	=	=	SYM
ejpam-3248	81	10	0	0	NUM
ejpam-3248	81	11	for	for	ADP
ejpam-3248	81	12	all	all	DET
ejpam-3248	81	13	x	x	NOUN
ejpam-3248	81	14	,	,	PUNCT
ejpam-3248	81	15	y	y	PROPN
ejpam-3248	81	16	,	,	PUNCT
ejpam-3248	81	17	z	z	PROPN
ejpam-3248	81	18	∈	∈	PROPN
ejpam-3248	81	19	i.	i.	NOUN
ejpam-3248	81	20	(	(	PUNCT
ejpam-3248	81	21	3.3	3.3	NUM
ejpam-3248	81	22	)	)	PUNCT
ejpam-3248	81	23	replacing	replace	VERB
ejpam-3248	81	24	x	x	PUNCT
ejpam-3248	81	25	by	by	ADP
ejpam-3248	81	26	zx	zx	PROPN
ejpam-3248	81	27	in	in	ADP
ejpam-3248	81	28	(	(	PUNCT
ejpam-3248	81	29	3.3	3.3	NUM
ejpam-3248	81	30	)	)	PUNCT
ejpam-3248	81	31	,	,	PUNCT
ejpam-3248	81	32	we	we	PRON
ejpam-3248	81	33	obtain	obtain	VERB
ejpam-3248	81	34	[	[	X
ejpam-3248	81	35	(	(	PUNCT
ejpam-3248	81	36	f	f	X
ejpam-3248	81	37	(	(	PUNCT
ejpam-3248	81	38	x)z	x)z	PUNCT
ejpam-3248	81	39	+	+	NUM
ejpam-3248	81	40	xd(z))yd(z	xd(z))yd(z	NOUN
ejpam-3248	81	41	)	)	PUNCT
ejpam-3248	81	42	,	,	PUNCT
ejpam-3248	82	1	z	z	X
ejpam-3248	82	2	]	]	X
ejpam-3248	82	3	+	+	CCONJ
ejpam-3248	83	1	[	[	X
ejpam-3248	83	2	zx[z	zx[z	NOUN
ejpam-3248	83	3	,	,	PUNCT
ejpam-3248	83	4	y	y	PROPN
ejpam-3248	83	5	]	]	X
ejpam-3248	83	6	,	,	PUNCT
ejpam-3248	83	7	z	z	X
ejpam-3248	83	8	]	]	X
ejpam-3248	83	9	=	=	SYM
ejpam-3248	83	10	0	0	X
ejpam-3248	83	11	.	.	PUNCT
ejpam-3248	83	12	therefore	therefore	ADV
ejpam-3248	83	13	we	we	PRON
ejpam-3248	83	14	get	get	VERB
ejpam-3248	83	15	[	[	X
ejpam-3248	83	16	f	f	X
ejpam-3248	83	17	(	(	PUNCT
ejpam-3248	83	18	x)zyd(z	x)zyd(z	PROPN
ejpam-3248	83	19	)	)	PUNCT
ejpam-3248	83	20	,	,	PUNCT
ejpam-3248	84	1	z	z	X
ejpam-3248	84	2	]	]	X
ejpam-3248	84	3	+	+	CCONJ
ejpam-3248	84	4	[	[	X
ejpam-3248	84	5	xd(z)yd(z	xd(z)yd(z	NOUN
ejpam-3248	84	6	)	)	PUNCT
ejpam-3248	84	7	,	,	PUNCT
ejpam-3248	85	1	z	z	X
ejpam-3248	85	2	]	]	X
ejpam-3248	86	1	+	+	CCONJ
ejpam-3248	87	1	[	[	X
ejpam-3248	87	2	zx[z	zx[z	NOUN
ejpam-3248	87	3	,	,	PUNCT
ejpam-3248	87	4	y	y	PROPN
ejpam-3248	87	5	]	]	X
ejpam-3248	87	6	,	,	PUNCT
ejpam-3248	87	7	z	z	X
ejpam-3248	87	8	]	]	X
ejpam-3248	87	9	=	=	SYM
ejpam-3248	87	10	0	0	X
ejpam-3248	87	11	.	.	PUNCT
ejpam-3248	87	12	(	(	PUNCT
ejpam-3248	87	13	3.4	3.4	NUM
ejpam-3248	87	14	)	)	PUNCT
ejpam-3248	87	15	replacing	replace	VERB
ejpam-3248	87	16	y	y	PRON
ejpam-3248	87	17	by	by	ADP
ejpam-3248	87	18	zy	zy	PROPN
ejpam-3248	87	19	in	in	ADP
ejpam-3248	87	20	(	(	PUNCT
ejpam-3248	87	21	3.3	3.3	NUM
ejpam-3248	87	22	)	)	PUNCT
ejpam-3248	87	23	,	,	PUNCT
ejpam-3248	87	24	we	we	PRON
ejpam-3248	87	25	get	get	VERB
ejpam-3248	87	26	[	[	X
ejpam-3248	87	27	f	f	X
ejpam-3248	87	28	(	(	PUNCT
ejpam-3248	87	29	x)zyd(z	x)zyd(z	PROPN
ejpam-3248	87	30	)	)	PUNCT
ejpam-3248	87	31	,	,	PUNCT
ejpam-3248	88	1	z	z	X
ejpam-3248	88	2	]	]	X
ejpam-3248	88	3	+	+	CCONJ
ejpam-3248	89	1	[	[	X
ejpam-3248	89	2	xz[z	xz[z	PROPN
ejpam-3248	89	3	,	,	PUNCT
ejpam-3248	89	4	y	y	PROPN
ejpam-3248	89	5	]	]	X
ejpam-3248	89	6	,	,	PUNCT
ejpam-3248	89	7	z	z	X
ejpam-3248	89	8	]	]	X
ejpam-3248	89	9	=	=	SYM
ejpam-3248	89	10	0	0	NUM
ejpam-3248	89	11	for	for	ADP
ejpam-3248	89	12	all	all	DET
ejpam-3248	89	13	x	x	NOUN
ejpam-3248	89	14	,	,	PUNCT
ejpam-3248	89	15	y	y	PROPN
ejpam-3248	89	16	,	,	PUNCT
ejpam-3248	89	17	z	z	PROPN
ejpam-3248	89	18	∈	∈	PROPN
ejpam-3248	89	19	i.	i.	NOUN
ejpam-3248	89	20	(	(	PUNCT
ejpam-3248	89	21	3.5	3.5	NUM
ejpam-3248	89	22	)	)	PUNCT
ejpam-3248	89	23	a.	a.	PROPN
ejpam-3248	89	24	ali	ali	PROPN
ejpam-3248	89	25	,	,	PUNCT
ejpam-3248	89	26	a.	a.	PROPN
ejpam-3248	89	27	bano	bano	PROPN
ejpam-3248	89	28	/	/	SYM
ejpam-3248	89	29	eur	eur	PROPN
ejpam-3248	89	30	.	.	PUNCT
ejpam-3248	90	1	j.	j.	PROPN
ejpam-3248	90	2	pure	pure	PROPN
ejpam-3248	90	3	appl	appl	PROPN
ejpam-3248	90	4	.	.	PROPN
ejpam-3248	90	5	math	math	PROPN
ejpam-3248	90	6	,	,	PUNCT
ejpam-3248	90	7	11	11	NUM
ejpam-3248	90	8	(	(	PUNCT
ejpam-3248	90	9	3	3	NUM
ejpam-3248	90	10	)	)	PUNCT
ejpam-3248	90	11	(	(	PUNCT
ejpam-3248	90	12	2018	2018	NUM
ejpam-3248	90	13	)	)	PUNCT
ejpam-3248	90	14	,	,	PUNCT
ejpam-3248	90	15	717	717	NUM
ejpam-3248	90	16	-	-	SYM
ejpam-3248	90	17	729	729	NUM
ejpam-3248	90	18	720	720	NUM
ejpam-3248	90	19	subtracting	subtract	VERB
ejpam-3248	90	20	(	(	PUNCT
ejpam-3248	90	21	3.5	3.5	NUM
ejpam-3248	90	22	)	)	PUNCT
ejpam-3248	90	23	from	from	ADP
ejpam-3248	90	24	(	(	PUNCT
ejpam-3248	90	25	3.4	3.4	NUM
ejpam-3248	90	26	)	)	PUNCT
ejpam-3248	90	27	,	,	PUNCT
ejpam-3248	90	28	we	we	PRON
ejpam-3248	90	29	obtain	obtain	VERB
ejpam-3248	90	30	[	[	X
ejpam-3248	90	31	xd(z)yd(z	xd(z)yd(z	NOUN
ejpam-3248	90	32	)	)	PUNCT
ejpam-3248	90	33	,	,	PUNCT
ejpam-3248	91	1	z	z	X
ejpam-3248	91	2	]	]	X
ejpam-3248	92	1	+	+	CCONJ
ejpam-3248	92	2	[	[	X
ejpam-3248	92	3	[	[	X
ejpam-3248	92	4	z	z	X
ejpam-3248	92	5	,	,	PUNCT
ejpam-3248	92	6	x][z	x][z	PROPN
ejpam-3248	92	7	,	,	PUNCT
ejpam-3248	92	8	y	y	PROPN
ejpam-3248	92	9	]	]	X
ejpam-3248	92	10	,	,	PUNCT
ejpam-3248	92	11	z	z	X
ejpam-3248	92	12	]	]	X
ejpam-3248	92	13	=	=	SYM
ejpam-3248	92	14	0	0	X
ejpam-3248	92	15	.	.	PUNCT
ejpam-3248	92	16	(	(	PUNCT
ejpam-3248	92	17	3.6	3.6	NUM
ejpam-3248	92	18	)	)	PUNCT
ejpam-3248	92	19	substituting	substitute	VERB
ejpam-3248	92	20	yz	yz	NOUN
ejpam-3248	92	21	for	for	ADP
ejpam-3248	92	22	y	y	PROPN
ejpam-3248	92	23	in	in	ADP
ejpam-3248	92	24	(	(	PUNCT
ejpam-3248	92	25	3.6	3.6	NUM
ejpam-3248	92	26	)	)	PUNCT
ejpam-3248	92	27	,	,	PUNCT
ejpam-3248	92	28	we	we	PRON
ejpam-3248	92	29	obtain	obtain	VERB
ejpam-3248	92	30	[	[	X
ejpam-3248	92	31	xd(z)yzd(z	xd(z)yzd(z	NOUN
ejpam-3248	92	32	)	)	PUNCT
ejpam-3248	92	33	,	,	PUNCT
ejpam-3248	93	1	z	z	X
ejpam-3248	93	2	]	]	X
ejpam-3248	94	1	+	+	CCONJ
ejpam-3248	94	2	[	[	X
ejpam-3248	94	3	[	[	X
ejpam-3248	94	4	z	z	X
ejpam-3248	94	5	,	,	PUNCT
ejpam-3248	94	6	x][z	x][z	PROPN
ejpam-3248	94	7	,	,	PUNCT
ejpam-3248	94	8	y	y	PROPN
ejpam-3248	94	9	]	]	X
ejpam-3248	94	10	,	,	PUNCT
ejpam-3248	94	11	z]z	z]z	NOUN
ejpam-3248	94	12	=	=	SYM
ejpam-3248	94	13	0	0	X
ejpam-3248	94	14	.	.	PUNCT
ejpam-3248	94	15	(	(	PUNCT
ejpam-3248	94	16	3.7	3.7	NUM
ejpam-3248	94	17	)	)	PUNCT
ejpam-3248	94	18	right	right	ADJ
ejpam-3248	94	19	multiplying	multiplying	NOUN
ejpam-3248	94	20	(	(	PUNCT
ejpam-3248	94	21	3.6	3.6	NUM
ejpam-3248	94	22	)	)	PUNCT
ejpam-3248	94	23	by	by	ADP
ejpam-3248	94	24	z	z	NOUN
ejpam-3248	94	25	and	and	CCONJ
ejpam-3248	94	26	subtracting	subtract	VERB
ejpam-3248	94	27	from	from	ADP
ejpam-3248	94	28	(	(	PUNCT
ejpam-3248	94	29	3.7	3.7	NUM
ejpam-3248	94	30	)	)	PUNCT
ejpam-3248	94	31	,	,	PUNCT
ejpam-3248	94	32	we	we	PRON
ejpam-3248	94	33	get	get	VERB
ejpam-3248	94	34	[	[	X
ejpam-3248	94	35	xd(z)y[d(z	xd(z)y[d(z	NOUN
ejpam-3248	94	36	)	)	PUNCT
ejpam-3248	94	37	,	,	PUNCT
ejpam-3248	95	1	z	z	X
ejpam-3248	95	2	]	]	X
ejpam-3248	95	3	,	,	PUNCT
ejpam-3248	95	4	z	z	X
ejpam-3248	95	5	]	]	X
ejpam-3248	95	6	=	=	SYM
ejpam-3248	95	7	0	0	NUM
ejpam-3248	95	8	for	for	ADP
ejpam-3248	95	9	all	all	DET
ejpam-3248	95	10	x	x	NOUN
ejpam-3248	95	11	,	,	PUNCT
ejpam-3248	95	12	y	y	PROPN
ejpam-3248	95	13	,	,	PUNCT
ejpam-3248	95	14	z	z	PROPN
ejpam-3248	95	15	∈	∈	PROPN
ejpam-3248	95	16	i.	i.	NOUN
ejpam-3248	95	17	(	(	PUNCT
ejpam-3248	95	18	3.8	3.8	NUM
ejpam-3248	95	19	)	)	PUNCT
ejpam-3248	95	20	replacing	replace	VERB
ejpam-3248	95	21	x	x	PUNCT
ejpam-3248	95	22	by	by	ADP
ejpam-3248	95	23	d(z)x	d(z)x	PROPN
ejpam-3248	95	24	in	in	ADP
ejpam-3248	95	25	(	(	PUNCT
ejpam-3248	95	26	3.8	3.8	NUM
ejpam-3248	95	27	)	)	PUNCT
ejpam-3248	95	28	and	and	CCONJ
ejpam-3248	95	29	using	use	VERB
ejpam-3248	95	30	(	(	PUNCT
ejpam-3248	95	31	3.8	3.8	NUM
ejpam-3248	95	32	)	)	PUNCT
ejpam-3248	95	33	,	,	PUNCT
ejpam-3248	95	34	we	we	PRON
ejpam-3248	95	35	find	find	VERB
ejpam-3248	95	36	[	[	X
ejpam-3248	95	37	d(z	d(z	NOUN
ejpam-3248	95	38	)	)	PUNCT
ejpam-3248	95	39	,	,	PUNCT
ejpam-3248	95	40	z]xd(z)y[d(z	z]xd(z)y[d(z	NUM
ejpam-3248	95	41	)	)	PUNCT
ejpam-3248	95	42	,	,	PUNCT
ejpam-3248	95	43	z	z	X
ejpam-3248	95	44	]	]	X
ejpam-3248	95	45	=	=	SYM
ejpam-3248	95	46	0	0	NUM
ejpam-3248	95	47	for	for	ADP
ejpam-3248	95	48	all	all	DET
ejpam-3248	95	49	x	x	NOUN
ejpam-3248	95	50	,	,	PUNCT
ejpam-3248	95	51	y	y	PROPN
ejpam-3248	95	52	,	,	PUNCT
ejpam-3248	95	53	z	z	PROPN
ejpam-3248	95	54	∈	∈	PROPN
ejpam-3248	95	55	i.	i.	NOUN
ejpam-3248	95	56	(	(	PUNCT
ejpam-3248	95	57	3.9	3.9	NUM
ejpam-3248	95	58	)	)	PUNCT
ejpam-3248	95	59	substituting	substitute	VERB
ejpam-3248	95	60	zy	zy	NOUN
ejpam-3248	95	61	for	for	ADP
ejpam-3248	95	62	y	y	PROPN
ejpam-3248	95	63	in	in	ADP
ejpam-3248	95	64	(	(	PUNCT
ejpam-3248	95	65	3.9	3.9	NUM
ejpam-3248	95	66	)	)	PUNCT
ejpam-3248	95	67	,	,	PUNCT
ejpam-3248	95	68	we	we	PRON
ejpam-3248	95	69	obtain	obtain	VERB
ejpam-3248	95	70	[	[	X
ejpam-3248	95	71	d(z	d(z	NOUN
ejpam-3248	95	72	)	)	PUNCT
ejpam-3248	95	73	,	,	PUNCT
ejpam-3248	95	74	z]xd(z)zy[d(z	z]xd(z)zy[d(z	PROPN
ejpam-3248	95	75	)	)	PUNCT
ejpam-3248	95	76	,	,	PUNCT
ejpam-3248	95	77	z	z	X
ejpam-3248	95	78	]	]	X
ejpam-3248	95	79	=	=	SYM
ejpam-3248	95	80	0	0	NUM
ejpam-3248	95	81	for	for	ADP
ejpam-3248	95	82	all	all	DET
ejpam-3248	95	83	x	x	NOUN
ejpam-3248	95	84	,	,	PUNCT
ejpam-3248	95	85	y	y	PROPN
ejpam-3248	95	86	,	,	PUNCT
ejpam-3248	95	87	z	z	PROPN
ejpam-3248	95	88	∈	∈	PROPN
ejpam-3248	95	89	i.	i.	NOUN
ejpam-3248	95	90	(	(	PUNCT
ejpam-3248	95	91	3.10	3.10	NUM
ejpam-3248	95	92	)	)	PUNCT
ejpam-3248	95	93	substituting	substitute	VERB
ejpam-3248	95	94	xz	xz	PROPN
ejpam-3248	95	95	for	for	ADP
ejpam-3248	95	96	x	x	SYM
ejpam-3248	95	97	in	in	ADP
ejpam-3248	95	98	(	(	PUNCT
ejpam-3248	95	99	3.9	3.9	NUM
ejpam-3248	95	100	)	)	PUNCT
ejpam-3248	95	101	,	,	PUNCT
ejpam-3248	95	102	we	we	PRON
ejpam-3248	95	103	get	get	VERB
ejpam-3248	95	104	[	[	X
ejpam-3248	95	105	d(z	d(z	NOUN
ejpam-3248	95	106	)	)	PUNCT
ejpam-3248	95	107	,	,	PUNCT
ejpam-3248	95	108	z]xzd(z)y[d(z	z]xzd(z)y[d(z	NUM
ejpam-3248	95	109	)	)	PUNCT
ejpam-3248	95	110	,	,	PUNCT
ejpam-3248	96	1	z	z	X
ejpam-3248	96	2	]	]	X
ejpam-3248	96	3	=	=	SYM
ejpam-3248	96	4	0	0	NUM
ejpam-3248	96	5	for	for	ADP
ejpam-3248	96	6	all	all	DET
ejpam-3248	96	7	x	x	NOUN
ejpam-3248	96	8	,	,	PUNCT
ejpam-3248	96	9	y	y	PROPN
ejpam-3248	96	10	,	,	PUNCT
ejpam-3248	96	11	z	z	PROPN
ejpam-3248	96	12	∈	∈	PROPN
ejpam-3248	96	13	i.	i.	NOUN
ejpam-3248	96	14	(	(	PUNCT
ejpam-3248	96	15	3.11	3.11	NUM
ejpam-3248	96	16	)	)	PUNCT
ejpam-3248	96	17	subtracting	subtract	VERB
ejpam-3248	96	18	(	(	PUNCT
ejpam-3248	96	19	3.11	3.11	NUM
ejpam-3248	96	20	)	)	PUNCT
ejpam-3248	96	21	from	from	ADP
ejpam-3248	96	22	(	(	PUNCT
ejpam-3248	96	23	3.10	3.10	NUM
ejpam-3248	96	24	)	)	PUNCT
ejpam-3248	96	25	,	,	PUNCT
ejpam-3248	96	26	we	we	PRON
ejpam-3248	96	27	have	have	VERB
ejpam-3248	96	28	[	[	X
ejpam-3248	96	29	d(z	d(z	NOUN
ejpam-3248	96	30	)	)	PUNCT
ejpam-3248	96	31	,	,	PUNCT
ejpam-3248	96	32	z]x[d(z	z]x[d(z	NOUN
ejpam-3248	96	33	)	)	PUNCT
ejpam-3248	96	34	,	,	PUNCT
ejpam-3248	96	35	z]y[d(z	z]y[d(z	NUM
ejpam-3248	96	36	)	)	PUNCT
ejpam-3248	96	37	,	,	PUNCT
ejpam-3248	96	38	z	z	X
ejpam-3248	96	39	]	]	X
ejpam-3248	96	40	=	=	SYM
ejpam-3248	96	41	0	0	NUM
ejpam-3248	96	42	for	for	ADP
ejpam-3248	96	43	all	all	DET
ejpam-3248	96	44	x	x	NOUN
ejpam-3248	96	45	,	,	PUNCT
ejpam-3248	96	46	y	y	PROPN
ejpam-3248	96	47	,	,	PUNCT
ejpam-3248	96	48	z	z	PROPN
ejpam-3248	96	49	∈	∈	PROPN
ejpam-3248	96	50	i.	i.	NOUN
ejpam-3248	96	51	this	this	PRON
ejpam-3248	96	52	implies	imply	VERB
ejpam-3248	96	53	that	that	SCONJ
ejpam-3248	96	54	(	(	PUNCT
ejpam-3248	96	55	i[d(z	i[d(z	NOUN
ejpam-3248	96	56	)	)	PUNCT
ejpam-3248	96	57	,	,	PUNCT
ejpam-3248	96	58	z])3	z])3	NUM
ejpam-3248	96	59	=	=	SYM
ejpam-3248	96	60	0	0	X
ejpam-3248	96	61	.	.	PUNCT
ejpam-3248	97	1	since	since	SCONJ
ejpam-3248	97	2	a	a	DET
ejpam-3248	97	3	semiprime	semiprime	NOUN
ejpam-3248	97	4	ring	ring	NOUN
ejpam-3248	97	5	has	have	VERB
ejpam-3248	97	6	no	no	DET
ejpam-3248	97	7	non	non	ADJ
ejpam-3248	97	8	-	-	ADJ
ejpam-3248	97	9	zero	zero	ADJ
ejpam-3248	97	10	nilpotent	nilpotent	NOUN
ejpam-3248	97	11	left	leave	VERB
ejpam-3248	97	12	ideal	ideal	ADJ
ejpam-3248	97	13	,	,	PUNCT
ejpam-3248	97	14	we	we	PRON
ejpam-3248	97	15	get	get	VERB
ejpam-3248	97	16	i[d(z	i[d(z	NOUN
ejpam-3248	97	17	)	)	PUNCT
ejpam-3248	97	18	,	,	PUNCT
ejpam-3248	97	19	z	z	X
ejpam-3248	97	20	]	]	X
ejpam-3248	97	21	=	=	SYM
ejpam-3248	97	22	0	0	NUM
ejpam-3248	97	23	for	for	ADP
ejpam-3248	97	24	all	all	DET
ejpam-3248	97	25	z	z	PROPN
ejpam-3248	97	26	∈	∈	PROPN
ejpam-3248	97	27	i.	i.	NOUN
ejpam-3248	97	28	therefore	therefore	ADV
ejpam-3248	97	29	,	,	PUNCT
ejpam-3248	97	30	we	we	PRON
ejpam-3248	97	31	get	get	VERB
ejpam-3248	97	32	[	[	X
ejpam-3248	97	33	d(z	d(z	NOUN
ejpam-3248	97	34	)	)	PUNCT
ejpam-3248	97	35	,	,	PUNCT
ejpam-3248	97	36	z	z	X
ejpam-3248	97	37	]	]	X
ejpam-3248	97	38	∈	∈	PROPN
ejpam-3248	98	1	i	i	PRON
ejpam-3248	98	2	∩	∩	ADJ
ejpam-3248	98	3	annr(i	annr(i	NUM
ejpam-3248	98	4	)	)	PUNCT
ejpam-3248	98	5	.	.	PUNCT
ejpam-3248	99	1	by	by	ADP
ejpam-3248	99	2	lemma	lemma	PROPN
ejpam-3248	99	3	2.2	2.2	NUM
ejpam-3248	99	4	,	,	PUNCT
ejpam-3248	99	5	we	we	PRON
ejpam-3248	99	6	get	get	VERB
ejpam-3248	99	7	[	[	X
ejpam-3248	99	8	d(z	d(z	NOUN
ejpam-3248	99	9	)	)	PUNCT
ejpam-3248	99	10	,	,	PUNCT
ejpam-3248	99	11	z	z	X
ejpam-3248	99	12	]	]	X
ejpam-3248	99	13	=	=	SYM
ejpam-3248	99	14	0	0	NUM
ejpam-3248	99	15	for	for	ADP
ejpam-3248	99	16	all	all	DET
ejpam-3248	99	17	z	z	PROPN
ejpam-3248	99	18	∈	∈	PROPN
ejpam-3248	99	19	i.	i.	NOUN
ejpam-3248	99	20	by	by	ADP
ejpam-3248	99	21	using	use	VERB
ejpam-3248	99	22	similar	similar	ADJ
ejpam-3248	99	23	argument	argument	NOUN
ejpam-3248	99	24	,	,	PUNCT
ejpam-3248	99	25	we	we	PRON
ejpam-3248	99	26	arrive	arrive	VERB
ejpam-3248	99	27	at	at	ADP
ejpam-3248	99	28	the	the	DET
ejpam-3248	99	29	same	same	ADJ
ejpam-3248	99	30	conclusion	conclusion	NOUN
ejpam-3248	99	31	for	for	ADP
ejpam-3248	99	32	f	f	PROPN
ejpam-3248	99	33	(	(	PUNCT
ejpam-3248	99	34	x)f	x)f	X
ejpam-3248	99	35	(	(	PUNCT
ejpam-3248	99	36	y)−	y)−	PROPN
ejpam-3248	99	37	xy	xy	PROPN
ejpam-3248	99	38	∈	∈	PROPN
ejpam-3248	99	39	z(r	z(r	PROPN
ejpam-3248	99	40	)	)	PUNCT
ejpam-3248	99	41	for	for	ADP
ejpam-3248	99	42	all	all	DET
ejpam-3248	99	43	x	x	NOUN
ejpam-3248	99	44	,	,	PUNCT
ejpam-3248	99	45	y	y	PROPN
ejpam-3248	99	46	∈	∈	PROPN
ejpam-3248	99	47	i.	i.	NOUN
ejpam-3248	99	48	theorem	theorem	VERB
ejpam-3248	99	49	3.2	3.2	NUM
ejpam-3248	99	50	.	.	PUNCT
ejpam-3248	100	1	let	let	VERB
ejpam-3248	100	2	r	r	PRON
ejpam-3248	100	3	be	be	AUX
ejpam-3248	100	4	a	a	DET
ejpam-3248	100	5	semiprime	semiprime	NOUN
ejpam-3248	100	6	ring	ring	NOUN
ejpam-3248	100	7	and	and	CCONJ
ejpam-3248	100	8	f	f	PROPN
ejpam-3248	100	9	be	be	AUX
ejpam-3248	100	10	a	a	DET
ejpam-3248	100	11	non	non	ADJ
ejpam-3248	100	12	-	-	ADJ
ejpam-3248	100	13	zero	zero	ADJ
ejpam-3248	100	14	multiplicative	multiplicative	ADJ
ejpam-3248	100	15	(	(	PUNCT
ejpam-3248	100	16	generalized	generalized	ADJ
ejpam-3248	100	17	)	)	PUNCT
ejpam-3248	100	18	reverse	reverse	ADJ
ejpam-3248	100	19	derivation	derivation	NOUN
ejpam-3248	100	20	associated	associate	VERB
ejpam-3248	100	21	with	with	ADP
ejpam-3248	100	22	a	a	DET
ejpam-3248	100	23	map	map	NOUN
ejpam-3248	101	1	d	d	NOUN
ejpam-3248	101	2	,	,	PUNCT
ejpam-3248	101	3	i	i	PRON
ejpam-3248	101	4	be	be	VERB
ejpam-3248	101	5	a	a	DET
ejpam-3248	101	6	non	non	ADJ
ejpam-3248	101	7	-	-	ADJ
ejpam-3248	101	8	zero	zero	NUM
ejpam-3248	101	9	ideal	ideal	NOUN
ejpam-3248	101	10	of	of	ADP
ejpam-3248	101	11	r.	r.	PROPN
ejpam-3248	101	12	if	if	SCONJ
ejpam-3248	101	13	f	f	PROPN
ejpam-3248	101	14	(	(	PUNCT
ejpam-3248	101	15	x)f	x)f	X
ejpam-3248	101	16	(	(	PUNCT
ejpam-3248	101	17	y)±yx	y)±yx	PROPN
ejpam-3248	101	18	∈	∈	PROPN
ejpam-3248	101	19	z(r	z(r	PROPN
ejpam-3248	101	20	)	)	PUNCT
ejpam-3248	101	21	for	for	ADP
ejpam-3248	101	22	all	all	DET
ejpam-3248	101	23	x	x	NOUN
ejpam-3248	101	24	,	,	PUNCT
ejpam-3248	101	25	y	y	PROPN
ejpam-3248	101	26	∈	∈	PROPN
ejpam-3248	102	1	i	i	PRON
ejpam-3248	102	2	,	,	PUNCT
ejpam-3248	102	3	then	then	ADV
ejpam-3248	102	4	[	[	X
ejpam-3248	102	5	d(x	d(x	NOUN
ejpam-3248	102	6	)	)	PUNCT
ejpam-3248	102	7	,	,	PUNCT
ejpam-3248	102	8	x	x	X
ejpam-3248	102	9	]	]	X
ejpam-3248	102	10	=	=	SYM
ejpam-3248	102	11	0	0	NUM
ejpam-3248	102	12	for	for	ADP
ejpam-3248	102	13	all	all	DET
ejpam-3248	102	14	x	x	SYM
ejpam-3248	102	15	∈	∈	NOUN
ejpam-3248	102	16	i.	i.	NOUN
ejpam-3248	102	17	proof	proof	NOUN
ejpam-3248	102	18	by	by	ADP
ejpam-3248	102	19	assumption	assumption	NOUN
ejpam-3248	102	20	,	,	PUNCT
ejpam-3248	102	21	we	we	PRON
ejpam-3248	102	22	have	have	VERB
ejpam-3248	102	23	f	f	PROPN
ejpam-3248	102	24	(	(	PUNCT
ejpam-3248	102	25	x)f	x)f	X
ejpam-3248	102	26	(	(	PUNCT
ejpam-3248	102	27	y	y	NOUN
ejpam-3248	102	28	)	)	PUNCT
ejpam-3248	102	29	+	+	CCONJ
ejpam-3248	103	1	yx	yx	X
ejpam-3248	103	2	∈	∈	PROPN
ejpam-3248	103	3	z(r	z(r	PROPN
ejpam-3248	103	4	)	)	PUNCT
ejpam-3248	103	5	for	for	ADP
ejpam-3248	103	6	all	all	DET
ejpam-3248	103	7	x	x	NOUN
ejpam-3248	103	8	,	,	PUNCT
ejpam-3248	103	9	y	y	PROPN
ejpam-3248	103	10	∈	∈	PROPN
ejpam-3248	103	11	i.	i.	NOUN
ejpam-3248	103	12	(	(	PUNCT
ejpam-3248	103	13	3.12	3.12	NUM
ejpam-3248	103	14	)	)	PUNCT
ejpam-3248	103	15	replacing	replace	VERB
ejpam-3248	103	16	y	y	PRON
ejpam-3248	103	17	by	by	ADP
ejpam-3248	103	18	zy	zy	PROPN
ejpam-3248	103	19	in	in	ADP
ejpam-3248	103	20	(	(	PUNCT
ejpam-3248	103	21	3.12	3.12	NUM
ejpam-3248	103	22	)	)	PUNCT
ejpam-3248	103	23	,	,	PUNCT
ejpam-3248	103	24	we	we	PRON
ejpam-3248	103	25	get	get	VERB
ejpam-3248	103	26	f	f	PROPN
ejpam-3248	103	27	(	(	PUNCT
ejpam-3248	103	28	x)(f	x)(f	PROPN
ejpam-3248	103	29	(	(	PUNCT
ejpam-3248	103	30	y)z	y)z	X
ejpam-3248	103	31	+	+	CCONJ
ejpam-3248	103	32	yd(z	yd(z	NOUN
ejpam-3248	103	33	)	)	PUNCT
ejpam-3248	103	34	)	)	PUNCT
ejpam-3248	104	1	+	+	CCONJ
ejpam-3248	104	2	zyx	zyx	PROPN
ejpam-3248	104	3	+	+	CCONJ
ejpam-3248	104	4	yxz	yxz	PROPN
ejpam-3248	104	5	−	−	PROPN
ejpam-3248	104	6	yxz	yxz	NOUN
ejpam-3248	104	7	∈	∈	PROPN
ejpam-3248	104	8	z(r	z(r	NOUN
ejpam-3248	104	9	)	)	PUNCT
ejpam-3248	104	10	for	for	ADP
ejpam-3248	104	11	all	all	DET
ejpam-3248	104	12	x	x	NOUN
ejpam-3248	104	13	,	,	PUNCT
ejpam-3248	104	14	y	y	PROPN
ejpam-3248	104	15	,	,	PUNCT
ejpam-3248	104	16	z	z	PROPN
ejpam-3248	104	17	∈	∈	PROPN
ejpam-3248	104	18	i.	i.	NOUN
ejpam-3248	104	19	this	this	PRON
ejpam-3248	104	20	implies	imply	VERB
ejpam-3248	104	21	that	that	SCONJ
ejpam-3248	104	22	(	(	PUNCT
ejpam-3248	104	23	f	f	X
ejpam-3248	104	24	(	(	PUNCT
ejpam-3248	104	25	x)f	x)f	X
ejpam-3248	104	26	(	(	PUNCT
ejpam-3248	104	27	y	y	NOUN
ejpam-3248	104	28	)	)	PUNCT
ejpam-3248	105	1	+	+	CCONJ
ejpam-3248	105	2	yx)z	yx)z	PROPN
ejpam-3248	106	1	+	+	NUM
ejpam-3248	106	2	f	f	X
ejpam-3248	106	3	(	(	PUNCT
ejpam-3248	106	4	x)yd(z	x)yd(z	PROPN
ejpam-3248	106	5	)	)	PUNCT
ejpam-3248	106	6	+	+	CCONJ
ejpam-3248	107	1	[	[	X
ejpam-3248	107	2	z	z	X
ejpam-3248	107	3	,	,	PUNCT
ejpam-3248	107	4	yx	yx	X
ejpam-3248	107	5	]	]	X
ejpam-3248	107	6	∈	∈	PROPN
ejpam-3248	107	7	z(r	z(r	PROPN
ejpam-3248	107	8	)	)	PUNCT
ejpam-3248	107	9	(	(	PUNCT
ejpam-3248	107	10	3.13	3.13	NUM
ejpam-3248	107	11	)	)	PUNCT
ejpam-3248	107	12	a.	a.	PROPN
ejpam-3248	107	13	ali	ali	PROPN
ejpam-3248	107	14	,	,	PUNCT
ejpam-3248	107	15	a.	a.	PROPN
ejpam-3248	107	16	bano	bano	PROPN
ejpam-3248	107	17	/	/	SYM
ejpam-3248	107	18	eur	eur	PROPN
ejpam-3248	107	19	.	.	PUNCT
ejpam-3248	108	1	j.	j.	PROPN
ejpam-3248	108	2	pure	pure	PROPN
ejpam-3248	108	3	appl	appl	PROPN
ejpam-3248	108	4	.	.	PROPN
ejpam-3248	108	5	math	math	PROPN
ejpam-3248	108	6	,	,	PUNCT
ejpam-3248	108	7	11	11	NUM
ejpam-3248	108	8	(	(	PUNCT
ejpam-3248	108	9	3	3	NUM
ejpam-3248	108	10	)	)	PUNCT
ejpam-3248	108	11	(	(	PUNCT
ejpam-3248	108	12	2018	2018	NUM
ejpam-3248	108	13	)	)	PUNCT
ejpam-3248	108	14	,	,	PUNCT
ejpam-3248	108	15	717	717	NUM
ejpam-3248	108	16	-	-	SYM
ejpam-3248	108	17	729	729	NUM
ejpam-3248	108	18	721	721	NUM
ejpam-3248	108	19	commuting	commuting	NOUN
ejpam-3248	108	20	(	(	PUNCT
ejpam-3248	108	21	3.13	3.13	NUM
ejpam-3248	108	22	)	)	PUNCT
ejpam-3248	108	23	with	with	ADP
ejpam-3248	108	24	z	z	NOUN
ejpam-3248	108	25	and	and	CCONJ
ejpam-3248	108	26	using	use	VERB
ejpam-3248	108	27	(	(	PUNCT
ejpam-3248	108	28	3.12	3.12	NUM
ejpam-3248	108	29	)	)	PUNCT
ejpam-3248	108	30	,	,	PUNCT
ejpam-3248	108	31	we	we	PRON
ejpam-3248	108	32	obtain	obtain	VERB
ejpam-3248	108	33	[	[	X
ejpam-3248	108	34	f	f	X
ejpam-3248	108	35	(	(	PUNCT
ejpam-3248	108	36	x)yd(z	x)yd(z	PROPN
ejpam-3248	108	37	)	)	PUNCT
ejpam-3248	108	38	,	,	PUNCT
ejpam-3248	109	1	z	z	X
ejpam-3248	109	2	]	]	X
ejpam-3248	110	1	+	+	CCONJ
ejpam-3248	110	2	[	[	X
ejpam-3248	110	3	[	[	X
ejpam-3248	110	4	z	z	NOUN
ejpam-3248	110	5	,	,	PUNCT
ejpam-3248	110	6	yx	yx	NOUN
ejpam-3248	110	7	]	]	X
ejpam-3248	110	8	,	,	PUNCT
ejpam-3248	110	9	z	z	X
ejpam-3248	110	10	]	]	X
ejpam-3248	110	11	=	=	SYM
ejpam-3248	110	12	0	0	NUM
ejpam-3248	110	13	for	for	ADP
ejpam-3248	110	14	all	all	DET
ejpam-3248	110	15	x	x	NOUN
ejpam-3248	110	16	,	,	PUNCT
ejpam-3248	110	17	y	y	PROPN
ejpam-3248	110	18	,	,	PUNCT
ejpam-3248	110	19	z	z	PROPN
ejpam-3248	110	20	∈	∈	PROPN
ejpam-3248	110	21	i.	i.	NOUN
ejpam-3248	110	22	this	this	PRON
ejpam-3248	110	23	implies	imply	VERB
ejpam-3248	110	24	that	that	SCONJ
ejpam-3248	111	1	[	[	X
ejpam-3248	111	2	f	f	X
ejpam-3248	111	3	(	(	PUNCT
ejpam-3248	111	4	x)yd(z	x)yd(z	PROPN
ejpam-3248	111	5	)	)	PUNCT
ejpam-3248	111	6	,	,	PUNCT
ejpam-3248	111	7	z	z	X
ejpam-3248	111	8	]	]	X
ejpam-3248	111	9	+	+	CCONJ
ejpam-3248	112	1	[	[	X
ejpam-3248	112	2	y[z	y[z	X
ejpam-3248	112	3	,	,	PUNCT
ejpam-3248	112	4	x	x	NOUN
ejpam-3248	112	5	]	]	X
ejpam-3248	112	6	,	,	PUNCT
ejpam-3248	112	7	z	z	X
ejpam-3248	112	8	]	]	X
ejpam-3248	112	9	+	+	CCONJ
ejpam-3248	113	1	[	[	X
ejpam-3248	113	2	[	[	X
ejpam-3248	113	3	z	z	NOUN
ejpam-3248	113	4	,	,	PUNCT
ejpam-3248	113	5	y]x	y]x	NOUN
ejpam-3248	113	6	,	,	PUNCT
ejpam-3248	113	7	z	z	X
ejpam-3248	113	8	]	]	X
ejpam-3248	113	9	=	=	SYM
ejpam-3248	113	10	0	0	X
ejpam-3248	113	11	.	.	PUNCT
ejpam-3248	114	1	(	(	PUNCT
ejpam-3248	114	2	3.14	3.14	NUM
ejpam-3248	114	3	)	)	PUNCT
ejpam-3248	114	4	replacing	replace	VERB
ejpam-3248	114	5	x	x	PUNCT
ejpam-3248	114	6	by	by	ADP
ejpam-3248	114	7	zx	zx	PROPN
ejpam-3248	114	8	in	in	ADP
ejpam-3248	114	9	(	(	PUNCT
ejpam-3248	114	10	3.14	3.14	NUM
ejpam-3248	114	11	)	)	PUNCT
ejpam-3248	114	12	,	,	PUNCT
ejpam-3248	114	13	we	we	PRON
ejpam-3248	114	14	obtain	obtain	VERB
ejpam-3248	114	15	[	[	X
ejpam-3248	114	16	f	f	X
ejpam-3248	114	17	(	(	PUNCT
ejpam-3248	114	18	x)zyd(z	x)zyd(z	PROPN
ejpam-3248	114	19	)	)	PUNCT
ejpam-3248	114	20	,	,	PUNCT
ejpam-3248	115	1	z	z	X
ejpam-3248	115	2	]	]	X
ejpam-3248	115	3	+	+	CCONJ
ejpam-3248	115	4	[	[	X
ejpam-3248	115	5	xd(z)yd(z	xd(z)yd(z	NOUN
ejpam-3248	115	6	)	)	PUNCT
ejpam-3248	115	7	,	,	PUNCT
ejpam-3248	116	1	z	z	X
ejpam-3248	116	2	]	]	X
ejpam-3248	116	3	+	+	CCONJ
ejpam-3248	116	4	[	[	X
ejpam-3248	116	5	yz[z	yz[z	NOUN
ejpam-3248	116	6	,	,	PUNCT
ejpam-3248	116	7	x	x	X
ejpam-3248	116	8	]	]	X
ejpam-3248	116	9	,	,	PUNCT
ejpam-3248	116	10	z	z	X
ejpam-3248	116	11	]	]	X
ejpam-3248	117	1	+	+	CCONJ
ejpam-3248	117	2	[	[	X
ejpam-3248	117	3	[	[	X
ejpam-3248	117	4	z	z	X
ejpam-3248	117	5	,	,	PUNCT
ejpam-3248	117	6	y]zx	y]zx	PROPN
ejpam-3248	117	7	,	,	PUNCT
ejpam-3248	117	8	z	z	NOUN
ejpam-3248	117	9	]	]	X
ejpam-3248	117	10	=	=	SYM
ejpam-3248	117	11	0	0	X
ejpam-3248	117	12	.	.	PUNCT
ejpam-3248	118	1	(	(	PUNCT
ejpam-3248	118	2	3.15	3.15	NUM
ejpam-3248	118	3	)	)	PUNCT
ejpam-3248	118	4	substituting	substitute	VERB
ejpam-3248	118	5	zy	zy	NOUN
ejpam-3248	118	6	for	for	ADP
ejpam-3248	118	7	y	y	PROPN
ejpam-3248	118	8	in	in	ADP
ejpam-3248	118	9	(	(	PUNCT
ejpam-3248	118	10	3.14	3.14	NUM
ejpam-3248	118	11	)	)	PUNCT
ejpam-3248	118	12	,	,	PUNCT
ejpam-3248	118	13	we	we	PRON
ejpam-3248	118	14	obtain	obtain	VERB
ejpam-3248	118	15	[	[	X
ejpam-3248	118	16	f	f	X
ejpam-3248	118	17	(	(	PUNCT
ejpam-3248	118	18	x)zyd(z	x)zyd(z	PROPN
ejpam-3248	118	19	)	)	PUNCT
ejpam-3248	118	20	,	,	PUNCT
ejpam-3248	119	1	z	z	X
ejpam-3248	119	2	]	]	X
ejpam-3248	120	1	+	+	CCONJ
ejpam-3248	121	1	[	[	X
ejpam-3248	121	2	zy[z	zy[z	PROPN
ejpam-3248	121	3	,	,	PUNCT
ejpam-3248	121	4	x	x	NOUN
ejpam-3248	121	5	]	]	X
ejpam-3248	121	6	,	,	PUNCT
ejpam-3248	121	7	z	z	X
ejpam-3248	121	8	]	]	X
ejpam-3248	121	9	+	+	CCONJ
ejpam-3248	121	10	[	[	X
ejpam-3248	121	11	z[z	z[z	NUM
ejpam-3248	121	12	,	,	PUNCT
ejpam-3248	121	13	y]x	y]x	NOUN
ejpam-3248	121	14	,	,	PUNCT
ejpam-3248	121	15	z	z	X
ejpam-3248	121	16	]	]	X
ejpam-3248	121	17	=	=	SYM
ejpam-3248	121	18	0	0	X
ejpam-3248	121	19	.	.	PUNCT
ejpam-3248	122	1	(	(	PUNCT
ejpam-3248	122	2	3.16	3.16	NUM
ejpam-3248	122	3	)	)	PUNCT
ejpam-3248	122	4	subtracting	subtract	VERB
ejpam-3248	122	5	(	(	PUNCT
ejpam-3248	122	6	3.16	3.16	NUM
ejpam-3248	122	7	)	)	PUNCT
ejpam-3248	122	8	from	from	ADP
ejpam-3248	122	9	(	(	PUNCT
ejpam-3248	122	10	3.15	3.15	NUM
ejpam-3248	122	11	)	)	PUNCT
ejpam-3248	122	12	,	,	PUNCT
ejpam-3248	122	13	we	we	PRON
ejpam-3248	122	14	get	get	VERB
ejpam-3248	122	15	[	[	X
ejpam-3248	122	16	xd(z)yd(z	xd(z)yd(z	NOUN
ejpam-3248	122	17	)	)	PUNCT
ejpam-3248	122	18	,	,	PUNCT
ejpam-3248	123	1	z	z	X
ejpam-3248	123	2	]	]	X
ejpam-3248	124	1	+	+	CCONJ
ejpam-3248	125	1	[	[	X
ejpam-3248	125	2	[	[	X
ejpam-3248	125	3	y	y	PROPN
ejpam-3248	125	4	,	,	PUNCT
ejpam-3248	125	5	z][z	z][z	NOUN
ejpam-3248	125	6	,	,	PUNCT
ejpam-3248	125	7	x	x	NOUN
ejpam-3248	125	8	]	]	X
ejpam-3248	125	9	,	,	PUNCT
ejpam-3248	125	10	z	z	X
ejpam-3248	125	11	]	]	X
ejpam-3248	126	1	+	+	CCONJ
ejpam-3248	127	1	[	[	X
ejpam-3248	127	2	[	[	X
ejpam-3248	127	3	[	[	X
ejpam-3248	127	4	z	z	PROPN
ejpam-3248	127	5	,	,	PUNCT
ejpam-3248	127	6	y	y	PROPN
ejpam-3248	127	7	]	]	X
ejpam-3248	127	8	,	,	PUNCT
ejpam-3248	127	9	z]x	z]x	X
ejpam-3248	127	10	,	,	PUNCT
ejpam-3248	127	11	z	z	X
ejpam-3248	127	12	]	]	X
ejpam-3248	127	13	=	=	SYM
ejpam-3248	127	14	0	0	X
ejpam-3248	127	15	.	.	PUNCT
ejpam-3248	128	1	(	(	PUNCT
ejpam-3248	128	2	3.17	3.17	NUM
ejpam-3248	128	3	)	)	PUNCT
ejpam-3248	128	4	replacing	replace	VERB
ejpam-3248	128	5	x	x	PUNCT
ejpam-3248	128	6	by	by	ADP
ejpam-3248	128	7	xz	xz	PROPN
ejpam-3248	128	8	in	in	ADP
ejpam-3248	128	9	(	(	PUNCT
ejpam-3248	128	10	3.17	3.17	NUM
ejpam-3248	128	11	)	)	PUNCT
ejpam-3248	128	12	,	,	PUNCT
ejpam-3248	128	13	we	we	PRON
ejpam-3248	128	14	obtain	obtain	VERB
ejpam-3248	128	15	[	[	X
ejpam-3248	128	16	xzd(z)yd(z	xzd(z)yd(z	NOUN
ejpam-3248	128	17	)	)	PUNCT
ejpam-3248	128	18	,	,	PUNCT
ejpam-3248	129	1	z	z	X
ejpam-3248	129	2	]	]	X
ejpam-3248	130	1	+	+	CCONJ
ejpam-3248	131	1	[	[	X
ejpam-3248	131	2	[	[	X
ejpam-3248	131	3	y	y	PROPN
ejpam-3248	131	4	,	,	PUNCT
ejpam-3248	131	5	z][z	z][z	NOUN
ejpam-3248	131	6	,	,	PUNCT
ejpam-3248	131	7	x	x	NOUN
ejpam-3248	131	8	]	]	X
ejpam-3248	131	9	,	,	PUNCT
ejpam-3248	131	10	z]z	z]z	NOUN
ejpam-3248	131	11	+	+	X
ejpam-3248	132	1	[	[	X
ejpam-3248	132	2	[	[	X
ejpam-3248	132	3	[	[	X
ejpam-3248	132	4	z	z	PROPN
ejpam-3248	132	5	,	,	PUNCT
ejpam-3248	132	6	y	y	PROPN
ejpam-3248	132	7	]	]	X
ejpam-3248	132	8	,	,	PUNCT
ejpam-3248	132	9	z]x	z]x	NOUN
ejpam-3248	132	10	,	,	PUNCT
ejpam-3248	132	11	z]z	z]z	NOUN
ejpam-3248	132	12	=	=	SYM
ejpam-3248	132	13	0	0	NUM
ejpam-3248	132	14	(	(	PUNCT
ejpam-3248	132	15	3.18	3.18	NUM
ejpam-3248	132	16	)	)	PUNCT
ejpam-3248	132	17	right	right	ADJ
ejpam-3248	132	18	multiplying	multiplying	NOUN
ejpam-3248	132	19	(	(	PUNCT
ejpam-3248	132	20	3.17	3.17	NUM
ejpam-3248	132	21	)	)	PUNCT
ejpam-3248	132	22	by	by	ADP
ejpam-3248	132	23	z	z	NOUN
ejpam-3248	132	24	and	and	CCONJ
ejpam-3248	132	25	subtracting	subtract	VERB
ejpam-3248	132	26	from	from	ADP
ejpam-3248	132	27	(	(	PUNCT
ejpam-3248	132	28	3.18	3.18	NUM
ejpam-3248	132	29	)	)	PUNCT
ejpam-3248	132	30	,	,	PUNCT
ejpam-3248	132	31	we	we	PRON
ejpam-3248	132	32	get	get	VERB
ejpam-3248	132	33	[	[	X
ejpam-3248	132	34	x[d(z)yd(z	x[d(z)yd(z	NOUN
ejpam-3248	132	35	)	)	PUNCT
ejpam-3248	132	36	,	,	PUNCT
ejpam-3248	133	1	z	z	X
ejpam-3248	133	2	]	]	X
ejpam-3248	133	3	,	,	PUNCT
ejpam-3248	133	4	z	z	X
ejpam-3248	133	5	]	]	X
ejpam-3248	133	6	=	=	SYM
ejpam-3248	133	7	0	0	NUM
ejpam-3248	133	8	for	for	ADP
ejpam-3248	133	9	all	all	DET
ejpam-3248	133	10	x	x	NOUN
ejpam-3248	133	11	,	,	PUNCT
ejpam-3248	133	12	y	y	PROPN
ejpam-3248	133	13	,	,	PUNCT
ejpam-3248	133	14	z	z	PROPN
ejpam-3248	133	15	∈	∈	PROPN
ejpam-3248	133	16	i.	i.	NOUN
ejpam-3248	133	17	(	(	PUNCT
ejpam-3248	133	18	3.19	3.19	NUM
ejpam-3248	133	19	)	)	PUNCT
ejpam-3248	133	20	this	this	PRON
ejpam-3248	133	21	implies	imply	VERB
ejpam-3248	133	22	that	that	SCONJ
ejpam-3248	134	1	[	[	X
ejpam-3248	134	2	x	x	X
ejpam-3248	134	3	,	,	PUNCT
ejpam-3248	134	4	z][d(z)yd(z	z][d(z)yd(z	NOUN
ejpam-3248	134	5	)	)	PUNCT
ejpam-3248	134	6	,	,	PUNCT
ejpam-3248	134	7	z	z	X
ejpam-3248	134	8	]	]	X
ejpam-3248	134	9	+	+	NUM
ejpam-3248	134	10	x[[d(z)yd(z	x[[d(z)yd(z	NOUN
ejpam-3248	134	11	)	)	PUNCT
ejpam-3248	134	12	,	,	PUNCT
ejpam-3248	134	13	z	z	X
ejpam-3248	134	14	]	]	X
ejpam-3248	134	15	,	,	PUNCT
ejpam-3248	134	16	z	z	X
ejpam-3248	134	17	]	]	X
ejpam-3248	134	18	=	=	SYM
ejpam-3248	134	19	0	0	X
ejpam-3248	134	20	.	.	PUNCT
ejpam-3248	135	1	(	(	PUNCT
ejpam-3248	135	2	3.20	3.20	NUM
ejpam-3248	135	3	)	)	PUNCT
ejpam-3248	135	4	substituting	substitute	VERB
ejpam-3248	135	5	ux	ux	NOUN
ejpam-3248	135	6	for	for	ADP
ejpam-3248	135	7	x	x	PRON
ejpam-3248	135	8	in	in	ADP
ejpam-3248	135	9	(	(	PUNCT
ejpam-3248	135	10	3.20	3.20	NUM
ejpam-3248	135	11	)	)	PUNCT
ejpam-3248	135	12	,	,	PUNCT
ejpam-3248	135	13	we	we	PRON
ejpam-3248	135	14	get	get	VERB
ejpam-3248	135	15	u[x	u[x	PRON
ejpam-3248	135	16	,	,	PUNCT
ejpam-3248	135	17	z][d(z)yd(z	z][d(z)yd(z	NOUN
ejpam-3248	135	18	)	)	PUNCT
ejpam-3248	135	19	,	,	PUNCT
ejpam-3248	136	1	z	z	X
ejpam-3248	136	2	]	]	X
ejpam-3248	136	3	+	+	CCONJ
ejpam-3248	136	4	[	[	X
ejpam-3248	136	5	u	u	X
ejpam-3248	136	6	,	,	PUNCT
ejpam-3248	136	7	z]x[d(z)yd(z	z]x[d(z)yd(z	NOUN
ejpam-3248	136	8	)	)	PUNCT
ejpam-3248	136	9	,	,	PUNCT
ejpam-3248	137	1	z	z	X
ejpam-3248	137	2	]	]	X
ejpam-3248	137	3	+	+	CCONJ
ejpam-3248	137	4	ux[[d(z)yd(z	ux[[d(z)yd(z	NOUN
ejpam-3248	137	5	)	)	PUNCT
ejpam-3248	137	6	,	,	PUNCT
ejpam-3248	138	1	z	z	X
ejpam-3248	138	2	]	]	X
ejpam-3248	138	3	,	,	PUNCT
ejpam-3248	138	4	z	z	X
ejpam-3248	138	5	]	]	X
ejpam-3248	138	6	=	=	SYM
ejpam-3248	138	7	0	0	X
ejpam-3248	138	8	.	.	PUNCT
ejpam-3248	139	1	for	for	ADP
ejpam-3248	139	2	all	all	DET
ejpam-3248	139	3	x	x	PROPN
ejpam-3248	139	4	,	,	PUNCT
ejpam-3248	139	5	y	y	PROPN
ejpam-3248	139	6	,	,	PUNCT
ejpam-3248	139	7	z	z	PROPN
ejpam-3248	139	8	,	,	PUNCT
ejpam-3248	139	9	u	u	PROPN
ejpam-3248	139	10	∈	∈	PROPN
ejpam-3248	139	11	i.	i.	NOUN
ejpam-3248	139	12	(	(	PUNCT
ejpam-3248	139	13	3.21	3.21	NUM
ejpam-3248	139	14	)	)	PUNCT
ejpam-3248	139	15	left	leave	VERB
ejpam-3248	139	16	multiplying	multiplying	NOUN
ejpam-3248	139	17	(	(	PUNCT
ejpam-3248	139	18	3.20	3.20	NUM
ejpam-3248	139	19	)	)	PUNCT
ejpam-3248	139	20	by	by	ADP
ejpam-3248	139	21	u	u	NOUN
ejpam-3248	139	22	and	and	CCONJ
ejpam-3248	139	23	subtracting	subtract	VERB
ejpam-3248	139	24	from	from	ADP
ejpam-3248	139	25	(	(	PUNCT
ejpam-3248	139	26	3.21	3.21	NUM
ejpam-3248	139	27	)	)	PUNCT
ejpam-3248	139	28	,	,	PUNCT
ejpam-3248	139	29	we	we	PRON
ejpam-3248	139	30	obtain	obtain	VERB
ejpam-3248	139	31	[	[	X
ejpam-3248	139	32	u	u	NOUN
ejpam-3248	139	33	,	,	PUNCT
ejpam-3248	139	34	z]x[d(z)yd(z	z]x[d(z)yd(z	NOUN
ejpam-3248	139	35	)	)	PUNCT
ejpam-3248	139	36	,	,	PUNCT
ejpam-3248	139	37	z	z	X
ejpam-3248	139	38	]	]	X
ejpam-3248	139	39	=	=	SYM
ejpam-3248	139	40	0	0	NUM
ejpam-3248	139	41	for	for	ADP
ejpam-3248	139	42	all	all	DET
ejpam-3248	139	43	x	x	NOUN
ejpam-3248	139	44	,	,	PUNCT
ejpam-3248	139	45	y	y	PROPN
ejpam-3248	139	46	,	,	PUNCT
ejpam-3248	139	47	z	z	PROPN
ejpam-3248	139	48	,	,	PUNCT
ejpam-3248	139	49	u	u	PROPN
ejpam-3248	139	50	∈	∈	PROPN
ejpam-3248	139	51	i.	i.	NOUN
ejpam-3248	139	52	(	(	PUNCT
ejpam-3248	139	53	3.22	3.22	NUM
ejpam-3248	139	54	)	)	PUNCT
ejpam-3248	139	55	putting	put	VERB
ejpam-3248	139	56	u	u	NOUN
ejpam-3248	139	57	=	=	PUNCT
ejpam-3248	139	58	d(z)yd(z	d(z)yd(z	NOUN
ejpam-3248	139	59	)	)	PUNCT
ejpam-3248	139	60	in	in	ADP
ejpam-3248	139	61	(	(	PUNCT
ejpam-3248	139	62	3.22	3.22	NUM
ejpam-3248	139	63	)	)	PUNCT
ejpam-3248	139	64	,	,	PUNCT
ejpam-3248	139	65	we	we	PRON
ejpam-3248	139	66	get	get	VERB
ejpam-3248	139	67	(	(	PUNCT
ejpam-3248	139	68	i[d(z)yd(z	i[d(z)yd(z	NOUN
ejpam-3248	139	69	)	)	PUNCT
ejpam-3248	139	70	,	,	PUNCT
ejpam-3248	139	71	z])2	z])2	NUM
ejpam-3248	139	72	=	=	SYM
ejpam-3248	139	73	0	0	NUM
ejpam-3248	139	74	for	for	ADP
ejpam-3248	139	75	all	all	DET
ejpam-3248	139	76	y	y	PROPN
ejpam-3248	139	77	,	,	PUNCT
ejpam-3248	139	78	z	z	PROPN
ejpam-3248	139	79	∈	∈	PROPN
ejpam-3248	139	80	i.	i.	NOUN
ejpam-3248	139	81	(	(	PUNCT
ejpam-3248	139	82	3.23	3.23	NUM
ejpam-3248	139	83	)	)	PUNCT
ejpam-3248	139	84	since	since	SCONJ
ejpam-3248	139	85	a	a	DET
ejpam-3248	139	86	semiprime	semiprime	NOUN
ejpam-3248	139	87	ring	ring	NOUN
ejpam-3248	139	88	has	have	VERB
ejpam-3248	139	89	no	no	DET
ejpam-3248	139	90	non	non	ADJ
ejpam-3248	139	91	-	-	ADJ
ejpam-3248	139	92	zero	zero	ADJ
ejpam-3248	139	93	nilpotent	nilpotent	NOUN
ejpam-3248	139	94	left	leave	VERB
ejpam-3248	139	95	ideal	ideal	NOUN
ejpam-3248	139	96	,	,	PUNCT
ejpam-3248	139	97	therefore	therefore	ADV
ejpam-3248	139	98	we	we	PRON
ejpam-3248	139	99	get	get	VERB
ejpam-3248	139	100	i[d(z)yd(z	i[d(z)yd(z	NOUN
ejpam-3248	139	101	)	)	PUNCT
ejpam-3248	139	102	,	,	PUNCT
ejpam-3248	139	103	z	z	X
ejpam-3248	139	104	]	]	X
ejpam-3248	139	105	=	=	SYM
ejpam-3248	139	106	0	0	NUM
ejpam-3248	139	107	,	,	PUNCT
ejpam-3248	139	108	this	this	PRON
ejpam-3248	139	109	implies	imply	VERB
ejpam-3248	139	110	that	that	SCONJ
ejpam-3248	139	111	[	[	X
ejpam-3248	139	112	d(z)yd(z	d(z)yd(z	NOUN
ejpam-3248	139	113	)	)	PUNCT
ejpam-3248	139	114	,	,	PUNCT
ejpam-3248	139	115	z	z	NOUN
ejpam-3248	139	116	)	)	PUNCT
ejpam-3248	139	117	]	]	PUNCT
ejpam-3248	140	1	∈	∈	PROPN
ejpam-3248	140	2	i	i	PRON
ejpam-3248	140	3	∩	∩	ADJ
ejpam-3248	140	4	annr(i	annr(i	NUM
ejpam-3248	140	5	)	)	PUNCT
ejpam-3248	140	6	.	.	PUNCT
ejpam-3248	141	1	by	by	ADP
ejpam-3248	141	2	lemma	lemma	PROPN
ejpam-3248	141	3	2.2	2.2	NUM
ejpam-3248	141	4	,	,	PUNCT
ejpam-3248	141	5	we	we	PRON
ejpam-3248	141	6	get	get	VERB
ejpam-3248	141	7	[	[	NOUN
ejpam-3248	141	8	d(z)yd(z	d(z)yd(z	NOUN
ejpam-3248	141	9	)	)	PUNCT
ejpam-3248	141	10	,	,	PUNCT
ejpam-3248	142	1	z	z	X
ejpam-3248	142	2	]	]	X
ejpam-3248	142	3	=	=	SYM
ejpam-3248	142	4	0	0	X
ejpam-3248	142	5	.	.	PUNCT
ejpam-3248	143	1	this	this	PRON
ejpam-3248	143	2	implies	imply	VERB
ejpam-3248	143	3	that	that	SCONJ
ejpam-3248	143	4	d(z)yd(z)z	d(z)yd(z)z	ADV
ejpam-3248	143	5	−	−	NUM
ejpam-3248	143	6	zd(z)yd(z	zd(z)yd(z	NOUN
ejpam-3248	143	7	)	)	PUNCT
ejpam-3248	143	8	=	=	SYM
ejpam-3248	143	9	0	0	NUM
ejpam-3248	143	10	for	for	ADP
ejpam-3248	143	11	all	all	DET
ejpam-3248	143	12	y	y	PROPN
ejpam-3248	143	13	,	,	PUNCT
ejpam-3248	143	14	z	z	PROPN
ejpam-3248	143	15	∈	∈	PROPN
ejpam-3248	143	16	i.	i.	NOUN
ejpam-3248	143	17	(	(	PUNCT
ejpam-3248	143	18	3.24	3.24	NUM
ejpam-3248	143	19	)	)	PUNCT
ejpam-3248	143	20	a.	a.	PROPN
ejpam-3248	143	21	ali	ali	PROPN
ejpam-3248	143	22	,	,	PUNCT
ejpam-3248	143	23	a.	a.	PROPN
ejpam-3248	143	24	bano	bano	PROPN
ejpam-3248	143	25	/	/	SYM
ejpam-3248	143	26	eur	eur	PROPN
ejpam-3248	143	27	.	.	PUNCT
ejpam-3248	144	1	j.	j.	PROPN
ejpam-3248	144	2	pure	pure	PROPN
ejpam-3248	144	3	appl	appl	PROPN
ejpam-3248	144	4	.	.	PROPN
ejpam-3248	144	5	math	math	PROPN
ejpam-3248	144	6	,	,	PUNCT
ejpam-3248	144	7	11	11	NUM
ejpam-3248	144	8	(	(	PUNCT
ejpam-3248	144	9	3	3	NUM
ejpam-3248	144	10	)	)	PUNCT
ejpam-3248	144	11	(	(	PUNCT
ejpam-3248	144	12	2018	2018	NUM
ejpam-3248	144	13	)	)	PUNCT
ejpam-3248	144	14	,	,	PUNCT
ejpam-3248	144	15	717	717	NUM
ejpam-3248	144	16	-	-	SYM
ejpam-3248	144	17	729	729	NUM
ejpam-3248	144	18	722	722	NUM
ejpam-3248	144	19	replacing	replace	VERB
ejpam-3248	144	20	y	y	PRON
ejpam-3248	144	21	by	by	ADP
ejpam-3248	144	22	yd(z)w	yd(z)w	PROPN
ejpam-3248	144	23	in	in	ADP
ejpam-3248	144	24	(	(	PUNCT
ejpam-3248	144	25	3.24	3.24	NUM
ejpam-3248	144	26	)	)	PUNCT
ejpam-3248	144	27	,	,	PUNCT
ejpam-3248	144	28	we	we	PRON
ejpam-3248	144	29	get	get	VERB
ejpam-3248	144	30	d(z)yd(z)wd(z)z	d(z)yd(z)wd(z)z	NOUN
ejpam-3248	144	31	−	−	PROPN
ejpam-3248	145	1	zd(z)yd(z)wd(z	zd(z)yd(z)wd(z	NOUN
ejpam-3248	145	2	)	)	PUNCT
ejpam-3248	145	3	=	=	SYM
ejpam-3248	145	4	0	0	NUM
ejpam-3248	145	5	for	for	ADP
ejpam-3248	145	6	all	all	DET
ejpam-3248	145	7	y	y	PROPN
ejpam-3248	145	8	,	,	PUNCT
ejpam-3248	145	9	z	z	NOUN
ejpam-3248	145	10	,	,	PUNCT
ejpam-3248	145	11	w	w	PROPN
ejpam-3248	145	12	∈	∈	PROPN
ejpam-3248	145	13	i.	i.	NOUN
ejpam-3248	145	14	(	(	PUNCT
ejpam-3248	145	15	3.25	3.25	NUM
ejpam-3248	145	16	)	)	PUNCT
ejpam-3248	145	17	using	use	VERB
ejpam-3248	145	18	(	(	PUNCT
ejpam-3248	145	19	3.24	3.24	NUM
ejpam-3248	145	20	)	)	PUNCT
ejpam-3248	145	21	,	,	PUNCT
ejpam-3248	145	22	(	(	PUNCT
ejpam-3248	145	23	3.25	3.25	NUM
ejpam-3248	145	24	)	)	PUNCT
ejpam-3248	145	25	gives	give	VERB
ejpam-3248	145	26	d(z)yzd(z)wd(z)−	d(z)yzd(z)wd(z)−	NUM
ejpam-3248	145	27	d(z)yd(z)zwd(z	d(z)yd(z)zwd(z	NOUN
ejpam-3248	145	28	)	)	PUNCT
ejpam-3248	145	29	=	=	SYM
ejpam-3248	146	1	0	0	X
ejpam-3248	146	2	.	.	PUNCT
ejpam-3248	147	1	this	this	PRON
ejpam-3248	147	2	implies	imply	VERB
ejpam-3248	147	3	that	that	SCONJ
ejpam-3248	147	4	d(z)y[d(z	d(z)y[d(z	NOUN
ejpam-3248	147	5	)	)	PUNCT
ejpam-3248	147	6	,	,	PUNCT
ejpam-3248	147	7	z]wd(z	z]wd(z	NUM
ejpam-3248	147	8	)	)	PUNCT
ejpam-3248	147	9	=	=	SYM
ejpam-3248	147	10	0	0	NUM
ejpam-3248	147	11	for	for	ADP
ejpam-3248	147	12	all	all	DET
ejpam-3248	147	13	y	y	PROPN
ejpam-3248	147	14	,	,	PUNCT
ejpam-3248	147	15	z	z	NOUN
ejpam-3248	147	16	,	,	PUNCT
ejpam-3248	147	17	w	w	PROPN
ejpam-3248	147	18	∈	∈	PROPN
ejpam-3248	147	19	i.	i.	NOUN
ejpam-3248	147	20	this	this	PRON
ejpam-3248	147	21	yields	yield	VERB
ejpam-3248	147	22	that	that	SCONJ
ejpam-3248	148	1	[	[	X
ejpam-3248	148	2	d(z	d(z	NOUN
ejpam-3248	148	3	)	)	PUNCT
ejpam-3248	148	4	,	,	PUNCT
ejpam-3248	148	5	z]y[d(z	z]y[d(z	NUM
ejpam-3248	148	6	)	)	PUNCT
ejpam-3248	148	7	,	,	PUNCT
ejpam-3248	148	8	z]w[d(z	z]w[d(z	NOUN
ejpam-3248	148	9	)	)	PUNCT
ejpam-3248	148	10	,	,	PUNCT
ejpam-3248	148	11	z	z	X
ejpam-3248	148	12	]	]	X
ejpam-3248	148	13	=	=	SYM
ejpam-3248	148	14	0	0	NUM
ejpam-3248	148	15	for	for	ADP
ejpam-3248	148	16	all	all	DET
ejpam-3248	148	17	y	y	PROPN
ejpam-3248	148	18	,	,	PUNCT
ejpam-3248	148	19	z	z	NOUN
ejpam-3248	148	20	,	,	PUNCT
ejpam-3248	148	21	w	w	PROPN
ejpam-3248	148	22	∈	∈	PROPN
ejpam-3248	148	23	i.	i.	NOUN
ejpam-3248	148	24	that	that	PRON
ejpam-3248	148	25	is	be	AUX
ejpam-3248	148	26	(	(	PUNCT
ejpam-3248	148	27	i[d(z	i[d(z	X
ejpam-3248	148	28	)	)	PUNCT
ejpam-3248	148	29	,	,	PUNCT
ejpam-3248	148	30	z])3	z])3	NUM
ejpam-3248	149	1	=	=	SYM
ejpam-3248	149	2	0	0	NUM
ejpam-3248	150	1	for	for	ADP
ejpam-3248	150	2	all	all	DET
ejpam-3248	150	3	z	z	PROPN
ejpam-3248	150	4	∈	∈	PROPN
ejpam-3248	150	5	i.	i.	NOUN
ejpam-3248	150	6	since	since	SCONJ
ejpam-3248	150	7	a	a	DET
ejpam-3248	150	8	semiprime	semiprime	NOUN
ejpam-3248	150	9	ring	ring	NOUN
ejpam-3248	150	10	has	have	VERB
ejpam-3248	150	11	no	no	DET
ejpam-3248	150	12	non	non	ADJ
ejpam-3248	150	13	-	-	ADJ
ejpam-3248	150	14	zero	zero	ADJ
ejpam-3248	150	15	nilpotent	nilpotent	NOUN
ejpam-3248	150	16	left	leave	VERB
ejpam-3248	150	17	ideal	ideal	ADJ
ejpam-3248	150	18	,	,	PUNCT
ejpam-3248	150	19	we	we	PRON
ejpam-3248	150	20	get	get	VERB
ejpam-3248	150	21	i[d(z	i[d(z	NOUN
ejpam-3248	150	22	)	)	PUNCT
ejpam-3248	150	23	,	,	PUNCT
ejpam-3248	150	24	z	z	X
ejpam-3248	150	25	]	]	X
ejpam-3248	150	26	=	=	SYM
ejpam-3248	150	27	0	0	NUM
ejpam-3248	150	28	which	which	PRON
ejpam-3248	150	29	implies	imply	VERB
ejpam-3248	150	30	that	that	SCONJ
ejpam-3248	151	1	[	[	X
ejpam-3248	151	2	d(z	d(z	NOUN
ejpam-3248	151	3	)	)	PUNCT
ejpam-3248	151	4	,	,	PUNCT
ejpam-3248	151	5	z	z	X
ejpam-3248	151	6	]	]	X
ejpam-3248	151	7	∈	∈	PROPN
ejpam-3248	151	8	i∩annr(i	i∩annr(i	NUM
ejpam-3248	151	9	)	)	PUNCT
ejpam-3248	151	10	.	.	PUNCT
ejpam-3248	152	1	by	by	ADP
ejpam-3248	152	2	lemma	lemma	PROPN
ejpam-3248	152	3	2.2	2.2	NUM
ejpam-3248	152	4	,	,	PUNCT
ejpam-3248	152	5	we	we	PRON
ejpam-3248	152	6	get	get	VERB
ejpam-3248	152	7	[	[	X
ejpam-3248	152	8	d(z	d(z	NOUN
ejpam-3248	152	9	)	)	PUNCT
ejpam-3248	152	10	,	,	PUNCT
ejpam-3248	153	1	z	z	X
ejpam-3248	153	2	]	]	X
ejpam-3248	153	3	=	=	SYM
ejpam-3248	153	4	0	0	X
ejpam-3248	153	5	.	.	PUNCT
ejpam-3248	154	1	similarly	similarly	ADV
ejpam-3248	154	2	we	we	PRON
ejpam-3248	154	3	can	can	AUX
ejpam-3248	154	4	prove	prove	VERB
ejpam-3248	154	5	the	the	DET
ejpam-3248	154	6	result	result	NOUN
ejpam-3248	154	7	for	for	ADP
ejpam-3248	154	8	the	the	DET
ejpam-3248	154	9	case	case	NOUN
ejpam-3248	154	10	f	f	X
ejpam-3248	154	11	(	(	PUNCT
ejpam-3248	154	12	x)f	x)f	X
ejpam-3248	154	13	(	(	PUNCT
ejpam-3248	154	14	y)−	y)−	PROPN
ejpam-3248	154	15	yx	yx	ADP
ejpam-3248	154	16	∈	∈	PROPN
ejpam-3248	154	17	z(r	z(r	PROPN
ejpam-3248	154	18	)	)	PUNCT
ejpam-3248	154	19	for	for	ADP
ejpam-3248	154	20	all	all	DET
ejpam-3248	154	21	x	x	NOUN
ejpam-3248	154	22	,	,	PUNCT
ejpam-3248	154	23	y	y	PROPN
ejpam-3248	154	24	∈	∈	PROPN
ejpam-3248	154	25	i.	i.	NOUN
ejpam-3248	154	26	theorem	theorem	VERB
ejpam-3248	154	27	3.3	3.3	NUM
ejpam-3248	154	28	.	.	PUNCT
ejpam-3248	155	1	let	let	VERB
ejpam-3248	155	2	r	r	PRON
ejpam-3248	155	3	be	be	AUX
ejpam-3248	155	4	a	a	DET
ejpam-3248	155	5	semiprime	semiprime	NOUN
ejpam-3248	155	6	ring	ring	NOUN
ejpam-3248	155	7	and	and	CCONJ
ejpam-3248	155	8	f	f	PROPN
ejpam-3248	155	9	be	be	AUX
ejpam-3248	155	10	a	a	DET
ejpam-3248	155	11	non	non	ADJ
ejpam-3248	155	12	-	-	ADJ
ejpam-3248	155	13	zero	zero	ADJ
ejpam-3248	155	14	multiplicative	multiplicative	ADJ
ejpam-3248	155	15	(	(	PUNCT
ejpam-3248	155	16	generalized	generalized	ADJ
ejpam-3248	155	17	)	)	PUNCT
ejpam-3248	155	18	reverse	reverse	ADJ
ejpam-3248	155	19	derivation	derivation	NOUN
ejpam-3248	155	20	associated	associate	VERB
ejpam-3248	155	21	with	with	ADP
ejpam-3248	155	22	a	a	DET
ejpam-3248	155	23	map	map	NOUN
ejpam-3248	156	1	d	d	NOUN
ejpam-3248	156	2	,	,	PUNCT
ejpam-3248	156	3	i	i	PRON
ejpam-3248	156	4	be	be	VERB
ejpam-3248	156	5	a	a	DET
ejpam-3248	156	6	non	non	ADJ
ejpam-3248	156	7	-	-	ADJ
ejpam-3248	156	8	zero	zero	NUM
ejpam-3248	156	9	ideal	ideal	NOUN
ejpam-3248	156	10	of	of	ADP
ejpam-3248	156	11	r.	r.	PROPN
ejpam-3248	156	12	if	if	SCONJ
ejpam-3248	156	13	f	f	PROPN
ejpam-3248	156	14	(	(	PUNCT
ejpam-3248	156	15	xy)±	xy)±	VERB
ejpam-3248	156	16	[	[	X
ejpam-3248	156	17	x	x	X
ejpam-3248	156	18	,	,	PUNCT
ejpam-3248	156	19	y	y	PROPN
ejpam-3248	156	20	]	]	X
ejpam-3248	156	21	∈	∈	PROPN
ejpam-3248	156	22	z(r	z(r	PROPN
ejpam-3248	156	23	)	)	PUNCT
ejpam-3248	156	24	for	for	ADP
ejpam-3248	156	25	all	all	DET
ejpam-3248	156	26	x	x	NOUN
ejpam-3248	156	27	,	,	PUNCT
ejpam-3248	156	28	y	y	PROPN
ejpam-3248	156	29	∈	∈	PROPN
ejpam-3248	157	1	i	i	PRON
ejpam-3248	157	2	,	,	PUNCT
ejpam-3248	157	3	then	then	ADV
ejpam-3248	157	4	x[d(x	x[d(x	PROPN
ejpam-3248	157	5	)	)	PUNCT
ejpam-3248	157	6	,	,	PUNCT
ejpam-3248	157	7	x]2	x]2	PUNCT
ejpam-3248	158	1	=	=	SYM
ejpam-3248	158	2	0	0	PROPN
ejpam-3248	158	3	for	for	ADP
ejpam-3248	158	4	all	all	DET
ejpam-3248	158	5	x	x	SYM
ejpam-3248	158	6	∈	∈	NOUN
ejpam-3248	158	7	i.	i.	NOUN
ejpam-3248	158	8	proof	proof	NOUN
ejpam-3248	158	9	by	by	ADP
ejpam-3248	158	10	the	the	DET
ejpam-3248	158	11	hypothesis	hypothesis	NOUN
ejpam-3248	158	12	,	,	PUNCT
ejpam-3248	158	13	we	we	PRON
ejpam-3248	158	14	have	have	VERB
ejpam-3248	158	15	f	f	PROPN
ejpam-3248	158	16	(	(	PUNCT
ejpam-3248	158	17	xy	xy	PROPN
ejpam-3248	158	18	)	)	PUNCT
ejpam-3248	159	1	+	+	CCONJ
ejpam-3248	160	1	[	[	X
ejpam-3248	160	2	x	x	X
ejpam-3248	160	3	,	,	PUNCT
ejpam-3248	160	4	y	y	PROPN
ejpam-3248	160	5	]	]	X
ejpam-3248	160	6	∈	∈	PROPN
ejpam-3248	160	7	z(r	z(r	PROPN
ejpam-3248	160	8	)	)	PUNCT
ejpam-3248	160	9	for	for	ADP
ejpam-3248	160	10	all	all	DET
ejpam-3248	160	11	x	x	NOUN
ejpam-3248	160	12	,	,	PUNCT
ejpam-3248	160	13	y	y	PROPN
ejpam-3248	160	14	∈	∈	PROPN
ejpam-3248	160	15	i.	i.	NOUN
ejpam-3248	160	16	(	(	PUNCT
ejpam-3248	160	17	3.26	3.26	NUM
ejpam-3248	160	18	)	)	PUNCT
ejpam-3248	160	19	replacing	replace	VERB
ejpam-3248	160	20	x	x	PUNCT
ejpam-3248	160	21	by	by	ADP
ejpam-3248	160	22	zx	zx	PROPN
ejpam-3248	160	23	in	in	ADP
ejpam-3248	160	24	(	(	PUNCT
ejpam-3248	160	25	3.26	3.26	NUM
ejpam-3248	160	26	)	)	PUNCT
ejpam-3248	160	27	,	,	PUNCT
ejpam-3248	160	28	we	we	PRON
ejpam-3248	160	29	get	get	VERB
ejpam-3248	160	30	f	f	PROPN
ejpam-3248	160	31	(	(	PUNCT
ejpam-3248	160	32	xy)z	xy)z	PROPN
ejpam-3248	160	33	+	+	NUM
ejpam-3248	160	34	xyd(z	xyd(z	PROPN
ejpam-3248	160	35	)	)	PUNCT
ejpam-3248	161	1	+	+	CCONJ
ejpam-3248	161	2	z[x	z[x	PROPN
ejpam-3248	161	3	,	,	PUNCT
ejpam-3248	161	4	y	y	X
ejpam-3248	161	5	]	]	PUNCT
ejpam-3248	162	1	+	+	CCONJ
ejpam-3248	163	1	[	[	X
ejpam-3248	163	2	z	z	X
ejpam-3248	163	3	,	,	PUNCT
ejpam-3248	163	4	y]x	y]x	PROPN
ejpam-3248	163	5	∈	∈	PROPN
ejpam-3248	163	6	z(r	z(r	PROPN
ejpam-3248	163	7	)	)	PUNCT
ejpam-3248	163	8	for	for	ADP
ejpam-3248	163	9	all	all	DET
ejpam-3248	163	10	x	x	NOUN
ejpam-3248	163	11	,	,	PUNCT
ejpam-3248	163	12	y	y	PROPN
ejpam-3248	163	13	,	,	PUNCT
ejpam-3248	163	14	z	z	PROPN
ejpam-3248	163	15	∈	∈	PROPN
ejpam-3248	163	16	i.	i.	NOUN
ejpam-3248	163	17	this	this	PRON
ejpam-3248	163	18	implies	imply	VERB
ejpam-3248	163	19	that	that	SCONJ
ejpam-3248	163	20	(	(	PUNCT
ejpam-3248	163	21	f	f	X
ejpam-3248	163	22	(	(	PUNCT
ejpam-3248	163	23	xy	xy	PROPN
ejpam-3248	163	24	)	)	PUNCT
ejpam-3248	164	1	+	+	CCONJ
ejpam-3248	165	1	[	[	X
ejpam-3248	165	2	x	x	X
ejpam-3248	165	3	,	,	PUNCT
ejpam-3248	165	4	y])z	y])z	PROPN
ejpam-3248	165	5	+	+	CCONJ
ejpam-3248	165	6	xyd(z	xyd(z	NOUN
ejpam-3248	165	7	)	)	PUNCT
ejpam-3248	166	1	+	+	CCONJ
ejpam-3248	167	1	[	[	X
ejpam-3248	167	2	z	z	X
ejpam-3248	167	3	,	,	PUNCT
ejpam-3248	167	4	[	[	X
ejpam-3248	167	5	x	x	X
ejpam-3248	167	6	,	,	PUNCT
ejpam-3248	167	7	y	y	PROPN
ejpam-3248	167	8	]	]	X
ejpam-3248	167	9	]	]	PUNCT
ejpam-3248	168	1	+	+	CCONJ
ejpam-3248	169	1	[	[	X
ejpam-3248	169	2	z	z	X
ejpam-3248	169	3	,	,	PUNCT
ejpam-3248	169	4	y]x	y]x	PROPN
ejpam-3248	169	5	∈	∈	PROPN
ejpam-3248	169	6	z(r	z(r	PROPN
ejpam-3248	169	7	)	)	PUNCT
ejpam-3248	169	8	.	.	PUNCT
ejpam-3248	170	1	(	(	PUNCT
ejpam-3248	170	2	3.27	3.27	NUM
ejpam-3248	170	3	)	)	PUNCT
ejpam-3248	170	4	commuting	commuting	NOUN
ejpam-3248	170	5	(	(	PUNCT
ejpam-3248	170	6	3.27	3.27	NUM
ejpam-3248	170	7	)	)	PUNCT
ejpam-3248	170	8	with	with	ADP
ejpam-3248	170	9	z	z	NOUN
ejpam-3248	170	10	and	and	CCONJ
ejpam-3248	170	11	using	use	VERB
ejpam-3248	170	12	(	(	PUNCT
ejpam-3248	170	13	3.26	3.26	NUM
ejpam-3248	170	14	)	)	PUNCT
ejpam-3248	170	15	,	,	PUNCT
ejpam-3248	170	16	we	we	PRON
ejpam-3248	170	17	get	get	VERB
ejpam-3248	170	18	[	[	X
ejpam-3248	170	19	xyd(z	xyd(z	NOUN
ejpam-3248	170	20	)	)	PUNCT
ejpam-3248	170	21	,	,	PUNCT
ejpam-3248	171	1	z	z	X
ejpam-3248	171	2	]	]	X
ejpam-3248	172	1	+	+	CCONJ
ejpam-3248	173	1	[	[	X
ejpam-3248	173	2	[	[	X
ejpam-3248	173	3	z	z	X
ejpam-3248	173	4	,	,	PUNCT
ejpam-3248	173	5	[	[	X
ejpam-3248	173	6	x	x	X
ejpam-3248	173	7	,	,	PUNCT
ejpam-3248	173	8	y	y	PROPN
ejpam-3248	173	9	]	]	X
ejpam-3248	173	10	]	]	X
ejpam-3248	173	11	,	,	PUNCT
ejpam-3248	173	12	z	z	X
ejpam-3248	173	13	]	]	X
ejpam-3248	173	14	+	+	CCONJ
ejpam-3248	174	1	[	[	X
ejpam-3248	174	2	[	[	X
ejpam-3248	174	3	z	z	NOUN
ejpam-3248	174	4	,	,	PUNCT
ejpam-3248	174	5	y]x	y]x	NOUN
ejpam-3248	174	6	,	,	PUNCT
ejpam-3248	174	7	z	z	X
ejpam-3248	174	8	]	]	X
ejpam-3248	174	9	=	=	SYM
ejpam-3248	174	10	0	0	NUM
ejpam-3248	174	11	for	for	ADP
ejpam-3248	174	12	all	all	DET
ejpam-3248	174	13	x	x	NOUN
ejpam-3248	174	14	,	,	PUNCT
ejpam-3248	174	15	y	y	PROPN
ejpam-3248	174	16	,	,	PUNCT
ejpam-3248	174	17	z	z	PROPN
ejpam-3248	174	18	∈	∈	PROPN
ejpam-3248	174	19	i.	i.	NOUN
ejpam-3248	174	20	(	(	PUNCT
ejpam-3248	174	21	3.28	3.28	NUM
ejpam-3248	174	22	)	)	PUNCT
ejpam-3248	174	23	replacing	replace	VERB
ejpam-3248	174	24	y	y	PRON
ejpam-3248	174	25	by	by	ADP
ejpam-3248	174	26	zy	zy	PROPN
ejpam-3248	174	27	in	in	ADP
ejpam-3248	174	28	(	(	PUNCT
ejpam-3248	174	29	3.28	3.28	NUM
ejpam-3248	174	30	)	)	PUNCT
ejpam-3248	174	31	,	,	PUNCT
ejpam-3248	174	32	we	we	PRON
ejpam-3248	174	33	get	get	VERB
ejpam-3248	174	34	[	[	X
ejpam-3248	174	35	xzyd(z	xzyd(z	PROPN
ejpam-3248	174	36	)	)	PUNCT
ejpam-3248	174	37	,	,	PUNCT
ejpam-3248	175	1	z	z	X
ejpam-3248	175	2	]	]	X
ejpam-3248	176	1	+	+	CCONJ
ejpam-3248	177	1	[	[	X
ejpam-3248	177	2	[	[	X
ejpam-3248	177	3	z	z	X
ejpam-3248	177	4	,	,	PUNCT
ejpam-3248	177	5	[	[	X
ejpam-3248	177	6	x	x	X
ejpam-3248	177	7	,	,	PUNCT
ejpam-3248	177	8	zy	zy	PROPN
ejpam-3248	177	9	]	]	X
ejpam-3248	177	10	]	]	X
ejpam-3248	177	11	,	,	PUNCT
ejpam-3248	177	12	z	z	X
ejpam-3248	177	13	]	]	X
ejpam-3248	178	1	+	+	CCONJ
ejpam-3248	178	2	[	[	X
ejpam-3248	178	3	[	[	X
ejpam-3248	178	4	z	z	PROPN
ejpam-3248	178	5	,	,	PUNCT
ejpam-3248	178	6	zy]x	zy]x	PROPN
ejpam-3248	178	7	,	,	PUNCT
ejpam-3248	178	8	z	z	X
ejpam-3248	178	9	]	]	X
ejpam-3248	178	10	=	=	SYM
ejpam-3248	178	11	0	0	X
ejpam-3248	178	12	.	.	PUNCT
ejpam-3248	179	1	[	[	X
ejpam-3248	179	2	xzyd(z	xzyd(z	NOUN
ejpam-3248	179	3	)	)	PUNCT
ejpam-3248	179	4	,	,	PUNCT
ejpam-3248	180	1	z	z	X
ejpam-3248	180	2	]	]	X
ejpam-3248	181	1	+	+	CCONJ
ejpam-3248	181	2	[	[	X
ejpam-3248	181	3	[	[	X
ejpam-3248	181	4	z	z	NOUN
ejpam-3248	181	5	,	,	PUNCT
ejpam-3248	181	6	z[x	z[x	PROPN
ejpam-3248	181	7	,	,	PUNCT
ejpam-3248	181	8	y	y	PROPN
ejpam-3248	181	9	]	]	PUNCT
ejpam-3248	182	1	+	+	CCONJ
ejpam-3248	183	1	[	[	X
ejpam-3248	183	2	x	x	X
ejpam-3248	183	3	,	,	PUNCT
ejpam-3248	183	4	z]y	z]y	PRON
ejpam-3248	183	5	]	]	X
ejpam-3248	183	6	,	,	PUNCT
ejpam-3248	183	7	z	z	X
ejpam-3248	183	8	]	]	X
ejpam-3248	184	1	+	+	CCONJ
ejpam-3248	184	2	[	[	X
ejpam-3248	184	3	z[z	z[z	NUM
ejpam-3248	184	4	,	,	PUNCT
ejpam-3248	184	5	y]x	y]x	NOUN
ejpam-3248	184	6	,	,	PUNCT
ejpam-3248	184	7	z	z	X
ejpam-3248	184	8	]	]	X
ejpam-3248	184	9	=	=	SYM
ejpam-3248	184	10	0	0	X
ejpam-3248	184	11	.	.	PUNCT
ejpam-3248	185	1	[	[	X
ejpam-3248	185	2	xzyd(z	xzyd(z	NOUN
ejpam-3248	185	3	)	)	PUNCT
ejpam-3248	185	4	,	,	PUNCT
ejpam-3248	186	1	z	z	X
ejpam-3248	186	2	]	]	X
ejpam-3248	187	1	+	+	CCONJ
ejpam-3248	187	2	[	[	X
ejpam-3248	187	3	[	[	X
ejpam-3248	187	4	z	z	NOUN
ejpam-3248	187	5	,	,	PUNCT
ejpam-3248	187	6	z[x	z[x	PROPN
ejpam-3248	187	7	,	,	PUNCT
ejpam-3248	187	8	y	y	PROPN
ejpam-3248	187	9	]	]	X
ejpam-3248	187	10	]	]	X
ejpam-3248	187	11	,	,	PUNCT
ejpam-3248	187	12	z	z	X
ejpam-3248	187	13	]	]	X
ejpam-3248	188	1	+	+	CCONJ
ejpam-3248	189	1	[	[	X
ejpam-3248	189	2	[	[	X
ejpam-3248	189	3	z	z	X
ejpam-3248	189	4	,	,	PUNCT
ejpam-3248	189	5	[	[	X
ejpam-3248	189	6	x	x	X
ejpam-3248	189	7	,	,	PUNCT
ejpam-3248	189	8	z]y	z]y	PRON
ejpam-3248	189	9	]	]	X
ejpam-3248	189	10	,	,	PUNCT
ejpam-3248	189	11	z	z	X
ejpam-3248	189	12	]	]	X
ejpam-3248	189	13	+	+	CCONJ
ejpam-3248	189	14	z[[z	z[[z	PROPN
ejpam-3248	189	15	,	,	PUNCT
ejpam-3248	189	16	y]x	y]x	NOUN
ejpam-3248	189	17	,	,	PUNCT
ejpam-3248	189	18	z	z	X
ejpam-3248	189	19	]	]	X
ejpam-3248	189	20	=	=	SYM
ejpam-3248	189	21	0	0	X
ejpam-3248	189	22	.	.	PUNCT
ejpam-3248	190	1	this	this	PRON
ejpam-3248	190	2	implies	imply	VERB
ejpam-3248	190	3	that	that	SCONJ
ejpam-3248	190	4	[	[	X
ejpam-3248	190	5	xzyd(z	xzyd(z	NOUN
ejpam-3248	190	6	)	)	PUNCT
ejpam-3248	190	7	,	,	PUNCT
ejpam-3248	190	8	z	z	X
ejpam-3248	190	9	]	]	X
ejpam-3248	191	1	+	+	CCONJ
ejpam-3248	191	2	z[[z	z[[z	PROPN
ejpam-3248	191	3	,	,	PUNCT
ejpam-3248	191	4	[	[	X
ejpam-3248	191	5	x	x	X
ejpam-3248	191	6	,	,	PUNCT
ejpam-3248	191	7	y	y	PROPN
ejpam-3248	191	8	]	]	X
ejpam-3248	191	9	]	]	X
ejpam-3248	191	10	,	,	PUNCT
ejpam-3248	191	11	z	z	X
ejpam-3248	191	12	]	]	X
ejpam-3248	192	1	+	+	CCONJ
ejpam-3248	193	1	[	[	X
ejpam-3248	193	2	[	[	X
ejpam-3248	193	3	x	x	X
ejpam-3248	193	4	,	,	PUNCT
ejpam-3248	193	5	z][z	z][z	PROPN
ejpam-3248	193	6	,	,	PUNCT
ejpam-3248	193	7	y	y	NOUN
ejpam-3248	193	8	]	]	X
ejpam-3248	193	9	,	,	PUNCT
ejpam-3248	193	10	z	z	X
ejpam-3248	193	11	]	]	X
ejpam-3248	194	1	+	+	CCONJ
ejpam-3248	195	1	[	[	X
ejpam-3248	195	2	[	[	X
ejpam-3248	195	3	z	z	X
ejpam-3248	195	4	,	,	PUNCT
ejpam-3248	195	5	[	[	X
ejpam-3248	195	6	x	x	X
ejpam-3248	195	7	,	,	PUNCT
ejpam-3248	195	8	z]]y	z]]y	PROPN
ejpam-3248	195	9	,	,	PUNCT
ejpam-3248	195	10	z	z	NOUN
ejpam-3248	195	11	]	]	X
ejpam-3248	195	12	+	+	CCONJ
ejpam-3248	195	13	z[[z	z[[z	PROPN
ejpam-3248	195	14	,	,	PUNCT
ejpam-3248	195	15	y]x	y]x	NOUN
ejpam-3248	195	16	,	,	PUNCT
ejpam-3248	195	17	z	z	X
ejpam-3248	195	18	]	]	X
ejpam-3248	195	19	=	=	SYM
ejpam-3248	195	20	0	0	X
ejpam-3248	195	21	.	.	PUNCT
ejpam-3248	195	22	(	(	PUNCT
ejpam-3248	195	23	3.29	3.29	NUM
ejpam-3248	195	24	)	)	PUNCT
ejpam-3248	195	25	left	leave	VERB
ejpam-3248	195	26	multiplying	multiplying	NOUN
ejpam-3248	195	27	(	(	PUNCT
ejpam-3248	195	28	3.28	3.28	NUM
ejpam-3248	195	29	)	)	PUNCT
ejpam-3248	195	30	by	by	ADP
ejpam-3248	195	31	z	z	NOUN
ejpam-3248	195	32	and	and	CCONJ
ejpam-3248	195	33	subtracting	subtract	VERB
ejpam-3248	195	34	from	from	ADP
ejpam-3248	195	35	(	(	PUNCT
ejpam-3248	195	36	3.29	3.29	NUM
ejpam-3248	195	37	)	)	PUNCT
ejpam-3248	195	38	,	,	PUNCT
ejpam-3248	195	39	we	we	PRON
ejpam-3248	195	40	obtain	obtain	VERB
ejpam-3248	195	41	[	[	X
ejpam-3248	195	42	[	[	X
ejpam-3248	195	43	z	z	X
ejpam-3248	195	44	,	,	PUNCT
ejpam-3248	195	45	x]yd(z	x]yd(z	PROPN
ejpam-3248	195	46	)	)	PUNCT
ejpam-3248	195	47	,	,	PUNCT
ejpam-3248	195	48	z]−	z]−	PUNCT
ejpam-3248	196	1	[	[	X
ejpam-3248	196	2	[	[	X
ejpam-3248	196	3	x	x	X
ejpam-3248	196	4	,	,	PUNCT
ejpam-3248	196	5	z][z	z][z	PROPN
ejpam-3248	196	6	,	,	PUNCT
ejpam-3248	196	7	y	y	NOUN
ejpam-3248	196	8	]	]	X
ejpam-3248	196	9	,	,	PUNCT
ejpam-3248	196	10	z]−	z]−	PUNCT
ejpam-3248	197	1	[	[	X
ejpam-3248	197	2	[	[	X
ejpam-3248	197	3	z	z	X
ejpam-3248	197	4	,	,	PUNCT
ejpam-3248	197	5	[	[	X
ejpam-3248	197	6	x	x	X
ejpam-3248	197	7	,	,	PUNCT
ejpam-3248	197	8	z]]y	z]]y	PROPN
ejpam-3248	197	9	,	,	PUNCT
ejpam-3248	197	10	z	z	NOUN
ejpam-3248	197	11	]	]	X
ejpam-3248	197	12	=	=	SYM
ejpam-3248	197	13	0	0	NUM
ejpam-3248	197	14	for	for	ADP
ejpam-3248	197	15	all	all	DET
ejpam-3248	197	16	x	x	NOUN
ejpam-3248	197	17	,	,	PUNCT
ejpam-3248	197	18	y	y	PROPN
ejpam-3248	197	19	,	,	PUNCT
ejpam-3248	197	20	z	z	PROPN
ejpam-3248	197	21	∈	∈	PROPN
ejpam-3248	197	22	i.	i.	NOUN
ejpam-3248	197	23	(	(	PUNCT
ejpam-3248	197	24	3.30	3.30	NUM
ejpam-3248	197	25	)	)	PUNCT
ejpam-3248	197	26	a.	a.	PROPN
ejpam-3248	197	27	ali	ali	PROPN
ejpam-3248	197	28	,	,	PUNCT
ejpam-3248	197	29	a.	a.	PROPN
ejpam-3248	197	30	bano	bano	PROPN
ejpam-3248	197	31	/	/	SYM
ejpam-3248	197	32	eur	eur	PROPN
ejpam-3248	197	33	.	.	PUNCT
ejpam-3248	198	1	j.	j.	PROPN
ejpam-3248	198	2	pure	pure	PROPN
ejpam-3248	198	3	appl	appl	PROPN
ejpam-3248	198	4	.	.	PROPN
ejpam-3248	198	5	math	math	PROPN
ejpam-3248	198	6	,	,	PUNCT
ejpam-3248	198	7	11	11	NUM
ejpam-3248	198	8	(	(	PUNCT
ejpam-3248	198	9	3	3	NUM
ejpam-3248	198	10	)	)	PUNCT
ejpam-3248	198	11	(	(	PUNCT
ejpam-3248	198	12	2018	2018	NUM
ejpam-3248	198	13	)	)	PUNCT
ejpam-3248	198	14	,	,	PUNCT
ejpam-3248	198	15	717	717	NUM
ejpam-3248	198	16	-	-	SYM
ejpam-3248	198	17	729	729	NUM
ejpam-3248	198	18	723	723	NUM
ejpam-3248	198	19	replacing	replace	VERB
ejpam-3248	198	20	y	y	PRON
ejpam-3248	198	21	by	by	ADP
ejpam-3248	198	22	yz	yz	PROPN
ejpam-3248	198	23	in	in	ADP
ejpam-3248	198	24	(	(	PUNCT
ejpam-3248	198	25	3.30	3.30	NUM
ejpam-3248	198	26	)	)	PUNCT
ejpam-3248	198	27	,	,	PUNCT
ejpam-3248	198	28	we	we	PRON
ejpam-3248	198	29	get	get	VERB
ejpam-3248	198	30	[	[	X
ejpam-3248	198	31	[	[	X
ejpam-3248	198	32	z	z	X
ejpam-3248	198	33	,	,	PUNCT
ejpam-3248	198	34	x]yzd(z	x]yzd(z	PROPN
ejpam-3248	198	35	)	)	PUNCT
ejpam-3248	198	36	,	,	PUNCT
ejpam-3248	198	37	z]−	z]−	PUNCT
ejpam-3248	199	1	[	[	X
ejpam-3248	199	2	[	[	X
ejpam-3248	199	3	x	x	X
ejpam-3248	199	4	,	,	PUNCT
ejpam-3248	199	5	z][z	z][z	PROPN
ejpam-3248	199	6	,	,	PUNCT
ejpam-3248	199	7	y	y	NOUN
ejpam-3248	199	8	]	]	X
ejpam-3248	199	9	,	,	PUNCT
ejpam-3248	199	10	z]z	z]z	NOUN
ejpam-3248	199	11	−	−	PUNCT
ejpam-3248	200	1	[	[	X
ejpam-3248	200	2	[	[	X
ejpam-3248	200	3	z	z	X
ejpam-3248	200	4	,	,	PUNCT
ejpam-3248	200	5	[	[	X
ejpam-3248	200	6	x	x	X
ejpam-3248	200	7	,	,	PUNCT
ejpam-3248	200	8	z]]y	z]]y	PROPN
ejpam-3248	200	9	,	,	PUNCT
ejpam-3248	200	10	z]z	z]z	NOUN
ejpam-3248	200	11	=	=	SYM
ejpam-3248	200	12	0	0	X
ejpam-3248	200	13	.	.	PUNCT
ejpam-3248	200	14	(	(	PUNCT
ejpam-3248	200	15	3.31	3.31	NUM
ejpam-3248	200	16	)	)	PUNCT
ejpam-3248	200	17	right	right	ADJ
ejpam-3248	200	18	multiplying	multiplying	NOUN
ejpam-3248	200	19	(	(	PUNCT
ejpam-3248	200	20	3.30	3.30	NUM
ejpam-3248	200	21	)	)	PUNCT
ejpam-3248	200	22	by	by	ADP
ejpam-3248	200	23	z	z	NOUN
ejpam-3248	200	24	and	and	CCONJ
ejpam-3248	200	25	subtracting	subtract	VERB
ejpam-3248	200	26	from	from	ADP
ejpam-3248	200	27	(	(	PUNCT
ejpam-3248	200	28	3.31	3.31	NUM
ejpam-3248	200	29	)	)	PUNCT
ejpam-3248	200	30	,	,	PUNCT
ejpam-3248	200	31	we	we	PRON
ejpam-3248	200	32	obtain	obtain	VERB
ejpam-3248	200	33	[	[	X
ejpam-3248	200	34	[	[	X
ejpam-3248	200	35	z	z	X
ejpam-3248	200	36	,	,	PUNCT
ejpam-3248	200	37	x]y[d(z	x]y[d(z	NOUN
ejpam-3248	200	38	)	)	PUNCT
ejpam-3248	200	39	,	,	PUNCT
ejpam-3248	200	40	z	z	X
ejpam-3248	200	41	]	]	X
ejpam-3248	200	42	,	,	PUNCT
ejpam-3248	200	43	z	z	X
ejpam-3248	200	44	]	]	X
ejpam-3248	200	45	=	=	SYM
ejpam-3248	200	46	0	0	NUM
ejpam-3248	200	47	for	for	ADP
ejpam-3248	200	48	all	all	DET
ejpam-3248	200	49	x	x	NOUN
ejpam-3248	200	50	,	,	PUNCT
ejpam-3248	200	51	y	y	PROPN
ejpam-3248	200	52	,	,	PUNCT
ejpam-3248	200	53	z	z	PROPN
ejpam-3248	200	54	∈	∈	PROPN
ejpam-3248	200	55	i.	i.	NOUN
ejpam-3248	200	56	(	(	PUNCT
ejpam-3248	200	57	3.32	3.32	NUM
ejpam-3248	200	58	)	)	PUNCT
ejpam-3248	200	59	substituting	substitute	VERB
ejpam-3248	200	60	zd(z	zd(z	NOUN
ejpam-3248	200	61	)	)	PUNCT
ejpam-3248	200	62	for	for	SCONJ
ejpam-3248	200	63	x	x	PRON
ejpam-3248	200	64	in	in	ADP
ejpam-3248	200	65	(	(	PUNCT
ejpam-3248	200	66	3.32	3.32	NUM
ejpam-3248	200	67	)	)	PUNCT
ejpam-3248	200	68	,	,	PUNCT
ejpam-3248	200	69	we	we	PRON
ejpam-3248	200	70	get	get	VERB
ejpam-3248	200	71	[	[	NOUN
ejpam-3248	200	72	z[z	z[z	NUM
ejpam-3248	200	73	,	,	PUNCT
ejpam-3248	200	74	d(z)]y[d(z	d(z)]y[d(z	PROPN
ejpam-3248	200	75	)	)	PUNCT
ejpam-3248	200	76	,	,	PUNCT
ejpam-3248	201	1	z	z	X
ejpam-3248	201	2	]	]	X
ejpam-3248	201	3	,	,	PUNCT
ejpam-3248	201	4	z	z	X
ejpam-3248	201	5	]	]	X
ejpam-3248	201	6	=	=	SYM
ejpam-3248	201	7	0	0	NUM
ejpam-3248	201	8	for	for	ADP
ejpam-3248	201	9	all	all	DET
ejpam-3248	201	10	y	y	PROPN
ejpam-3248	201	11	,	,	PUNCT
ejpam-3248	201	12	z	z	PROPN
ejpam-3248	201	13	∈	∈	PROPN
ejpam-3248	201	14	i.	i.	NOUN
ejpam-3248	201	15	(	(	PUNCT
ejpam-3248	201	16	3.33	3.33	NUM
ejpam-3248	201	17	)	)	PUNCT
ejpam-3248	201	18	replacing	replace	VERB
ejpam-3248	201	19	y	y	PRON
ejpam-3248	201	20	by	by	ADP
ejpam-3248	201	21	yz	yz	PROPN
ejpam-3248	201	22	in	in	ADP
ejpam-3248	201	23	(	(	PUNCT
ejpam-3248	201	24	3.33	3.33	NUM
ejpam-3248	201	25	)	)	PUNCT
ejpam-3248	201	26	,	,	PUNCT
ejpam-3248	201	27	we	we	PRON
ejpam-3248	201	28	obtain	obtain	VERB
ejpam-3248	201	29	[	[	X
ejpam-3248	201	30	z[d(z	z[d(z	NOUN
ejpam-3248	201	31	)	)	PUNCT
ejpam-3248	201	32	,	,	PUNCT
ejpam-3248	201	33	z]yz[d(z	z]yz[d(z	X
ejpam-3248	201	34	)	)	PUNCT
ejpam-3248	201	35	,	,	PUNCT
ejpam-3248	202	1	z	z	X
ejpam-3248	202	2	]	]	X
ejpam-3248	202	3	,	,	PUNCT
ejpam-3248	202	4	z	z	X
ejpam-3248	202	5	]	]	X
ejpam-3248	202	6	=	=	SYM
ejpam-3248	202	7	0	0	NUM
ejpam-3248	202	8	for	for	ADP
ejpam-3248	202	9	all	all	DET
ejpam-3248	202	10	y	y	PROPN
ejpam-3248	202	11	,	,	PUNCT
ejpam-3248	202	12	z	z	PROPN
ejpam-3248	202	13	∈	∈	PROPN
ejpam-3248	202	14	i.	i.	NOUN
ejpam-3248	202	15	this	this	PRON
ejpam-3248	202	16	implies	imply	VERB
ejpam-3248	202	17	that	that	SCONJ
ejpam-3248	202	18	z[d(z	z[d(z	NOUN
ejpam-3248	202	19	)	)	PUNCT
ejpam-3248	202	20	,	,	PUNCT
ejpam-3248	202	21	z]yz[d(z	z]yz[d(z	X
ejpam-3248	202	22	)	)	PUNCT
ejpam-3248	202	23	,	,	PUNCT
ejpam-3248	202	24	z]z	z]z	NOUN
ejpam-3248	202	25	−	−	PROPN
ejpam-3248	202	26	z2[d(z	z2[d(z	NOUN
ejpam-3248	202	27	)	)	PUNCT
ejpam-3248	202	28	,	,	PUNCT
ejpam-3248	202	29	z]yz[d(z	z]yz[d(z	X
ejpam-3248	202	30	)	)	PUNCT
ejpam-3248	202	31	,	,	PUNCT
ejpam-3248	203	1	z	z	X
ejpam-3248	203	2	]	]	X
ejpam-3248	203	3	=	=	SYM
ejpam-3248	203	4	0	0	X
ejpam-3248	203	5	.	.	PUNCT
ejpam-3248	204	1	(	(	PUNCT
ejpam-3248	204	2	3.34	3.34	NUM
ejpam-3248	204	3	)	)	PUNCT
ejpam-3248	204	4	replacing	replace	VERB
ejpam-3248	204	5	y	y	PRON
ejpam-3248	204	6	by	by	ADP
ejpam-3248	204	7	yz[d(z	yz[d(z	PROPN
ejpam-3248	204	8	)	)	PUNCT
ejpam-3248	204	9	,	,	PUNCT
ejpam-3248	204	10	z]w	z]w	NOUN
ejpam-3248	204	11	in	in	ADP
ejpam-3248	204	12	(	(	PUNCT
ejpam-3248	204	13	3.34	3.34	NUM
ejpam-3248	204	14	)	)	PUNCT
ejpam-3248	204	15	,	,	PUNCT
ejpam-3248	204	16	we	we	PRON
ejpam-3248	204	17	get	get	VERB
ejpam-3248	204	18	z[d(z	z[d(z	NOUN
ejpam-3248	204	19	)	)	PUNCT
ejpam-3248	204	20	,	,	PUNCT
ejpam-3248	204	21	z]yz[d(z	z]yz[d(z	X
ejpam-3248	204	22	)	)	PUNCT
ejpam-3248	204	23	,	,	PUNCT
ejpam-3248	204	24	z]wz[d(z	z]wz[d(z	NOUN
ejpam-3248	204	25	)	)	PUNCT
ejpam-3248	204	26	,	,	PUNCT
ejpam-3248	204	27	z]z	z]z	NOUN
ejpam-3248	204	28	−	−	PROPN
ejpam-3248	204	29	z2[d(z	z2[d(z	NOUN
ejpam-3248	204	30	)	)	PUNCT
ejpam-3248	204	31	,	,	PUNCT
ejpam-3248	204	32	z]yz[d(z	z]yz[d(z	X
ejpam-3248	204	33	)	)	PUNCT
ejpam-3248	204	34	,	,	PUNCT
ejpam-3248	204	35	z]wz[d(z	z]wz[d(z	NOUN
ejpam-3248	204	36	)	)	PUNCT
ejpam-3248	204	37	,	,	PUNCT
ejpam-3248	205	1	z	z	X
ejpam-3248	205	2	]	]	X
ejpam-3248	205	3	=	=	SYM
ejpam-3248	205	4	0	0	NUM
ejpam-3248	205	5	for	for	ADP
ejpam-3248	205	6	all	all	DET
ejpam-3248	205	7	y	y	PROPN
ejpam-3248	205	8	,	,	PUNCT
ejpam-3248	205	9	z	z	NOUN
ejpam-3248	205	10	,	,	PUNCT
ejpam-3248	205	11	w	w	PROPN
ejpam-3248	205	12	∈	∈	PROPN
ejpam-3248	205	13	i.	i.	NOUN
ejpam-3248	205	14	(	(	PUNCT
ejpam-3248	205	15	3.35	3.35	NUM
ejpam-3248	205	16	)	)	PUNCT
ejpam-3248	205	17	using	use	VERB
ejpam-3248	205	18	(	(	PUNCT
ejpam-3248	205	19	3.34	3.34	NUM
ejpam-3248	205	20	)	)	PUNCT
ejpam-3248	205	21	in	in	ADP
ejpam-3248	205	22	(	(	PUNCT
ejpam-3248	205	23	3.35	3.35	NUM
ejpam-3248	205	24	)	)	PUNCT
ejpam-3248	205	25	,	,	PUNCT
ejpam-3248	205	26	(	(	PUNCT
ejpam-3248	205	27	3.35	3.35	NUM
ejpam-3248	205	28	)	)	PUNCT
ejpam-3248	205	29	yields	yield	NOUN
ejpam-3248	205	30	that	that	SCONJ
ejpam-3248	205	31	z[d(z	z[d(z	NOUN
ejpam-3248	205	32	)	)	PUNCT
ejpam-3248	205	33	,	,	PUNCT
ejpam-3248	205	34	z]yz2[d(z	z]yz2[d(z	NUM
ejpam-3248	205	35	)	)	PUNCT
ejpam-3248	205	36	,	,	PUNCT
ejpam-3248	205	37	z]wz[d(z	z]wz[d(z	NOUN
ejpam-3248	205	38	)	)	PUNCT
ejpam-3248	205	39	,	,	PUNCT
ejpam-3248	205	40	z]−	z]−	PROPN
ejpam-3248	205	41	z[d(z	z[d(z	NOUN
ejpam-3248	205	42	)	)	PUNCT
ejpam-3248	205	43	,	,	PUNCT
ejpam-3248	205	44	z]yz[d(z	z]yz[d(z	X
ejpam-3248	205	45	)	)	PUNCT
ejpam-3248	205	46	,	,	PUNCT
ejpam-3248	205	47	z]zwz[d(z	z]zwz[d(z	X
ejpam-3248	205	48	)	)	PUNCT
ejpam-3248	205	49	,	,	PUNCT
ejpam-3248	205	50	z	z	X
ejpam-3248	205	51	]	]	X
ejpam-3248	205	52	=	=	SYM
ejpam-3248	205	53	0	0	X
ejpam-3248	205	54	.	.	PUNCT
ejpam-3248	206	1	this	this	PRON
ejpam-3248	206	2	implies	imply	VERB
ejpam-3248	206	3	that	that	SCONJ
ejpam-3248	206	4	z[d(z	z[d(z	NOUN
ejpam-3248	206	5	)	)	PUNCT
ejpam-3248	206	6	,	,	PUNCT
ejpam-3248	206	7	z]y[z[d(z	z]y[z[d(z	PROPN
ejpam-3248	206	8	)	)	PUNCT
ejpam-3248	206	9	,	,	PUNCT
ejpam-3248	206	10	z	z	X
ejpam-3248	206	11	]	]	X
ejpam-3248	206	12	,	,	PUNCT
ejpam-3248	206	13	z]wz[d(z	z]wz[d(z	NOUN
ejpam-3248	206	14	)	)	PUNCT
ejpam-3248	206	15	,	,	PUNCT
ejpam-3248	206	16	z	z	X
ejpam-3248	206	17	]	]	X
ejpam-3248	206	18	=	=	SYM
ejpam-3248	206	19	0	0	NUM
ejpam-3248	206	20	for	for	ADP
ejpam-3248	206	21	all	all	DET
ejpam-3248	206	22	y	y	PROPN
ejpam-3248	206	23	,	,	PUNCT
ejpam-3248	206	24	z	z	NOUN
ejpam-3248	206	25	,	,	PUNCT
ejpam-3248	206	26	w	w	PROPN
ejpam-3248	206	27	∈	∈	PROPN
ejpam-3248	206	28	i.	i.	NOUN
ejpam-3248	206	29	after	after	ADP
ejpam-3248	206	30	a	a	DET
ejpam-3248	206	31	simple	simple	ADJ
ejpam-3248	206	32	calculation	calculation	NOUN
ejpam-3248	206	33	this	this	PRON
ejpam-3248	206	34	gives	give	VERB
ejpam-3248	206	35	that	that	SCONJ
ejpam-3248	206	36	[	[	X
ejpam-3248	206	37	z[d(z	z[d(z	NOUN
ejpam-3248	206	38	)	)	PUNCT
ejpam-3248	206	39	,	,	PUNCT
ejpam-3248	206	40	z	z	X
ejpam-3248	206	41	]	]	X
ejpam-3248	206	42	,	,	PUNCT
ejpam-3248	206	43	z]y[z[d(z	z]y[z[d(z	PROPN
ejpam-3248	206	44	)	)	PUNCT
ejpam-3248	206	45	,	,	PUNCT
ejpam-3248	206	46	z	z	X
ejpam-3248	206	47	]	]	X
ejpam-3248	206	48	,	,	PUNCT
ejpam-3248	206	49	z]w[z[d(z	z]w[z[d(z	NOUN
ejpam-3248	206	50	)	)	PUNCT
ejpam-3248	206	51	,	,	PUNCT
ejpam-3248	206	52	z	z	X
ejpam-3248	206	53	]	]	X
ejpam-3248	206	54	,	,	PUNCT
ejpam-3248	206	55	z	z	X
ejpam-3248	206	56	]	]	X
ejpam-3248	206	57	=	=	SYM
ejpam-3248	206	58	0	0	X
ejpam-3248	206	59	.	.	PUNCT
ejpam-3248	207	1	(	(	PUNCT
ejpam-3248	207	2	3.36	3.36	NUM
ejpam-3248	207	3	)	)	PUNCT
ejpam-3248	207	4	this	this	PRON
ejpam-3248	207	5	implies	imply	VERB
ejpam-3248	207	6	that	that	SCONJ
ejpam-3248	207	7	(	(	PUNCT
ejpam-3248	207	8	i[z[d(z	i[z[d(z	NOUN
ejpam-3248	207	9	)	)	PUNCT
ejpam-3248	207	10	,	,	PUNCT
ejpam-3248	208	1	z	z	X
ejpam-3248	208	2	]	]	X
ejpam-3248	208	3	,	,	PUNCT
ejpam-3248	208	4	z])3	z])3	NUM
ejpam-3248	208	5	=	=	SYM
ejpam-3248	208	6	0	0	NUM
ejpam-3248	208	7	for	for	ADP
ejpam-3248	208	8	all	all	DET
ejpam-3248	208	9	z	z	PROPN
ejpam-3248	208	10	∈	∈	PROPN
ejpam-3248	208	11	i.	i.	NOUN
ejpam-3248	208	12	since	since	SCONJ
ejpam-3248	208	13	a	a	DET
ejpam-3248	208	14	semiprime	semiprime	NOUN
ejpam-3248	208	15	ring	ring	NOUN
ejpam-3248	208	16	has	have	VERB
ejpam-3248	208	17	no	no	DET
ejpam-3248	208	18	non	non	ADJ
ejpam-3248	208	19	-	-	ADJ
ejpam-3248	208	20	zero	zero	ADJ
ejpam-3248	208	21	nilpotent	nilpotent	NOUN
ejpam-3248	208	22	left	leave	VERB
ejpam-3248	208	23	ideal	ideal	ADJ
ejpam-3248	208	24	,	,	PUNCT
ejpam-3248	208	25	we	we	PRON
ejpam-3248	208	26	get	get	VERB
ejpam-3248	208	27	i[z[d(z	i[z[d(z	NOUN
ejpam-3248	208	28	)	)	PUNCT
ejpam-3248	208	29	,	,	PUNCT
ejpam-3248	209	1	z	z	X
ejpam-3248	209	2	]	]	X
ejpam-3248	209	3	,	,	PUNCT
ejpam-3248	209	4	z	z	X
ejpam-3248	209	5	]	]	X
ejpam-3248	209	6	=	=	SYM
ejpam-3248	209	7	0	0	NUM
ejpam-3248	209	8	for	for	ADP
ejpam-3248	209	9	all	all	DET
ejpam-3248	209	10	z	z	PROPN
ejpam-3248	209	11	∈	∈	PROPN
ejpam-3248	209	12	i.	i.	NOUN
ejpam-3248	209	13	this	this	PRON
ejpam-3248	209	14	implies	imply	VERB
ejpam-3248	209	15	that	that	SCONJ
ejpam-3248	209	16	[	[	X
ejpam-3248	209	17	z[d(z	z[d(z	NOUN
ejpam-3248	209	18	)	)	PUNCT
ejpam-3248	209	19	,	,	PUNCT
ejpam-3248	209	20	z	z	X
ejpam-3248	209	21	]	]	X
ejpam-3248	209	22	,	,	PUNCT
ejpam-3248	209	23	z	z	X
ejpam-3248	209	24	]	]	X
ejpam-3248	209	25	∈	∈	PROPN
ejpam-3248	209	26	i	i	PRON
ejpam-3248	209	27	∩	∩	ADJ
ejpam-3248	209	28	annr(i	annr(i	NUM
ejpam-3248	209	29	)	)	PUNCT
ejpam-3248	209	30	.	.	PUNCT
ejpam-3248	210	1	by	by	ADP
ejpam-3248	210	2	lemma	lemma	PROPN
ejpam-3248	210	3	2.2	2.2	NUM
ejpam-3248	210	4	,	,	PUNCT
ejpam-3248	210	5	we	we	PRON
ejpam-3248	210	6	get	get	VERB
ejpam-3248	210	7	that	that	PRON
ejpam-3248	210	8	[	[	X
ejpam-3248	210	9	z[d(z	z[d(z	NOUN
ejpam-3248	210	10	)	)	PUNCT
ejpam-3248	210	11	,	,	PUNCT
ejpam-3248	211	1	z	z	X
ejpam-3248	211	2	]	]	X
ejpam-3248	211	3	,	,	PUNCT
ejpam-3248	211	4	z	z	X
ejpam-3248	211	5	]	]	X
ejpam-3248	211	6	=	=	SYM
ejpam-3248	211	7	0	0	NUM
ejpam-3248	211	8	that	that	PRON
ejpam-3248	211	9	is	be	AUX
ejpam-3248	211	10	z[d(z	z[d(z	NOUN
ejpam-3248	211	11	)	)	PUNCT
ejpam-3248	211	12	,	,	PUNCT
ejpam-3248	211	13	z]2	z]2	X
ejpam-3248	212	1	=	=	PUNCT
ejpam-3248	212	2	0	0	PROPN
ejpam-3248	212	3	for	for	ADP
ejpam-3248	212	4	all	all	DET
ejpam-3248	212	5	z	z	PROPN
ejpam-3248	212	6	∈	∈	PROPN
ejpam-3248	212	7	i.	i.	NOUN
ejpam-3248	212	8	by	by	ADP
ejpam-3248	212	9	using	use	VERB
ejpam-3248	212	10	similar	similar	ADJ
ejpam-3248	212	11	argument	argument	NOUN
ejpam-3248	212	12	we	we	PRON
ejpam-3248	212	13	can	can	AUX
ejpam-3248	212	14	get	get	VERB
ejpam-3248	212	15	the	the	DET
ejpam-3248	212	16	result	result	NOUN
ejpam-3248	212	17	for	for	ADP
ejpam-3248	212	18	the	the	DET
ejpam-3248	212	19	case	case	NOUN
ejpam-3248	212	20	f	f	X
ejpam-3248	212	21	(	(	PUNCT
ejpam-3248	212	22	xy)−	xy)−	X
ejpam-3248	213	1	[	[	X
ejpam-3248	213	2	x	x	X
ejpam-3248	213	3	,	,	PUNCT
ejpam-3248	213	4	y	y	PROPN
ejpam-3248	213	5	]	]	X
ejpam-3248	213	6	∈	∈	PROPN
ejpam-3248	213	7	z(r	z(r	PROPN
ejpam-3248	213	8	)	)	PUNCT
ejpam-3248	213	9	for	for	ADP
ejpam-3248	213	10	all	all	DET
ejpam-3248	213	11	x	x	NOUN
ejpam-3248	213	12	,	,	PUNCT
ejpam-3248	213	13	y	y	PROPN
ejpam-3248	213	14	∈	∈	PROPN
ejpam-3248	213	15	i.	i.	NOUN
ejpam-3248	213	16	theorem	theorem	VERB
ejpam-3248	213	17	3.4	3.4	NUM
ejpam-3248	213	18	.	.	PUNCT
ejpam-3248	214	1	let	let	VERB
ejpam-3248	214	2	r	r	PRON
ejpam-3248	214	3	be	be	AUX
ejpam-3248	214	4	a	a	DET
ejpam-3248	214	5	semiprime	semiprime	NOUN
ejpam-3248	214	6	ring	ring	NOUN
ejpam-3248	214	7	and	and	CCONJ
ejpam-3248	214	8	f	f	PROPN
ejpam-3248	214	9	be	be	AUX
ejpam-3248	214	10	a	a	DET
ejpam-3248	214	11	non	non	ADJ
ejpam-3248	214	12	-	-	ADJ
ejpam-3248	214	13	zero	zero	ADJ
ejpam-3248	214	14	multiplicative	multiplicative	ADJ
ejpam-3248	214	15	(	(	PUNCT
ejpam-3248	214	16	generalized	generalized	ADJ
ejpam-3248	214	17	)	)	PUNCT
ejpam-3248	214	18	reverse	reverse	ADJ
ejpam-3248	214	19	derivation	derivation	NOUN
ejpam-3248	214	20	associated	associate	VERB
ejpam-3248	214	21	with	with	ADP
ejpam-3248	214	22	a	a	DET
ejpam-3248	214	23	map	map	NOUN
ejpam-3248	215	1	d	d	NOUN
ejpam-3248	215	2	,	,	PUNCT
ejpam-3248	215	3	i	i	PRON
ejpam-3248	215	4	be	be	VERB
ejpam-3248	215	5	a	a	DET
ejpam-3248	215	6	non	non	ADJ
ejpam-3248	215	7	-	-	ADJ
ejpam-3248	215	8	zero	zero	NUM
ejpam-3248	215	9	ideal	ideal	NOUN
ejpam-3248	215	10	of	of	ADP
ejpam-3248	215	11	r.	r.	PROPN
ejpam-3248	215	12	if	if	SCONJ
ejpam-3248	215	13	f	f	PROPN
ejpam-3248	215	14	(	(	PUNCT
ejpam-3248	215	15	xy)±	xy)±	VERB
ejpam-3248	215	16	x	x	PUNCT
ejpam-3248	215	17	◦	◦	VERB
ejpam-3248	215	18	y	y	PROPN
ejpam-3248	215	19	∈	∈	PROPN
ejpam-3248	215	20	z(r	z(r	PROPN
ejpam-3248	215	21	)	)	PUNCT
ejpam-3248	215	22	for	for	ADP
ejpam-3248	215	23	all	all	DET
ejpam-3248	215	24	x	x	NOUN
ejpam-3248	215	25	,	,	PUNCT
ejpam-3248	215	26	y	y	PROPN
ejpam-3248	215	27	∈	∈	PROPN
ejpam-3248	216	1	i	i	PRON
ejpam-3248	216	2	,	,	PUNCT
ejpam-3248	216	3	then	then	ADV
ejpam-3248	216	4	x[d(x	x[d(x	PROPN
ejpam-3248	216	5	)	)	PUNCT
ejpam-3248	216	6	,	,	PUNCT
ejpam-3248	216	7	x]2	x]2	PUNCT
ejpam-3248	217	1	=	=	SYM
ejpam-3248	217	2	0	0	PROPN
ejpam-3248	217	3	for	for	ADP
ejpam-3248	217	4	all	all	DET
ejpam-3248	217	5	x	x	SYM
ejpam-3248	217	6	∈	∈	PROPN
ejpam-3248	217	7	i.	i.	PROPN
ejpam-3248	217	8	a.	a.	PROPN
ejpam-3248	217	9	ali	ali	PROPN
ejpam-3248	217	10	,	,	PUNCT
ejpam-3248	217	11	a.	a.	PROPN
ejpam-3248	217	12	bano	bano	PROPN
ejpam-3248	217	13	/	/	SYM
ejpam-3248	217	14	eur	eur	PROPN
ejpam-3248	217	15	.	.	PUNCT
ejpam-3248	218	1	j.	j.	PROPN
ejpam-3248	218	2	pure	pure	PROPN
ejpam-3248	218	3	appl	appl	PROPN
ejpam-3248	218	4	.	.	PROPN
ejpam-3248	218	5	math	math	PROPN
ejpam-3248	218	6	,	,	PUNCT
ejpam-3248	218	7	11	11	NUM
ejpam-3248	218	8	(	(	PUNCT
ejpam-3248	218	9	3	3	NUM
ejpam-3248	218	10	)	)	PUNCT
ejpam-3248	218	11	(	(	PUNCT
ejpam-3248	218	12	2018	2018	NUM
ejpam-3248	218	13	)	)	PUNCT
ejpam-3248	218	14	,	,	PUNCT
ejpam-3248	218	15	717	717	NUM
ejpam-3248	218	16	-	-	SYM
ejpam-3248	218	17	729	729	NUM
ejpam-3248	218	18	724	724	NUM
ejpam-3248	218	19	proof	proof	NOUN
ejpam-3248	218	20	by	by	ADP
ejpam-3248	218	21	the	the	DET
ejpam-3248	218	22	hypothesis	hypothesis	NOUN
ejpam-3248	219	1	,	,	PUNCT
ejpam-3248	219	2	we	we	PRON
ejpam-3248	219	3	have	have	VERB
ejpam-3248	219	4	f	f	PROPN
ejpam-3248	219	5	(	(	PUNCT
ejpam-3248	219	6	xy	xy	PROPN
ejpam-3248	219	7	)	)	PUNCT
ejpam-3248	220	1	+	+	CCONJ
ejpam-3248	220	2	x	x	PUNCT
ejpam-3248	220	3	◦	◦	NOUN
ejpam-3248	220	4	y	y	PROPN
ejpam-3248	220	5	∈	∈	PROPN
ejpam-3248	220	6	z(r	z(r	PROPN
ejpam-3248	220	7	)	)	PUNCT
ejpam-3248	220	8	for	for	ADP
ejpam-3248	220	9	all	all	DET
ejpam-3248	220	10	x	x	NOUN
ejpam-3248	220	11	,	,	PUNCT
ejpam-3248	220	12	y	y	PROPN
ejpam-3248	220	13	∈	∈	PROPN
ejpam-3248	220	14	i.	i.	NOUN
ejpam-3248	220	15	(	(	PUNCT
ejpam-3248	220	16	3.37	3.37	NUM
ejpam-3248	220	17	)	)	PUNCT
ejpam-3248	220	18	replacing	replace	VERB
ejpam-3248	220	19	x	x	PUNCT
ejpam-3248	220	20	by	by	ADP
ejpam-3248	220	21	zx	zx	PROPN
ejpam-3248	220	22	in	in	ADP
ejpam-3248	220	23	(	(	PUNCT
ejpam-3248	220	24	3.37	3.37	NUM
ejpam-3248	220	25	)	)	PUNCT
ejpam-3248	220	26	,	,	PUNCT
ejpam-3248	220	27	we	we	PRON
ejpam-3248	220	28	get	get	VERB
ejpam-3248	220	29	f	f	PROPN
ejpam-3248	220	30	(	(	PUNCT
ejpam-3248	220	31	xy)z	xy)z	PROPN
ejpam-3248	220	32	+	+	NUM
ejpam-3248	220	33	xyd(z	xyd(z	NOUN
ejpam-3248	220	34	)	)	PUNCT
ejpam-3248	221	1	+	+	PUNCT
ejpam-3248	221	2	z(x	z(x	NUM
ejpam-3248	221	3	◦	◦	NOUN
ejpam-3248	221	4	y)−	y)−	PROPN
ejpam-3248	221	5	[	[	X
ejpam-3248	221	6	z	z	NOUN
ejpam-3248	221	7	,	,	PUNCT
ejpam-3248	221	8	y]x	y]x	NOUN
ejpam-3248	221	9	+	+	CCONJ
ejpam-3248	221	10	(	(	PUNCT
ejpam-3248	221	11	x	x	SYM
ejpam-3248	221	12	◦	◦	VERB
ejpam-3248	221	13	y)z	y)z	X
ejpam-3248	221	14	−	−	PROPN
ejpam-3248	221	15	(	(	PUNCT
ejpam-3248	221	16	x	x	SYM
ejpam-3248	221	17	◦	◦	VERB
ejpam-3248	221	18	y)z	y)z	X
ejpam-3248	221	19	∈	∈	PROPN
ejpam-3248	221	20	z(r	z(r	NOUN
ejpam-3248	221	21	)	)	PUNCT
ejpam-3248	221	22	for	for	ADP
ejpam-3248	221	23	all	all	DET
ejpam-3248	221	24	x	x	NOUN
ejpam-3248	221	25	,	,	PUNCT
ejpam-3248	221	26	y	y	PROPN
ejpam-3248	221	27	,	,	PUNCT
ejpam-3248	221	28	z	z	PROPN
ejpam-3248	221	29	∈	∈	PROPN
ejpam-3248	221	30	i.	i.	NOUN
ejpam-3248	221	31	this	this	PRON
ejpam-3248	221	32	implies	imply	VERB
ejpam-3248	221	33	that	that	SCONJ
ejpam-3248	221	34	(	(	PUNCT
ejpam-3248	221	35	f	f	X
ejpam-3248	221	36	(	(	PUNCT
ejpam-3248	221	37	xy	xy	PROPN
ejpam-3248	221	38	)	)	PUNCT
ejpam-3248	222	1	+	+	CCONJ
ejpam-3248	222	2	x	x	PUNCT
ejpam-3248	222	3	◦	◦	NOUN
ejpam-3248	222	4	y)z	y)z	NOUN
ejpam-3248	223	1	+	+	X
ejpam-3248	223	2	xyd(z	xyd(z	X
ejpam-3248	223	3	)	)	PUNCT
ejpam-3248	224	1	+	+	CCONJ
ejpam-3248	225	1	[	[	X
ejpam-3248	225	2	z	z	X
ejpam-3248	225	3	,	,	PUNCT
ejpam-3248	225	4	x	x	PUNCT
ejpam-3248	225	5	◦	◦	NOUN
ejpam-3248	225	6	y]−	y]−	NOUN
ejpam-3248	226	1	[	[	X
ejpam-3248	226	2	z	z	NOUN
ejpam-3248	226	3	,	,	PUNCT
ejpam-3248	226	4	y]x	y]x	PROPN
ejpam-3248	226	5	∈	∈	PROPN
ejpam-3248	226	6	z(r	z(r	PROPN
ejpam-3248	226	7	)	)	PUNCT
ejpam-3248	226	8	.	.	PUNCT
ejpam-3248	227	1	(	(	PUNCT
ejpam-3248	227	2	3.38	3.38	NUM
ejpam-3248	227	3	)	)	PUNCT
ejpam-3248	227	4	commuting	commuting	NOUN
ejpam-3248	227	5	(	(	PUNCT
ejpam-3248	227	6	3.38	3.38	NUM
ejpam-3248	227	7	)	)	PUNCT
ejpam-3248	227	8	with	with	ADP
ejpam-3248	227	9	z	z	NOUN
ejpam-3248	227	10	and	and	CCONJ
ejpam-3248	227	11	using	use	VERB
ejpam-3248	227	12	(	(	PUNCT
ejpam-3248	227	13	3.37	3.37	NUM
ejpam-3248	227	14	)	)	PUNCT
ejpam-3248	227	15	we	we	PRON
ejpam-3248	227	16	get	get	VERB
ejpam-3248	227	17	[	[	X
ejpam-3248	227	18	xyd(z	xyd(z	NOUN
ejpam-3248	227	19	)	)	PUNCT
ejpam-3248	227	20	,	,	PUNCT
ejpam-3248	228	1	z	z	X
ejpam-3248	228	2	]	]	X
ejpam-3248	229	1	+	+	CCONJ
ejpam-3248	230	1	[	[	X
ejpam-3248	230	2	[	[	X
ejpam-3248	230	3	z	z	NOUN
ejpam-3248	230	4	,	,	PUNCT
ejpam-3248	230	5	x	x	PUNCT
ejpam-3248	230	6	◦	◦	VERB
ejpam-3248	230	7	y	y	PRON
ejpam-3248	230	8	]	]	X
ejpam-3248	230	9	,	,	PUNCT
ejpam-3248	230	10	z]−	z]−	PUNCT
ejpam-3248	231	1	[	[	X
ejpam-3248	231	2	[	[	X
ejpam-3248	231	3	z	z	PROPN
ejpam-3248	231	4	,	,	PUNCT
ejpam-3248	231	5	y]x	y]x	NOUN
ejpam-3248	231	6	,	,	PUNCT
ejpam-3248	231	7	z	z	X
ejpam-3248	231	8	]	]	X
ejpam-3248	231	9	=	=	SYM
ejpam-3248	231	10	0	0	NUM
ejpam-3248	231	11	for	for	ADP
ejpam-3248	231	12	all	all	DET
ejpam-3248	231	13	x	x	NOUN
ejpam-3248	231	14	,	,	PUNCT
ejpam-3248	231	15	y	y	PROPN
ejpam-3248	231	16	,	,	PUNCT
ejpam-3248	231	17	z	z	PROPN
ejpam-3248	231	18	∈	∈	PROPN
ejpam-3248	231	19	i.	i.	NOUN
ejpam-3248	231	20	(	(	PUNCT
ejpam-3248	231	21	3.39	3.39	NUM
ejpam-3248	231	22	)	)	PUNCT
ejpam-3248	231	23	substituting	substitute	VERB
ejpam-3248	231	24	zy	zy	NOUN
ejpam-3248	231	25	for	for	ADP
ejpam-3248	231	26	y	y	PROPN
ejpam-3248	231	27	in	in	ADP
ejpam-3248	231	28	(	(	PUNCT
ejpam-3248	231	29	3.39	3.39	NUM
ejpam-3248	231	30	)	)	PUNCT
ejpam-3248	231	31	,	,	PUNCT
ejpam-3248	231	32	we	we	PRON
ejpam-3248	231	33	obtain	obtain	VERB
ejpam-3248	231	34	[	[	X
ejpam-3248	231	35	xzyd(z	xzyd(z	PROPN
ejpam-3248	231	36	)	)	PUNCT
ejpam-3248	231	37	,	,	PUNCT
ejpam-3248	232	1	z	z	X
ejpam-3248	232	2	]	]	X
ejpam-3248	233	1	+	+	CCONJ
ejpam-3248	234	1	[	[	X
ejpam-3248	234	2	[	[	X
ejpam-3248	234	3	z	z	NOUN
ejpam-3248	234	4	,	,	PUNCT
ejpam-3248	234	5	x	x	PUNCT
ejpam-3248	234	6	◦	◦	VERB
ejpam-3248	234	7	zy	zy	NOUN
ejpam-3248	234	8	]	]	PUNCT
ejpam-3248	234	9	,	,	PUNCT
ejpam-3248	234	10	z]−	z]−	PROPN
ejpam-3248	235	1	[	[	X
ejpam-3248	235	2	z[z	z[z	NUM
ejpam-3248	235	3	,	,	PUNCT
ejpam-3248	235	4	y]x	y]x	NOUN
ejpam-3248	235	5	,	,	PUNCT
ejpam-3248	235	6	z	z	X
ejpam-3248	235	7	]	]	X
ejpam-3248	235	8	=	=	SYM
ejpam-3248	235	9	0	0	X
ejpam-3248	235	10	.	.	PUNCT
ejpam-3248	236	1	this	this	PRON
ejpam-3248	236	2	implies	imply	VERB
ejpam-3248	236	3	that	that	SCONJ
ejpam-3248	236	4	[	[	X
ejpam-3248	236	5	xzyd(z	xzyd(z	NOUN
ejpam-3248	236	6	)	)	PUNCT
ejpam-3248	236	7	,	,	PUNCT
ejpam-3248	236	8	z	z	X
ejpam-3248	236	9	]	]	X
ejpam-3248	237	1	+	+	CCONJ
ejpam-3248	237	2	[	[	X
ejpam-3248	237	3	[	[	X
ejpam-3248	237	4	z	z	NOUN
ejpam-3248	237	5	,	,	PUNCT
ejpam-3248	237	6	z(x	z(x	PROPN
ejpam-3248	237	7	◦	◦	NOUN
ejpam-3248	237	8	y	y	NOUN
ejpam-3248	237	9	)	)	PUNCT
ejpam-3248	238	1	+	+	CCONJ
ejpam-3248	239	1	[	[	X
ejpam-3248	239	2	x	x	X
ejpam-3248	239	3	,	,	PUNCT
ejpam-3248	239	4	z]y	z]y	PRON
ejpam-3248	239	5	]	]	X
ejpam-3248	239	6	,	,	PUNCT
ejpam-3248	239	7	z]−	z]−	PROPN
ejpam-3248	240	1	[	[	X
ejpam-3248	240	2	z[z	z[z	NUM
ejpam-3248	240	3	,	,	PUNCT
ejpam-3248	240	4	y]x	y]x	NOUN
ejpam-3248	240	5	,	,	PUNCT
ejpam-3248	240	6	z	z	X
ejpam-3248	240	7	]	]	X
ejpam-3248	240	8	=	=	SYM
ejpam-3248	240	9	0	0	X
ejpam-3248	240	10	.	.	PUNCT
ejpam-3248	241	1	a	a	DET
ejpam-3248	241	2	simple	simple	ADJ
ejpam-3248	241	3	calculation	calculation	NOUN
ejpam-3248	241	4	yields	yield	VERB
ejpam-3248	241	5	that	that	SCONJ
ejpam-3248	242	1	[	[	X
ejpam-3248	242	2	xzyd(z	xzyd(z	NOUN
ejpam-3248	242	3	)	)	PUNCT
ejpam-3248	242	4	,	,	PUNCT
ejpam-3248	242	5	z	z	X
ejpam-3248	242	6	]	]	X
ejpam-3248	242	7	+	+	CCONJ
ejpam-3248	242	8	z[[z	z[[z	PROPN
ejpam-3248	242	9	,	,	PUNCT
ejpam-3248	242	10	x	x	PUNCT
ejpam-3248	242	11	◦	◦	VERB
ejpam-3248	242	12	y	y	X
ejpam-3248	242	13	]	]	X
ejpam-3248	242	14	,	,	PUNCT
ejpam-3248	242	15	z	z	X
ejpam-3248	242	16	]	]	X
ejpam-3248	243	1	+	+	CCONJ
ejpam-3248	244	1	[	[	X
ejpam-3248	244	2	[	[	X
ejpam-3248	244	3	x	x	X
ejpam-3248	244	4	,	,	PUNCT
ejpam-3248	244	5	z][z	z][z	PROPN
ejpam-3248	244	6	,	,	PUNCT
ejpam-3248	244	7	y	y	NOUN
ejpam-3248	244	8	]	]	X
ejpam-3248	244	9	,	,	PUNCT
ejpam-3248	244	10	z	z	X
ejpam-3248	244	11	]	]	X
ejpam-3248	245	1	+	+	CCONJ
ejpam-3248	246	1	[	[	X
ejpam-3248	246	2	[	[	X
ejpam-3248	246	3	z	z	X
ejpam-3248	246	4	,	,	PUNCT
ejpam-3248	246	5	[	[	X
ejpam-3248	246	6	x	x	X
ejpam-3248	246	7	,	,	PUNCT
ejpam-3248	246	8	z]]y	z]]y	PROPN
ejpam-3248	246	9	,	,	PUNCT
ejpam-3248	246	10	z]−	z]−	PROPN
ejpam-3248	246	11	z[[z	z[[z	PROPN
ejpam-3248	246	12	,	,	PUNCT
ejpam-3248	246	13	y]x	y]x	PROPN
ejpam-3248	246	14	,	,	PUNCT
ejpam-3248	246	15	z	z	X
ejpam-3248	246	16	]	]	X
ejpam-3248	246	17	=	=	SYM
ejpam-3248	246	18	0	0	X
ejpam-3248	246	19	.	.	PUNCT
ejpam-3248	246	20	(	(	PUNCT
ejpam-3248	246	21	3.40	3.40	NUM
ejpam-3248	246	22	)	)	PUNCT
ejpam-3248	246	23	left	leave	VERB
ejpam-3248	246	24	multiplying	multiplying	NOUN
ejpam-3248	246	25	(	(	PUNCT
ejpam-3248	246	26	3.39	3.39	NUM
ejpam-3248	246	27	)	)	PUNCT
ejpam-3248	246	28	by	by	ADP
ejpam-3248	246	29	z	z	NOUN
ejpam-3248	246	30	and	and	CCONJ
ejpam-3248	246	31	subtracting	subtract	VERB
ejpam-3248	246	32	from	from	ADP
ejpam-3248	246	33	(	(	PUNCT
ejpam-3248	246	34	3.40	3.40	NUM
ejpam-3248	246	35	)	)	PUNCT
ejpam-3248	246	36	,	,	PUNCT
ejpam-3248	246	37	we	we	PRON
ejpam-3248	246	38	obtain	obtain	VERB
ejpam-3248	246	39	[	[	X
ejpam-3248	246	40	[	[	X
ejpam-3248	246	41	z	z	X
ejpam-3248	246	42	,	,	PUNCT
ejpam-3248	246	43	x]yd(z	x]yd(z	PROPN
ejpam-3248	246	44	)	)	PUNCT
ejpam-3248	246	45	,	,	PUNCT
ejpam-3248	246	46	z]−	z]−	PUNCT
ejpam-3248	247	1	[	[	X
ejpam-3248	247	2	[	[	X
ejpam-3248	247	3	x	x	X
ejpam-3248	247	4	,	,	PUNCT
ejpam-3248	247	5	z][z	z][z	PROPN
ejpam-3248	247	6	,	,	PUNCT
ejpam-3248	247	7	y	y	NOUN
ejpam-3248	247	8	]	]	X
ejpam-3248	247	9	,	,	PUNCT
ejpam-3248	247	10	z]−	z]−	PUNCT
ejpam-3248	248	1	[	[	X
ejpam-3248	248	2	[	[	X
ejpam-3248	248	3	z	z	X
ejpam-3248	248	4	,	,	PUNCT
ejpam-3248	248	5	[	[	X
ejpam-3248	248	6	x	x	X
ejpam-3248	248	7	,	,	PUNCT
ejpam-3248	248	8	z]]y	z]]y	PROPN
ejpam-3248	248	9	,	,	PUNCT
ejpam-3248	248	10	z	z	NOUN
ejpam-3248	248	11	]	]	X
ejpam-3248	248	12	=	=	SYM
ejpam-3248	248	13	0	0	X
ejpam-3248	248	14	.	.	PUNCT
ejpam-3248	249	1	(	(	PUNCT
ejpam-3248	249	2	3.41	3.41	NUM
ejpam-3248	249	3	)	)	PUNCT
ejpam-3248	249	4	this	this	PRON
ejpam-3248	249	5	is	be	AUX
ejpam-3248	249	6	the	the	DET
ejpam-3248	249	7	same	same	ADJ
ejpam-3248	249	8	as	as	ADP
ejpam-3248	249	9	(	(	PUNCT
ejpam-3248	249	10	3.30	3.30	NUM
ejpam-3248	249	11	)	)	PUNCT
ejpam-3248	249	12	in	in	ADP
ejpam-3248	249	13	theorem	theorem	ADJ
ejpam-3248	249	14	3.3	3.3	NUM
ejpam-3248	249	15	.	.	PUNCT
ejpam-3248	250	1	then	then	ADV
ejpam-3248	250	2	by	by	ADP
ejpam-3248	250	3	the	the	DET
ejpam-3248	250	4	same	same	ADJ
ejpam-3248	250	5	argument	argument	NOUN
ejpam-3248	250	6	as	as	SCONJ
ejpam-3248	250	7	we	we	PRON
ejpam-3248	250	8	have	have	AUX
ejpam-3248	250	9	used	use	VERB
ejpam-3248	250	10	in	in	ADP
ejpam-3248	250	11	theorem	theorem	ADJ
ejpam-3248	250	12	3.3	3.3	NUM
ejpam-3248	250	13	,	,	PUNCT
ejpam-3248	250	14	we	we	PRON
ejpam-3248	250	15	get	get	VERB
ejpam-3248	250	16	the	the	DET
ejpam-3248	250	17	result	result	NOUN
ejpam-3248	250	18	.	.	PUNCT
ejpam-3248	251	1	in	in	ADP
ejpam-3248	251	2	the	the	DET
ejpam-3248	251	3	similar	similar	ADJ
ejpam-3248	251	4	manner	manner	NOUN
ejpam-3248	251	5	the	the	DET
ejpam-3248	251	6	conclusion	conclusion	NOUN
ejpam-3248	251	7	can	can	AUX
ejpam-3248	251	8	be	be	AUX
ejpam-3248	251	9	obtained	obtain	VERB
ejpam-3248	251	10	for	for	ADP
ejpam-3248	251	11	the	the	DET
ejpam-3248	251	12	case	case	NOUN
ejpam-3248	251	13	f	f	X
ejpam-3248	251	14	(	(	PUNCT
ejpam-3248	251	15	xy)−	xy)−	PUNCT
ejpam-3248	251	16	x	x	PUNCT
ejpam-3248	251	17	◦	◦	VERB
ejpam-3248	251	18	y	y	PROPN
ejpam-3248	251	19	∈	∈	PROPN
ejpam-3248	251	20	z(r	z(r	PROPN
ejpam-3248	251	21	)	)	PUNCT
ejpam-3248	251	22	for	for	ADP
ejpam-3248	251	23	all	all	DET
ejpam-3248	251	24	x	x	NOUN
ejpam-3248	251	25	,	,	PUNCT
ejpam-3248	251	26	y	y	PROPN
ejpam-3248	251	27	∈	∈	PROPN
ejpam-3248	251	28	i.	i.	NOUN
ejpam-3248	251	29	theorem	theorem	VERB
ejpam-3248	251	30	3.5	3.5	NUM
ejpam-3248	251	31	.	.	PUNCT
ejpam-3248	252	1	let	let	VERB
ejpam-3248	252	2	r	r	PRON
ejpam-3248	252	3	be	be	AUX
ejpam-3248	252	4	a	a	DET
ejpam-3248	252	5	semiprime	semiprime	NOUN
ejpam-3248	252	6	ring	ring	NOUN
ejpam-3248	252	7	and	and	CCONJ
ejpam-3248	252	8	f	f	PROPN
ejpam-3248	252	9	be	be	AUX
ejpam-3248	252	10	a	a	DET
ejpam-3248	252	11	non	non	ADJ
ejpam-3248	252	12	-	-	ADJ
ejpam-3248	252	13	zero	zero	ADJ
ejpam-3248	252	14	multiplicative	multiplicative	ADJ
ejpam-3248	252	15	(	(	PUNCT
ejpam-3248	252	16	generalized	generalized	ADJ
ejpam-3248	252	17	)	)	PUNCT
ejpam-3248	252	18	reverse	reverse	ADJ
ejpam-3248	252	19	derivation	derivation	NOUN
ejpam-3248	252	20	associated	associate	VERB
ejpam-3248	252	21	with	with	ADP
ejpam-3248	252	22	a	a	DET
ejpam-3248	252	23	map	map	NOUN
ejpam-3248	253	1	d	d	NOUN
ejpam-3248	253	2	,	,	PUNCT
ejpam-3248	253	3	i	i	PRON
ejpam-3248	253	4	be	be	VERB
ejpam-3248	253	5	a	a	DET
ejpam-3248	253	6	non	non	ADJ
ejpam-3248	253	7	-	-	ADJ
ejpam-3248	253	8	zero	zero	NUM
ejpam-3248	253	9	ideal	ideal	NOUN
ejpam-3248	253	10	of	of	ADP
ejpam-3248	253	11	r.	r.	PROPN
ejpam-3248	253	12	if	if	SCONJ
ejpam-3248	253	13	f	f	PROPN
ejpam-3248	253	14	(	(	PUNCT
ejpam-3248	253	15	xy)±	xy)±	VERB
ejpam-3248	253	16	f	f	PROPN
ejpam-3248	253	17	(	(	PUNCT
ejpam-3248	253	18	y)f	y)f	NOUN
ejpam-3248	253	19	(	(	PUNCT
ejpam-3248	253	20	x	x	X
ejpam-3248	253	21	)	)	PUNCT
ejpam-3248	253	22	∈	∈	PROPN
ejpam-3248	253	23	z(r	z(r	PROPN
ejpam-3248	253	24	)	)	PUNCT
ejpam-3248	253	25	for	for	ADP
ejpam-3248	253	26	all	all	DET
ejpam-3248	253	27	x	x	NOUN
ejpam-3248	253	28	,	,	PUNCT
ejpam-3248	253	29	y	y	PROPN
ejpam-3248	253	30	∈	∈	PROPN
ejpam-3248	254	1	i	i	PRON
ejpam-3248	254	2	,	,	PUNCT
ejpam-3248	254	3	then	then	ADV
ejpam-3248	254	4	x[d(x	x[d(x	PROPN
ejpam-3248	254	5	)	)	PUNCT
ejpam-3248	254	6	,	,	PUNCT
ejpam-3248	254	7	x]2	x]2	PUNCT
ejpam-3248	255	1	=	=	SYM
ejpam-3248	255	2	0	0	PROPN
ejpam-3248	255	3	for	for	ADP
ejpam-3248	255	4	all	all	DET
ejpam-3248	255	5	x	x	SYM
ejpam-3248	255	6	∈	∈	NOUN
ejpam-3248	255	7	i.	i.	NOUN
ejpam-3248	255	8	proof	proof	NOUN
ejpam-3248	255	9	by	by	ADP
ejpam-3248	255	10	the	the	DET
ejpam-3248	255	11	hypothesis	hypothesis	NOUN
ejpam-3248	255	12	,	,	PUNCT
ejpam-3248	255	13	we	we	PRON
ejpam-3248	255	14	have	have	VERB
ejpam-3248	255	15	f	f	PROPN
ejpam-3248	255	16	(	(	PUNCT
ejpam-3248	255	17	xy	xy	PROPN
ejpam-3248	255	18	)	)	PUNCT
ejpam-3248	256	1	+	+	CCONJ
ejpam-3248	256	2	f	f	X
ejpam-3248	256	3	(	(	PUNCT
ejpam-3248	256	4	y)f	y)f	NOUN
ejpam-3248	256	5	(	(	PUNCT
ejpam-3248	256	6	x	x	X
ejpam-3248	256	7	)	)	PUNCT
ejpam-3248	256	8	∈	∈	PROPN
ejpam-3248	256	9	z(r	z(r	PROPN
ejpam-3248	256	10	)	)	PUNCT
ejpam-3248	256	11	for	for	ADP
ejpam-3248	256	12	all	all	DET
ejpam-3248	256	13	x	x	NOUN
ejpam-3248	256	14	,	,	PUNCT
ejpam-3248	256	15	y	y	PROPN
ejpam-3248	256	16	∈	∈	PROPN
ejpam-3248	256	17	i.	i.	NOUN
ejpam-3248	256	18	(	(	PUNCT
ejpam-3248	256	19	3.42	3.42	NUM
ejpam-3248	256	20	)	)	PUNCT
ejpam-3248	256	21	replacing	replace	VERB
ejpam-3248	256	22	x	x	PUNCT
ejpam-3248	256	23	by	by	ADP
ejpam-3248	256	24	zx	zx	PROPN
ejpam-3248	256	25	in	in	ADP
ejpam-3248	256	26	(	(	PUNCT
ejpam-3248	256	27	3.42	3.42	NUM
ejpam-3248	256	28	)	)	PUNCT
ejpam-3248	256	29	,	,	PUNCT
ejpam-3248	256	30	we	we	PRON
ejpam-3248	256	31	get	get	VERB
ejpam-3248	256	32	f	f	PROPN
ejpam-3248	256	33	(	(	PUNCT
ejpam-3248	256	34	xy)z	xy)z	PROPN
ejpam-3248	256	35	+	+	NUM
ejpam-3248	256	36	xyd(z	xyd(z	NOUN
ejpam-3248	256	37	)	)	PUNCT
ejpam-3248	257	1	+	+	CCONJ
ejpam-3248	257	2	f	f	X
ejpam-3248	257	3	(	(	PUNCT
ejpam-3248	257	4	y)f	y)f	NOUN
ejpam-3248	257	5	(	(	PUNCT
ejpam-3248	257	6	x)z	x)z	PUNCT
ejpam-3248	257	7	+	+	NUM
ejpam-3248	257	8	f	f	X
ejpam-3248	257	9	(	(	PUNCT
ejpam-3248	257	10	y)xd(z	y)xd(z	PROPN
ejpam-3248	257	11	)	)	PUNCT
ejpam-3248	257	12	∈	∈	PROPN
ejpam-3248	257	13	z(r	z(r	PROPN
ejpam-3248	257	14	)	)	PUNCT
ejpam-3248	257	15	for	for	ADP
ejpam-3248	257	16	all	all	DET
ejpam-3248	257	17	x	x	NOUN
ejpam-3248	257	18	,	,	PUNCT
ejpam-3248	257	19	y	y	PROPN
ejpam-3248	257	20	,	,	PUNCT
ejpam-3248	257	21	z	z	PROPN
ejpam-3248	257	22	∈	∈	PROPN
ejpam-3248	257	23	i.	i.	NOUN
ejpam-3248	257	24	(	(	PUNCT
ejpam-3248	257	25	3.43	3.43	NUM
ejpam-3248	257	26	)	)	PUNCT
ejpam-3248	257	27	a.	a.	PROPN
ejpam-3248	257	28	ali	ali	PROPN
ejpam-3248	257	29	,	,	PUNCT
ejpam-3248	257	30	a.	a.	PROPN
ejpam-3248	257	31	bano	bano	PROPN
ejpam-3248	257	32	/	/	SYM
ejpam-3248	257	33	eur	eur	PROPN
ejpam-3248	257	34	.	.	PUNCT
ejpam-3248	258	1	j.	j.	PROPN
ejpam-3248	258	2	pure	pure	PROPN
ejpam-3248	258	3	appl	appl	PROPN
ejpam-3248	258	4	.	.	PROPN
ejpam-3248	258	5	math	math	PROPN
ejpam-3248	258	6	,	,	PUNCT
ejpam-3248	258	7	11	11	NUM
ejpam-3248	258	8	(	(	PUNCT
ejpam-3248	258	9	3	3	NUM
ejpam-3248	258	10	)	)	PUNCT
ejpam-3248	258	11	(	(	PUNCT
ejpam-3248	258	12	2018	2018	NUM
ejpam-3248	258	13	)	)	PUNCT
ejpam-3248	258	14	,	,	PUNCT
ejpam-3248	258	15	717	717	NUM
ejpam-3248	258	16	-	-	SYM
ejpam-3248	258	17	729	729	NUM
ejpam-3248	258	18	725	725	NUM
ejpam-3248	258	19	commuting	commuting	NOUN
ejpam-3248	258	20	(	(	PUNCT
ejpam-3248	258	21	3.43	3.43	NUM
ejpam-3248	258	22	)	)	PUNCT
ejpam-3248	258	23	with	with	ADP
ejpam-3248	258	24	z	z	NOUN
ejpam-3248	258	25	and	and	CCONJ
ejpam-3248	258	26	using	use	VERB
ejpam-3248	258	27	(	(	PUNCT
ejpam-3248	258	28	3.42	3.42	NUM
ejpam-3248	258	29	)	)	PUNCT
ejpam-3248	259	1	,	,	PUNCT
ejpam-3248	259	2	we	we	PRON
ejpam-3248	259	3	have	have	VERB
ejpam-3248	259	4	[	[	X
ejpam-3248	259	5	xyd(z	xyd(z	NOUN
ejpam-3248	259	6	)	)	PUNCT
ejpam-3248	259	7	,	,	PUNCT
ejpam-3248	260	1	z	z	X
ejpam-3248	260	2	]	]	X
ejpam-3248	261	1	+	+	CCONJ
ejpam-3248	261	2	[	[	X
ejpam-3248	261	3	f	f	X
ejpam-3248	261	4	(	(	PUNCT
ejpam-3248	261	5	y)xd(z	y)xd(z	PROPN
ejpam-3248	261	6	)	)	PUNCT
ejpam-3248	261	7	,	,	PUNCT
ejpam-3248	261	8	z	z	X
ejpam-3248	261	9	]	]	X
ejpam-3248	261	10	=	=	SYM
ejpam-3248	261	11	0	0	NUM
ejpam-3248	261	12	for	for	ADP
ejpam-3248	261	13	all	all	DET
ejpam-3248	261	14	x	x	NOUN
ejpam-3248	261	15	,	,	PUNCT
ejpam-3248	261	16	y	y	PROPN
ejpam-3248	261	17	,	,	PUNCT
ejpam-3248	261	18	z	z	PROPN
ejpam-3248	261	19	∈	∈	PROPN
ejpam-3248	261	20	i.	i.	NOUN
ejpam-3248	261	21	(	(	PUNCT
ejpam-3248	261	22	3.44	3.44	NUM
ejpam-3248	261	23	)	)	PUNCT
ejpam-3248	261	24	replacing	replace	VERB
ejpam-3248	261	25	y	y	PRON
ejpam-3248	261	26	by	by	ADP
ejpam-3248	261	27	z2	z2	PROPN
ejpam-3248	261	28	and	and	CCONJ
ejpam-3248	261	29	applying	apply	VERB
ejpam-3248	261	30	definition	definition	NOUN
ejpam-3248	261	31	of	of	ADP
ejpam-3248	261	32	f	f	PROPN
ejpam-3248	261	33	in	in	ADP
ejpam-3248	261	34	(	(	PUNCT
ejpam-3248	261	35	3.44	3.44	NUM
ejpam-3248	261	36	)	)	PUNCT
ejpam-3248	261	37	,	,	PUNCT
ejpam-3248	261	38	we	we	PRON
ejpam-3248	261	39	get	get	VERB
ejpam-3248	261	40	[	[	X
ejpam-3248	261	41	xz2d(z	xz2d(z	NOUN
ejpam-3248	261	42	)	)	PUNCT
ejpam-3248	261	43	,	,	PUNCT
ejpam-3248	262	1	z	z	X
ejpam-3248	262	2	]	]	X
ejpam-3248	263	1	+	+	CCONJ
ejpam-3248	264	1	[	[	X
ejpam-3248	264	2	f	f	X
ejpam-3248	264	3	(	(	PUNCT
ejpam-3248	264	4	z)zxd(z	z)zxd(z	NUM
ejpam-3248	264	5	)	)	PUNCT
ejpam-3248	264	6	,	,	PUNCT
ejpam-3248	264	7	z	z	X
ejpam-3248	264	8	]	]	X
ejpam-3248	264	9	+	+	CCONJ
ejpam-3248	264	10	[	[	X
ejpam-3248	264	11	zd(z)xd(z	zd(z)xd(z	NOUN
ejpam-3248	264	12	)	)	PUNCT
ejpam-3248	264	13	,	,	PUNCT
ejpam-3248	265	1	z	z	X
ejpam-3248	265	2	]	]	X
ejpam-3248	265	3	=	=	SYM
ejpam-3248	265	4	0	0	X
ejpam-3248	265	5	.	.	PUNCT
ejpam-3248	265	6	(	(	PUNCT
ejpam-3248	265	7	3.45	3.45	NUM
ejpam-3248	265	8	)	)	PUNCT
ejpam-3248	265	9	replacing	replace	VERB
ejpam-3248	265	10	x	x	PUNCT
ejpam-3248	265	11	by	by	ADP
ejpam-3248	265	12	zx	zx	PROPN
ejpam-3248	265	13	and	and	CCONJ
ejpam-3248	265	14	y	y	PROPN
ejpam-3248	265	15	by	by	ADP
ejpam-3248	265	16	z	z	PROPN
ejpam-3248	265	17	in	in	ADP
ejpam-3248	265	18	(	(	PUNCT
ejpam-3248	265	19	3.44	3.44	NUM
ejpam-3248	265	20	)	)	PUNCT
ejpam-3248	265	21	,	,	PUNCT
ejpam-3248	265	22	we	we	PRON
ejpam-3248	265	23	get	get	VERB
ejpam-3248	265	24	[	[	X
ejpam-3248	265	25	zxzd(z	zxzd(z	NOUN
ejpam-3248	265	26	)	)	PUNCT
ejpam-3248	265	27	,	,	PUNCT
ejpam-3248	266	1	z	z	X
ejpam-3248	266	2	]	]	X
ejpam-3248	267	1	+	+	CCONJ
ejpam-3248	267	2	[	[	X
ejpam-3248	267	3	f	f	X
ejpam-3248	267	4	(	(	PUNCT
ejpam-3248	267	5	z)zxd(z	z)zxd(z	NUM
ejpam-3248	267	6	)	)	PUNCT
ejpam-3248	267	7	,	,	PUNCT
ejpam-3248	267	8	z	z	X
ejpam-3248	267	9	]	]	X
ejpam-3248	267	10	=	=	SYM
ejpam-3248	267	11	0	0	NUM
ejpam-3248	267	12	for	for	ADP
ejpam-3248	267	13	all	all	DET
ejpam-3248	267	14	x	x	NOUN
ejpam-3248	267	15	,	,	PUNCT
ejpam-3248	267	16	z	z	PROPN
ejpam-3248	267	17	∈	∈	PROPN
ejpam-3248	267	18	i.	i.	NOUN
ejpam-3248	267	19	(	(	PUNCT
ejpam-3248	267	20	3.46	3.46	NUM
ejpam-3248	267	21	)	)	PUNCT
ejpam-3248	267	22	subtracting	subtract	VERB
ejpam-3248	267	23	(	(	PUNCT
ejpam-3248	267	24	3.46	3.46	NUM
ejpam-3248	267	25	)	)	PUNCT
ejpam-3248	267	26	from	from	ADP
ejpam-3248	267	27	(	(	PUNCT
ejpam-3248	267	28	3.45	3.45	NUM
ejpam-3248	267	29	)	)	PUNCT
ejpam-3248	267	30	,	,	PUNCT
ejpam-3248	267	31	we	we	PRON
ejpam-3248	267	32	obtain	obtain	VERB
ejpam-3248	267	33	[	[	X
ejpam-3248	267	34	[	[	X
ejpam-3248	267	35	x	x	X
ejpam-3248	267	36	,	,	PUNCT
ejpam-3248	267	37	z]zd(z	z]zd(z	NUM
ejpam-3248	267	38	)	)	PUNCT
ejpam-3248	267	39	,	,	PUNCT
ejpam-3248	268	1	z	z	X
ejpam-3248	268	2	]	]	X
ejpam-3248	268	3	+	+	CCONJ
ejpam-3248	268	4	[	[	X
ejpam-3248	268	5	zd(z)xd(z	zd(z)xd(z	NOUN
ejpam-3248	268	6	)	)	PUNCT
ejpam-3248	268	7	,	,	PUNCT
ejpam-3248	268	8	z	z	X
ejpam-3248	268	9	]	]	X
ejpam-3248	268	10	=	=	SYM
ejpam-3248	268	11	0	0	NUM
ejpam-3248	268	12	for	for	ADP
ejpam-3248	268	13	all	all	DET
ejpam-3248	268	14	x	x	NOUN
ejpam-3248	268	15	,	,	PUNCT
ejpam-3248	268	16	z	z	PROPN
ejpam-3248	268	17	∈	∈	PROPN
ejpam-3248	268	18	i.	i.	NOUN
ejpam-3248	268	19	(	(	PUNCT
ejpam-3248	268	20	3.47	3.47	NUM
ejpam-3248	268	21	)	)	PUNCT
ejpam-3248	268	22	substituting	substitute	VERB
ejpam-3248	268	23	zx	zx	PROPN
ejpam-3248	268	24	for	for	ADP
ejpam-3248	268	25	x	x	SYM
ejpam-3248	268	26	in	in	ADP
ejpam-3248	268	27	(	(	PUNCT
ejpam-3248	268	28	3.47	3.47	NUM
ejpam-3248	268	29	)	)	PUNCT
ejpam-3248	268	30	,	,	PUNCT
ejpam-3248	268	31	we	we	PRON
ejpam-3248	268	32	get	get	VERB
ejpam-3248	268	33	z[[x	z[[x	PROPN
ejpam-3248	268	34	,	,	PUNCT
ejpam-3248	268	35	z]zd(z	z]zd(z	NUM
ejpam-3248	268	36	)	)	PUNCT
ejpam-3248	268	37	,	,	PUNCT
ejpam-3248	269	1	z	z	X
ejpam-3248	269	2	]	]	X
ejpam-3248	269	3	+	+	CCONJ
ejpam-3248	270	1	[	[	X
ejpam-3248	270	2	zd(z)zxd(z	zd(z)zxd(z	NOUN
ejpam-3248	270	3	)	)	PUNCT
ejpam-3248	270	4	,	,	PUNCT
ejpam-3248	271	1	z	z	X
ejpam-3248	271	2	]	]	X
ejpam-3248	271	3	=	=	SYM
ejpam-3248	271	4	0	0	X
ejpam-3248	271	5	.	.	PUNCT
ejpam-3248	272	1	(	(	PUNCT
ejpam-3248	272	2	3.48	3.48	NUM
ejpam-3248	272	3	)	)	PUNCT
ejpam-3248	272	4	left	leave	VERB
ejpam-3248	272	5	multiplying	multiplying	NOUN
ejpam-3248	272	6	(	(	PUNCT
ejpam-3248	272	7	3.47	3.47	NUM
ejpam-3248	272	8	)	)	PUNCT
ejpam-3248	272	9	by	by	ADP
ejpam-3248	272	10	z	z	NOUN
ejpam-3248	272	11	and	and	CCONJ
ejpam-3248	272	12	subtracting	subtract	VERB
ejpam-3248	272	13	from	from	ADP
ejpam-3248	272	14	(	(	PUNCT
ejpam-3248	272	15	3.48	3.48	NUM
ejpam-3248	272	16	)	)	PUNCT
ejpam-3248	272	17	,	,	PUNCT
ejpam-3248	272	18	we	we	PRON
ejpam-3248	272	19	obtain	obtain	VERB
ejpam-3248	272	20	[	[	X
ejpam-3248	272	21	z[d(z	z[d(z	NOUN
ejpam-3248	272	22	)	)	PUNCT
ejpam-3248	272	23	,	,	PUNCT
ejpam-3248	272	24	z]xd(z	z]xd(z	PROPN
ejpam-3248	272	25	)	)	PUNCT
ejpam-3248	272	26	,	,	PUNCT
ejpam-3248	272	27	z	z	X
ejpam-3248	272	28	]	]	X
ejpam-3248	272	29	=	=	SYM
ejpam-3248	272	30	0	0	NUM
ejpam-3248	273	1	for	for	ADP
ejpam-3248	273	2	all	all	DET
ejpam-3248	273	3	x	x	NOUN
ejpam-3248	273	4	,	,	PUNCT
ejpam-3248	273	5	z	z	PROPN
ejpam-3248	273	6	∈	∈	PROPN
ejpam-3248	273	7	i.	i.	NOUN
ejpam-3248	273	8	(	(	PUNCT
ejpam-3248	273	9	3.49	3.49	NUM
ejpam-3248	273	10	)	)	PUNCT
ejpam-3248	273	11	substituting	substitute	VERB
ejpam-3248	273	12	xz	xz	PROPN
ejpam-3248	273	13	for	for	ADP
ejpam-3248	273	14	x	x	SYM
ejpam-3248	273	15	in	in	ADP
ejpam-3248	273	16	(	(	PUNCT
ejpam-3248	273	17	3.49	3.49	NUM
ejpam-3248	273	18	)	)	PUNCT
ejpam-3248	273	19	,	,	PUNCT
ejpam-3248	273	20	we	we	PRON
ejpam-3248	273	21	get	get	VERB
ejpam-3248	273	22	[	[	X
ejpam-3248	273	23	z[d(z	z[d(z	NOUN
ejpam-3248	273	24	)	)	PUNCT
ejpam-3248	273	25	,	,	PUNCT
ejpam-3248	273	26	z]xzd(z	z]xzd(z	NUM
ejpam-3248	273	27	)	)	PUNCT
ejpam-3248	273	28	,	,	PUNCT
ejpam-3248	273	29	z	z	X
ejpam-3248	273	30	]	]	X
ejpam-3248	273	31	=	=	SYM
ejpam-3248	273	32	0	0	NUM
ejpam-3248	273	33	for	for	ADP
ejpam-3248	273	34	all	all	DET
ejpam-3248	273	35	x	x	NOUN
ejpam-3248	273	36	,	,	PUNCT
ejpam-3248	273	37	z	z	PROPN
ejpam-3248	273	38	∈	∈	PROPN
ejpam-3248	273	39	i.	i.	NOUN
ejpam-3248	273	40	(	(	PUNCT
ejpam-3248	273	41	3.50	3.50	NUM
ejpam-3248	273	42	)	)	PUNCT
ejpam-3248	273	43	right	right	ADJ
ejpam-3248	273	44	multiplying	multiplying	NOUN
ejpam-3248	273	45	(	(	PUNCT
ejpam-3248	273	46	3.49	3.49	NUM
ejpam-3248	273	47	)	)	PUNCT
ejpam-3248	273	48	by	by	ADP
ejpam-3248	273	49	z	z	NOUN
ejpam-3248	273	50	and	and	CCONJ
ejpam-3248	273	51	subtracting	subtract	VERB
ejpam-3248	273	52	from	from	ADP
ejpam-3248	273	53	(	(	PUNCT
ejpam-3248	273	54	3.50	3.50	NUM
ejpam-3248	273	55	)	)	PUNCT
ejpam-3248	273	56	,	,	PUNCT
ejpam-3248	273	57	we	we	PRON
ejpam-3248	273	58	get	get	VERB
ejpam-3248	273	59	[	[	X
ejpam-3248	273	60	z[d(z	z[d(z	NOUN
ejpam-3248	273	61	)	)	PUNCT
ejpam-3248	273	62	,	,	PUNCT
ejpam-3248	273	63	z]x[d(z	z]x[d(z	NOUN
ejpam-3248	273	64	)	)	PUNCT
ejpam-3248	273	65	,	,	PUNCT
ejpam-3248	274	1	z	z	X
ejpam-3248	274	2	]	]	X
ejpam-3248	274	3	,	,	PUNCT
ejpam-3248	274	4	z	z	X
ejpam-3248	274	5	]	]	X
ejpam-3248	274	6	=	=	SYM
ejpam-3248	274	7	0	0	NUM
ejpam-3248	274	8	for	for	ADP
ejpam-3248	274	9	all	all	DET
ejpam-3248	274	10	x	x	NOUN
ejpam-3248	274	11	,	,	PUNCT
ejpam-3248	274	12	z	z	PROPN
ejpam-3248	274	13	∈	∈	PROPN
ejpam-3248	274	14	i.	i.	NOUN
ejpam-3248	274	15	(	(	PUNCT
ejpam-3248	274	16	3.51	3.51	NUM
ejpam-3248	274	17	)	)	PUNCT
ejpam-3248	274	18	this	this	PRON
ejpam-3248	274	19	is	be	AUX
ejpam-3248	274	20	the	the	DET
ejpam-3248	274	21	same	same	ADJ
ejpam-3248	274	22	as	as	ADP
ejpam-3248	274	23	(	(	PUNCT
ejpam-3248	274	24	3.33	3.33	NUM
ejpam-3248	274	25	)	)	PUNCT
ejpam-3248	274	26	in	in	ADP
ejpam-3248	274	27	theorem	theorem	ADJ
ejpam-3248	274	28	3.3	3.3	NUM
ejpam-3248	274	29	.	.	PUNCT
ejpam-3248	275	1	then	then	ADV
ejpam-3248	275	2	by	by	ADP
ejpam-3248	275	3	using	use	VERB
ejpam-3248	275	4	the	the	DET
ejpam-3248	275	5	same	same	ADJ
ejpam-3248	275	6	technique	technique	NOUN
ejpam-3248	275	7	as	as	SCONJ
ejpam-3248	275	8	we	we	PRON
ejpam-3248	275	9	have	have	AUX
ejpam-3248	275	10	used	use	VERB
ejpam-3248	275	11	in	in	ADP
ejpam-3248	275	12	theorem	theorem	ADJ
ejpam-3248	275	13	3.3	3.3	NUM
ejpam-3248	275	14	,	,	PUNCT
ejpam-3248	275	15	we	we	PRON
ejpam-3248	275	16	get	get	VERB
ejpam-3248	275	17	the	the	DET
ejpam-3248	275	18	result	result	NOUN
ejpam-3248	275	19	.	.	PUNCT
ejpam-3248	276	1	in	in	ADP
ejpam-3248	276	2	a	a	DET
ejpam-3248	276	3	similar	similar	ADJ
ejpam-3248	276	4	manner	manner	NOUN
ejpam-3248	276	5	we	we	PRON
ejpam-3248	276	6	can	can	AUX
ejpam-3248	276	7	prove	prove	VERB
ejpam-3248	276	8	the	the	DET
ejpam-3248	276	9	result	result	NOUN
ejpam-3248	276	10	for	for	ADP
ejpam-3248	276	11	the	the	DET
ejpam-3248	276	12	case	case	NOUN
ejpam-3248	276	13	f	f	X
ejpam-3248	276	14	(	(	PUNCT
ejpam-3248	276	15	xy)−	xy)−	X
ejpam-3248	276	16	f	f	PROPN
ejpam-3248	276	17	(	(	PUNCT
ejpam-3248	276	18	y)f	y)f	NOUN
ejpam-3248	276	19	(	(	PUNCT
ejpam-3248	276	20	x	x	X
ejpam-3248	276	21	)	)	PUNCT
ejpam-3248	276	22	∈	∈	PROPN
ejpam-3248	276	23	z(r	z(r	PROPN
ejpam-3248	276	24	)	)	PUNCT
ejpam-3248	276	25	for	for	ADP
ejpam-3248	276	26	all	all	DET
ejpam-3248	276	27	x	x	NOUN
ejpam-3248	276	28	,	,	PUNCT
ejpam-3248	276	29	y	y	PROPN
ejpam-3248	276	30	∈	∈	PROPN
ejpam-3248	276	31	i.	i.	NOUN
ejpam-3248	276	32	an	an	DET
ejpam-3248	276	33	immediate	immediate	ADJ
ejpam-3248	276	34	consequence	consequence	NOUN
ejpam-3248	276	35	of	of	ADP
ejpam-3248	276	36	above	above	ADJ
ejpam-3248	276	37	theorems	theorem	NOUN
ejpam-3248	276	38	and	and	CCONJ
ejpam-3248	276	39	together	together	ADV
ejpam-3248	276	40	with	with	ADP
ejpam-3248	276	41	lemma	lemma	PROPN
ejpam-3248	276	42	2.3	2.3	NUM
ejpam-3248	276	43	we	we	PRON
ejpam-3248	276	44	have	have	VERB
ejpam-3248	276	45	the	the	DET
ejpam-3248	276	46	following	follow	VERB
ejpam-3248	276	47	corollary	corollary	ADJ
ejpam-3248	276	48	:	:	PUNCT
ejpam-3248	276	49	corollary	corollary	ADJ
ejpam-3248	276	50	3.1	3.1	NUM
ejpam-3248	276	51	.	.	PUNCT
ejpam-3248	277	1	let	let	VERB
ejpam-3248	277	2	r	r	PRON
ejpam-3248	277	3	be	be	AUX
ejpam-3248	277	4	a	a	DET
ejpam-3248	277	5	semiprime	semiprime	NOUN
ejpam-3248	277	6	ring	ring	NOUN
ejpam-3248	277	7	and	and	CCONJ
ejpam-3248	277	8	f	f	PROPN
ejpam-3248	277	9	be	be	AUX
ejpam-3248	277	10	a	a	DET
ejpam-3248	277	11	non	non	ADJ
ejpam-3248	277	12	-	-	ADJ
ejpam-3248	277	13	zero	zero	ADJ
ejpam-3248	277	14	multiplicative	multiplicative	ADJ
ejpam-3248	277	15	(	(	PUNCT
ejpam-3248	277	16	generalized	generalized	ADJ
ejpam-3248	277	17	)	)	PUNCT
ejpam-3248	277	18	reverse	reverse	ADJ
ejpam-3248	277	19	derivation	derivation	NOUN
ejpam-3248	277	20	associated	associate	VERB
ejpam-3248	277	21	with	with	ADP
ejpam-3248	277	22	a	a	DET
ejpam-3248	277	23	non	non	ADJ
ejpam-3248	277	24	-	-	ADJ
ejpam-3248	277	25	zero	zero	NUM
ejpam-3248	277	26	derivation	derivation	NOUN
ejpam-3248	277	27	d	d	NOUN
ejpam-3248	277	28	:	:	PUNCT
ejpam-3248	277	29	r→	r→	PROPN
ejpam-3248	277	30	r.	r.	PROPN
ejpam-3248	277	31	then	then	ADV
ejpam-3248	277	32	d	d	PROPN
ejpam-3248	277	33	maps	map	VERB
ejpam-3248	277	34	r	r	NOUN
ejpam-3248	277	35	into	into	ADP
ejpam-3248	277	36	z(r	z(r	NOUN
ejpam-3248	277	37	)	)	PUNCT
ejpam-3248	277	38	,	,	PUNCT
ejpam-3248	277	39	the	the	DET
ejpam-3248	277	40	centre	centre	NOUN
ejpam-3248	277	41	of	of	ADP
ejpam-3248	277	42	r	r	NOUN
ejpam-3248	277	43	if	if	SCONJ
ejpam-3248	277	44	for	for	ADP
ejpam-3248	277	45	all	all	DET
ejpam-3248	277	46	x	x	NOUN
ejpam-3248	277	47	,	,	PUNCT
ejpam-3248	277	48	y	y	PROPN
ejpam-3248	277	49	∈	∈	PROPN
ejpam-3248	277	50	r	r	NOUN
ejpam-3248	277	51	,	,	PUNCT
ejpam-3248	277	52	one	one	NUM
ejpam-3248	277	53	of	of	ADP
ejpam-3248	277	54	the	the	DET
ejpam-3248	277	55	following	follow	VERB
ejpam-3248	277	56	holds	hold	VERB
ejpam-3248	277	57	:	:	PUNCT
ejpam-3248	277	58	(	(	PUNCT
ejpam-3248	277	59	i)f	i)f	X
ejpam-3248	277	60	(	(	PUNCT
ejpam-3248	277	61	xy)±	xy)±	VERB
ejpam-3248	278	1	[	[	X
ejpam-3248	278	2	x	x	X
ejpam-3248	278	3	,	,	PUNCT
ejpam-3248	278	4	y	y	PROPN
ejpam-3248	278	5	]	]	X
ejpam-3248	278	6	∈	∈	PROPN
ejpam-3248	278	7	z(r	z(r	PROPN
ejpam-3248	278	8	)	)	PUNCT
ejpam-3248	278	9	.	.	PUNCT
ejpam-3248	279	1	(	(	PUNCT
ejpam-3248	279	2	ii)f	ii)f	PROPN
ejpam-3248	279	3	(	(	PUNCT
ejpam-3248	279	4	xy)±	xy)±	VERB
ejpam-3248	279	5	x	x	PUNCT
ejpam-3248	279	6	◦	◦	VERB
ejpam-3248	279	7	y	y	PROPN
ejpam-3248	279	8	∈	∈	PROPN
ejpam-3248	279	9	z(r	z(r	PROPN
ejpam-3248	279	10	)	)	PUNCT
ejpam-3248	279	11	.	.	PUNCT
ejpam-3248	280	1	(	(	PUNCT
ejpam-3248	280	2	iii)f	iii)f	PROPN
ejpam-3248	280	3	(	(	PUNCT
ejpam-3248	280	4	xy)±	xy)±	VERB
ejpam-3248	280	5	f	f	PROPN
ejpam-3248	280	6	(	(	PUNCT
ejpam-3248	280	7	y)f	y)f	NOUN
ejpam-3248	280	8	(	(	PUNCT
ejpam-3248	280	9	x	x	X
ejpam-3248	280	10	)	)	PUNCT
ejpam-3248	280	11	∈	∈	PROPN
ejpam-3248	280	12	z(r	z(r	PROPN
ejpam-3248	280	13	)	)	PUNCT
ejpam-3248	280	14	.	.	PUNCT
ejpam-3248	280	15	a.	a.	PROPN
ejpam-3248	280	16	ali	ali	PROPN
ejpam-3248	280	17	,	,	PUNCT
ejpam-3248	280	18	a.	a.	PROPN
ejpam-3248	280	19	bano	bano	PROPN
ejpam-3248	280	20	/	/	SYM
ejpam-3248	280	21	eur	eur	PROPN
ejpam-3248	280	22	.	.	PUNCT
ejpam-3248	281	1	j.	j.	PROPN
ejpam-3248	281	2	pure	pure	PROPN
ejpam-3248	281	3	appl	appl	PROPN
ejpam-3248	281	4	.	.	PROPN
ejpam-3248	281	5	math	math	PROPN
ejpam-3248	281	6	,	,	PUNCT
ejpam-3248	281	7	11	11	NUM
ejpam-3248	281	8	(	(	PUNCT
ejpam-3248	281	9	3	3	NUM
ejpam-3248	281	10	)	)	PUNCT
ejpam-3248	281	11	(	(	PUNCT
ejpam-3248	281	12	2018	2018	NUM
ejpam-3248	281	13	)	)	PUNCT
ejpam-3248	281	14	,	,	PUNCT
ejpam-3248	281	15	717	717	NUM
ejpam-3248	281	16	-	-	SYM
ejpam-3248	281	17	729	729	NUM
ejpam-3248	281	18	726	726	NUM
ejpam-3248	281	19	theorem	theorem	NOUN
ejpam-3248	281	20	3.6	3.6	NUM
ejpam-3248	281	21	.	.	PUNCT
ejpam-3248	282	1	let	let	VERB
ejpam-3248	282	2	r	r	PRON
ejpam-3248	282	3	be	be	AUX
ejpam-3248	282	4	a	a	DET
ejpam-3248	282	5	semiprime	semiprime	NOUN
ejpam-3248	282	6	ring	ring	NOUN
ejpam-3248	282	7	and	and	CCONJ
ejpam-3248	282	8	f	f	PROPN
ejpam-3248	282	9	be	be	AUX
ejpam-3248	282	10	a	a	DET
ejpam-3248	282	11	non	non	ADJ
ejpam-3248	282	12	-	-	ADJ
ejpam-3248	282	13	zero	zero	ADJ
ejpam-3248	282	14	multiplicative	multiplicative	ADJ
ejpam-3248	282	15	(	(	PUNCT
ejpam-3248	282	16	generalized	generalized	ADJ
ejpam-3248	282	17	)	)	PUNCT
ejpam-3248	282	18	reverse	reverse	ADJ
ejpam-3248	282	19	derivation	derivation	NOUN
ejpam-3248	282	20	associated	associate	VERB
ejpam-3248	282	21	with	with	ADP
ejpam-3248	282	22	a	a	DET
ejpam-3248	282	23	map	map	NOUN
ejpam-3248	283	1	d	d	NOUN
ejpam-3248	283	2	,	,	PUNCT
ejpam-3248	283	3	i	i	PRON
ejpam-3248	283	4	be	be	VERB
ejpam-3248	283	5	a	a	DET
ejpam-3248	283	6	non	non	ADJ
ejpam-3248	283	7	-	-	ADJ
ejpam-3248	283	8	zero	zero	NUM
ejpam-3248	283	9	ideal	ideal	NOUN
ejpam-3248	283	10	of	of	ADP
ejpam-3248	283	11	r.	r.	PROPN
ejpam-3248	283	12	if	if	SCONJ
ejpam-3248	283	13	[	[	X
ejpam-3248	283	14	f	f	X
ejpam-3248	283	15	(	(	PUNCT
ejpam-3248	283	16	x	x	NOUN
ejpam-3248	283	17	)	)	PUNCT
ejpam-3248	283	18	,	,	PUNCT
ejpam-3248	283	19	y]±	y]±	PROPN
ejpam-3248	283	20	xy	xy	PROPN
ejpam-3248	283	21	∈	∈	PROPN
ejpam-3248	283	22	z(r	z(r	PROPN
ejpam-3248	283	23	)	)	PUNCT
ejpam-3248	283	24	for	for	ADP
ejpam-3248	283	25	all	all	DET
ejpam-3248	283	26	x	x	NOUN
ejpam-3248	283	27	,	,	PUNCT
ejpam-3248	283	28	y	y	PROPN
ejpam-3248	283	29	∈	∈	PROPN
ejpam-3248	284	1	i	i	PRON
ejpam-3248	284	2	,	,	PUNCT
ejpam-3248	284	3	then	then	ADV
ejpam-3248	284	4	[	[	X
ejpam-3248	284	5	d(x	d(x	NOUN
ejpam-3248	284	6	)	)	PUNCT
ejpam-3248	284	7	,	,	PUNCT
ejpam-3248	284	8	x	x	X
ejpam-3248	284	9	]	]	X
ejpam-3248	284	10	=	=	SYM
ejpam-3248	284	11	0	0	NUM
ejpam-3248	284	12	for	for	ADP
ejpam-3248	284	13	all	all	DET
ejpam-3248	284	14	x	x	SYM
ejpam-3248	284	15	∈	∈	NOUN
ejpam-3248	284	16	i.	i.	NOUN
ejpam-3248	284	17	proof	proof	NOUN
ejpam-3248	284	18	by	by	ADP
ejpam-3248	284	19	the	the	DET
ejpam-3248	284	20	hypothesis	hypothesis	NOUN
ejpam-3248	284	21	,	,	PUNCT
ejpam-3248	284	22	we	we	PRON
ejpam-3248	284	23	have	have	VERB
ejpam-3248	284	24	[	[	X
ejpam-3248	284	25	f	f	X
ejpam-3248	284	26	(	(	PUNCT
ejpam-3248	284	27	x	x	NOUN
ejpam-3248	284	28	)	)	PUNCT
ejpam-3248	284	29	,	,	PUNCT
ejpam-3248	284	30	y	y	PROPN
ejpam-3248	284	31	]	]	X
ejpam-3248	285	1	+	+	CCONJ
ejpam-3248	285	2	xy	xy	PROPN
ejpam-3248	285	3	∈	∈	PROPN
ejpam-3248	285	4	z(r	z(r	PROPN
ejpam-3248	285	5	)	)	PUNCT
ejpam-3248	285	6	for	for	ADP
ejpam-3248	285	7	all	all	DET
ejpam-3248	285	8	x	x	NOUN
ejpam-3248	285	9	,	,	PUNCT
ejpam-3248	285	10	y	y	PROPN
ejpam-3248	285	11	∈	∈	PROPN
ejpam-3248	285	12	i.	i.	NOUN
ejpam-3248	285	13	(	(	PUNCT
ejpam-3248	285	14	3.52	3.52	NUM
ejpam-3248	285	15	)	)	PUNCT
ejpam-3248	285	16	replacing	replace	VERB
ejpam-3248	285	17	x	x	PUNCT
ejpam-3248	285	18	by	by	ADP
ejpam-3248	285	19	zx	zx	PROPN
ejpam-3248	285	20	in	in	ADP
ejpam-3248	285	21	(	(	PUNCT
ejpam-3248	285	22	3.52	3.52	NUM
ejpam-3248	285	23	)	)	PUNCT
ejpam-3248	285	24	,	,	PUNCT
ejpam-3248	285	25	we	we	PRON
ejpam-3248	285	26	get	get	VERB
ejpam-3248	285	27	[	[	X
ejpam-3248	285	28	f	f	X
ejpam-3248	285	29	(	(	PUNCT
ejpam-3248	285	30	x)z	x)z	PUNCT
ejpam-3248	285	31	+	+	NUM
ejpam-3248	285	32	xd(z	xd(z	NUM
ejpam-3248	285	33	)	)	PUNCT
ejpam-3248	285	34	,	,	PUNCT
ejpam-3248	285	35	y	y	PROPN
ejpam-3248	285	36	]	]	X
ejpam-3248	286	1	+	+	NUM
ejpam-3248	286	2	zxy	zxy	NOUN
ejpam-3248	286	3	+	+	CCONJ
ejpam-3248	286	4	xyz	xyz	PROPN
ejpam-3248	286	5	−	−	PROPN
ejpam-3248	286	6	xyz	xyz	PROPN
ejpam-3248	286	7	∈	∈	PROPN
ejpam-3248	286	8	z(r	z(r	PROPN
ejpam-3248	286	9	)	)	PUNCT
ejpam-3248	286	10	for	for	ADP
ejpam-3248	286	11	all	all	DET
ejpam-3248	286	12	x	x	NOUN
ejpam-3248	286	13	,	,	PUNCT
ejpam-3248	286	14	y	y	PROPN
ejpam-3248	286	15	,	,	PUNCT
ejpam-3248	286	16	z	z	PROPN
ejpam-3248	286	17	∈	∈	PROPN
ejpam-3248	286	18	i.	i.	NOUN
ejpam-3248	286	19	this	this	PRON
ejpam-3248	286	20	gives	give	VERB
ejpam-3248	286	21	that	that	DET
ejpam-3248	286	22	f	f	PROPN
ejpam-3248	286	23	(	(	PUNCT
ejpam-3248	286	24	x)[z	x)[z	PROPN
ejpam-3248	286	25	,	,	PUNCT
ejpam-3248	286	26	y	y	PROPN
ejpam-3248	286	27	]	]	PUNCT
ejpam-3248	287	1	+	+	CCONJ
ejpam-3248	288	1	[	[	X
ejpam-3248	288	2	f	f	X
ejpam-3248	288	3	(	(	PUNCT
ejpam-3248	288	4	x	x	NOUN
ejpam-3248	288	5	)	)	PUNCT
ejpam-3248	288	6	,	,	PUNCT
ejpam-3248	288	7	y]z	y]z	NOUN
ejpam-3248	288	8	+	+	CCONJ
ejpam-3248	288	9	x[d(z	x[d(z	X
ejpam-3248	288	10	)	)	PUNCT
ejpam-3248	288	11	,	,	PUNCT
ejpam-3248	288	12	y	y	X
ejpam-3248	288	13	]	]	PUNCT
ejpam-3248	288	14	+	+	CCONJ
ejpam-3248	289	1	[	[	X
ejpam-3248	289	2	x	x	X
ejpam-3248	289	3	,	,	PUNCT
ejpam-3248	289	4	y]d(z	y]d(z	PROPN
ejpam-3248	289	5	)	)	PUNCT
ejpam-3248	289	6	+	+	NUM
ejpam-3248	289	7	xyz	xyz	NOUN
ejpam-3248	289	8	+	+	X
ejpam-3248	290	1	[	[	X
ejpam-3248	290	2	z	z	X
ejpam-3248	290	3	,	,	PUNCT
ejpam-3248	290	4	xy	xy	PROPN
ejpam-3248	290	5	]	]	X
ejpam-3248	290	6	∈	∈	PROPN
ejpam-3248	290	7	z(r	z(r	PROPN
ejpam-3248	290	8	)	)	PUNCT
ejpam-3248	290	9	.	.	PUNCT
ejpam-3248	291	1	(	(	PUNCT
ejpam-3248	291	2	3.53	3.53	NUM
ejpam-3248	291	3	)	)	PUNCT
ejpam-3248	291	4	commuting	commuting	NOUN
ejpam-3248	291	5	(	(	PUNCT
ejpam-3248	291	6	3.53	3.53	NUM
ejpam-3248	291	7	)	)	PUNCT
ejpam-3248	291	8	with	with	ADP
ejpam-3248	291	9	z	z	NOUN
ejpam-3248	291	10	and	and	CCONJ
ejpam-3248	291	11	using	use	VERB
ejpam-3248	291	12	(	(	PUNCT
ejpam-3248	291	13	3.52	3.52	NUM
ejpam-3248	291	14	)	)	PUNCT
ejpam-3248	291	15	,	,	PUNCT
ejpam-3248	291	16	we	we	PRON
ejpam-3248	291	17	obtain	obtain	VERB
ejpam-3248	292	1	[	[	X
ejpam-3248	293	1	f	f	X
ejpam-3248	293	2	(	(	PUNCT
ejpam-3248	293	3	x)[z	x)[z	PROPN
ejpam-3248	293	4	,	,	PUNCT
ejpam-3248	293	5	y	y	PROPN
ejpam-3248	293	6	]	]	X
ejpam-3248	293	7	,	,	PUNCT
ejpam-3248	293	8	z	z	X
ejpam-3248	293	9	]	]	X
ejpam-3248	293	10	+	+	CCONJ
ejpam-3248	294	1	[	[	X
ejpam-3248	294	2	x[d(z	x[d(z	X
ejpam-3248	294	3	)	)	PUNCT
ejpam-3248	294	4	,	,	PUNCT
ejpam-3248	294	5	y	y	PROPN
ejpam-3248	294	6	]	]	X
ejpam-3248	294	7	,	,	PUNCT
ejpam-3248	294	8	z	z	X
ejpam-3248	294	9	]	]	X
ejpam-3248	295	1	+	+	CCONJ
ejpam-3248	296	1	[	[	X
ejpam-3248	296	2	[	[	X
ejpam-3248	296	3	x	x	X
ejpam-3248	296	4	,	,	PUNCT
ejpam-3248	296	5	y]d(z	y]d(z	PROPN
ejpam-3248	296	6	)	)	PUNCT
ejpam-3248	296	7	,	,	PUNCT
ejpam-3248	296	8	z	z	X
ejpam-3248	296	9	]	]	X
ejpam-3248	296	10	+	+	CCONJ
ejpam-3248	297	1	[	[	X
ejpam-3248	297	2	x[z	x[z	X
ejpam-3248	297	3	,	,	PUNCT
ejpam-3248	297	4	y	y	X
ejpam-3248	297	5	]	]	PUNCT
ejpam-3248	298	1	+	+	CCONJ
ejpam-3248	299	1	[	[	X
ejpam-3248	299	2	z	z	X
ejpam-3248	299	3	,	,	PUNCT
ejpam-3248	299	4	x]y	x]y	PROPN
ejpam-3248	299	5	,	,	PUNCT
ejpam-3248	299	6	z	z	X
ejpam-3248	299	7	]	]	X
ejpam-3248	299	8	=	=	SYM
ejpam-3248	299	9	0	0	X
ejpam-3248	299	10	.	.	PUNCT
ejpam-3248	300	1	this	this	PRON
ejpam-3248	300	2	implies	imply	VERB
ejpam-3248	300	3	that	that	SCONJ
ejpam-3248	301	1	[	[	X
ejpam-3248	301	2	f	f	X
ejpam-3248	301	3	(	(	PUNCT
ejpam-3248	301	4	x)[z	x)[z	PROPN
ejpam-3248	301	5	,	,	PUNCT
ejpam-3248	301	6	y	y	PROPN
ejpam-3248	301	7	]	]	X
ejpam-3248	301	8	,	,	PUNCT
ejpam-3248	301	9	z	z	X
ejpam-3248	301	10	]	]	X
ejpam-3248	301	11	+	+	CCONJ
ejpam-3248	301	12	[	[	X
ejpam-3248	301	13	x[d(z	x[d(z	X
ejpam-3248	301	14	)	)	PUNCT
ejpam-3248	301	15	,	,	PUNCT
ejpam-3248	301	16	y	y	PROPN
ejpam-3248	301	17	]	]	X
ejpam-3248	301	18	,	,	PUNCT
ejpam-3248	302	1	z	z	X
ejpam-3248	302	2	]	]	X
ejpam-3248	303	1	+	+	CCONJ
ejpam-3248	304	1	[	[	X
ejpam-3248	304	2	[	[	X
ejpam-3248	304	3	x	x	X
ejpam-3248	304	4	,	,	PUNCT
ejpam-3248	304	5	y]d(z	y]d(z	PROPN
ejpam-3248	304	6	)	)	PUNCT
ejpam-3248	304	7	,	,	PUNCT
ejpam-3248	304	8	z	z	X
ejpam-3248	304	9	]	]	X
ejpam-3248	304	10	+	+	CCONJ
ejpam-3248	305	1	[	[	X
ejpam-3248	305	2	x[z	x[z	X
ejpam-3248	305	3	,	,	PUNCT
ejpam-3248	305	4	y	y	PROPN
ejpam-3248	305	5	]	]	X
ejpam-3248	305	6	,	,	PUNCT
ejpam-3248	305	7	z	z	X
ejpam-3248	305	8	]	]	X
ejpam-3248	306	1	+	+	CCONJ
ejpam-3248	306	2	[	[	X
ejpam-3248	306	3	[	[	X
ejpam-3248	306	4	z	z	X
ejpam-3248	306	5	,	,	PUNCT
ejpam-3248	306	6	x]y	x]y	PROPN
ejpam-3248	306	7	,	,	PUNCT
ejpam-3248	306	8	z	z	X
ejpam-3248	306	9	]	]	X
ejpam-3248	306	10	=	=	SYM
ejpam-3248	306	11	0	0	X
ejpam-3248	306	12	.	.	PUNCT
ejpam-3248	307	1	(	(	PUNCT
ejpam-3248	307	2	3.54	3.54	NUM
ejpam-3248	307	3	)	)	PUNCT
ejpam-3248	307	4	substituting	substitute	VERB
ejpam-3248	307	5	yz	yz	PROPN
ejpam-3248	307	6	for	for	ADP
ejpam-3248	307	7	y	y	PROPN
ejpam-3248	307	8	in	in	ADP
ejpam-3248	307	9	(	(	PUNCT
ejpam-3248	307	10	3.54	3.54	NUM
ejpam-3248	307	11	)	)	PUNCT
ejpam-3248	307	12	,	,	PUNCT
ejpam-3248	307	13	we	we	PRON
ejpam-3248	307	14	get	get	VERB
ejpam-3248	307	15	[	[	X
ejpam-3248	307	16	f	f	X
ejpam-3248	307	17	(	(	PUNCT
ejpam-3248	307	18	x)[z	x)[z	PROPN
ejpam-3248	307	19	,	,	PUNCT
ejpam-3248	307	20	y	y	PROPN
ejpam-3248	307	21	]	]	X
ejpam-3248	307	22	,	,	PUNCT
ejpam-3248	307	23	z]z	z]z	NOUN
ejpam-3248	307	24	+	+	X
ejpam-3248	308	1	[	[	X
ejpam-3248	308	2	xy[d(z	xy[d(z	NOUN
ejpam-3248	308	3	)	)	PUNCT
ejpam-3248	308	4	,	,	PUNCT
ejpam-3248	309	1	z	z	X
ejpam-3248	309	2	]	]	X
ejpam-3248	309	3	,	,	PUNCT
ejpam-3248	309	4	z	z	X
ejpam-3248	309	5	]	]	X
ejpam-3248	310	1	+	+	CCONJ
ejpam-3248	310	2	[	[	X
ejpam-3248	310	3	x[d(z	x[d(z	X
ejpam-3248	310	4	)	)	PUNCT
ejpam-3248	310	5	,	,	PUNCT
ejpam-3248	310	6	y	y	PROPN
ejpam-3248	310	7	]	]	X
ejpam-3248	310	8	,	,	PUNCT
ejpam-3248	310	9	z]z	z]z	NOUN
ejpam-3248	310	10	+	+	PUNCT
ejpam-3248	310	11	[	[	X
ejpam-3248	310	12	y[x	y[x	NOUN
ejpam-3248	310	13	,	,	PUNCT
ejpam-3248	310	14	z]d(z	z]d(z	NUM
ejpam-3248	310	15	)	)	PUNCT
ejpam-3248	310	16	,	,	PUNCT
ejpam-3248	311	1	z	z	X
ejpam-3248	311	2	]	]	X
ejpam-3248	312	1	+	+	PUNCT
ejpam-3248	312	2	[	[	X
ejpam-3248	312	3	[	[	X
ejpam-3248	312	4	x	x	X
ejpam-3248	312	5	,	,	PUNCT
ejpam-3248	312	6	y]zd(z	y]zd(z	PROPN
ejpam-3248	312	7	)	)	PUNCT
ejpam-3248	312	8	,	,	PUNCT
ejpam-3248	313	1	z	z	X
ejpam-3248	313	2	]	]	X
ejpam-3248	313	3	+	+	CCONJ
ejpam-3248	314	1	[	[	X
ejpam-3248	314	2	x[z	x[z	X
ejpam-3248	314	3	,	,	PUNCT
ejpam-3248	314	4	y	y	PROPN
ejpam-3248	314	5	]	]	X
ejpam-3248	314	6	,	,	PUNCT
ejpam-3248	314	7	z]z	z]z	NOUN
ejpam-3248	314	8	+	+	X
ejpam-3248	315	1	[	[	X
ejpam-3248	315	2	[	[	X
ejpam-3248	315	3	z	z	X
ejpam-3248	315	4	,	,	PUNCT
ejpam-3248	315	5	x]y	x]y	PROPN
ejpam-3248	315	6	,	,	PUNCT
ejpam-3248	315	7	z]z	z]z	NOUN
ejpam-3248	315	8	=	=	SYM
ejpam-3248	315	9	0	0	X
ejpam-3248	315	10	.	.	PUNCT
ejpam-3248	315	11	(	(	PUNCT
ejpam-3248	315	12	3.55	3.55	NUM
ejpam-3248	315	13	)	)	PUNCT
ejpam-3248	315	14	right	right	ADJ
ejpam-3248	315	15	multiplying	multiplying	NOUN
ejpam-3248	315	16	(	(	PUNCT
ejpam-3248	315	17	3.54	3.54	NUM
ejpam-3248	315	18	)	)	PUNCT
ejpam-3248	315	19	by	by	ADP
ejpam-3248	315	20	z	z	NOUN
ejpam-3248	315	21	and	and	CCONJ
ejpam-3248	315	22	subtracting	subtract	VERB
ejpam-3248	315	23	from	from	ADP
ejpam-3248	315	24	(	(	PUNCT
ejpam-3248	315	25	3.55	3.55	NUM
ejpam-3248	315	26	)	)	PUNCT
ejpam-3248	315	27	,	,	PUNCT
ejpam-3248	315	28	we	we	PRON
ejpam-3248	315	29	obtain	obtain	VERB
ejpam-3248	315	30	[	[	X
ejpam-3248	315	31	[	[	X
ejpam-3248	315	32	x	x	X
ejpam-3248	315	33	,	,	PUNCT
ejpam-3248	315	34	y]d(z)z	y]d(z)z	NUM
ejpam-3248	315	35	,	,	PUNCT
ejpam-3248	315	36	z]−	z]−	PUNCT
ejpam-3248	316	1	[	[	X
ejpam-3248	316	2	xy[d(z	xy[d(z	PROPN
ejpam-3248	316	3	)	)	PUNCT
ejpam-3248	316	4	,	,	PUNCT
ejpam-3248	317	1	z	z	X
ejpam-3248	317	2	]	]	X
ejpam-3248	317	3	,	,	PUNCT
ejpam-3248	317	4	z]−	z]−	PUNCT
ejpam-3248	318	1	[	[	X
ejpam-3248	318	2	y[x	y[x	NOUN
ejpam-3248	318	3	,	,	PUNCT
ejpam-3248	318	4	z]d(z	z]d(z	NUM
ejpam-3248	318	5	)	)	PUNCT
ejpam-3248	318	6	,	,	PUNCT
ejpam-3248	318	7	z]−	z]−	PUNCT
ejpam-3248	319	1	[	[	X
ejpam-3248	319	2	[	[	X
ejpam-3248	319	3	x	x	X
ejpam-3248	319	4	,	,	PUNCT
ejpam-3248	319	5	y]zd(z	y]zd(z	PROPN
ejpam-3248	319	6	)	)	PUNCT
ejpam-3248	319	7	,	,	PUNCT
ejpam-3248	319	8	z	z	X
ejpam-3248	319	9	]	]	X
ejpam-3248	319	10	=	=	SYM
ejpam-3248	319	11	0	0	X
ejpam-3248	319	12	.	.	PUNCT
ejpam-3248	320	1	(	(	PUNCT
ejpam-3248	320	2	3.56	3.56	NUM
ejpam-3248	320	3	)	)	PUNCT
ejpam-3248	320	4	this	this	PRON
ejpam-3248	320	5	implies	imply	VERB
ejpam-3248	320	6	that	that	SCONJ
ejpam-3248	320	7	[	[	X
ejpam-3248	320	8	xyd(z)z−yxd(z)z−xyd(z)z+xyzd(z	xyd(z)z−yxd(z)z−xyd(z)z+xyzd(z	NOUN
ejpam-3248	320	9	)	)	PUNCT
ejpam-3248	320	10	,	,	PUNCT
ejpam-3248	320	11	z]−[yxzd(z)−yzxd(z	z]−[yxzd(z)−yzxd(z	PROPN
ejpam-3248	320	12	)	)	PUNCT
ejpam-3248	320	13	,	,	PUNCT
ejpam-3248	320	14	z]−[xyzd(z)−yxzd(z	z]−[xyzd(z)−yxzd(z	PROPN
ejpam-3248	320	15	)	)	PUNCT
ejpam-3248	320	16	,	,	PUNCT
ejpam-3248	321	1	z	z	X
ejpam-3248	321	2	]	]	X
ejpam-3248	321	3	=	=	SYM
ejpam-3248	321	4	0	0	X
ejpam-3248	321	5	.	.	PUNCT
ejpam-3248	322	1	after	after	ADP
ejpam-3248	322	2	a	a	DET
ejpam-3248	322	3	simple	simple	ADJ
ejpam-3248	322	4	calculation	calculation	NOUN
ejpam-3248	322	5	this	this	PRON
ejpam-3248	322	6	yields	yield	VERB
ejpam-3248	322	7	that	that	SCONJ
ejpam-3248	323	1	[	[	X
ejpam-3248	323	2	y[xd(z	y[xd(z	PROPN
ejpam-3248	323	3	)	)	PUNCT
ejpam-3248	323	4	,	,	PUNCT
ejpam-3248	323	5	z	z	X
ejpam-3248	323	6	]	]	X
ejpam-3248	323	7	,	,	PUNCT
ejpam-3248	323	8	z	z	X
ejpam-3248	323	9	]	]	X
ejpam-3248	323	10	=	=	SYM
ejpam-3248	323	11	0	0	NUM
ejpam-3248	323	12	for	for	ADP
ejpam-3248	323	13	all	all	DET
ejpam-3248	323	14	x	x	NOUN
ejpam-3248	323	15	,	,	PUNCT
ejpam-3248	323	16	y	y	PROPN
ejpam-3248	323	17	,	,	PUNCT
ejpam-3248	323	18	z	z	PROPN
ejpam-3248	323	19	∈	∈	PROPN
ejpam-3248	323	20	i.	i.	NOUN
ejpam-3248	323	21	(	(	PUNCT
ejpam-3248	323	22	3.57	3.57	NUM
ejpam-3248	323	23	)	)	PUNCT
ejpam-3248	323	24	replacing	replace	VERB
ejpam-3248	323	25	x	x	PUNCT
ejpam-3248	323	26	by	by	ADP
ejpam-3248	323	27	d(z)x	d(z)x	PROPN
ejpam-3248	323	28	in	in	ADP
ejpam-3248	323	29	(	(	PUNCT
ejpam-3248	323	30	3.57	3.57	NUM
ejpam-3248	323	31	)	)	PUNCT
ejpam-3248	323	32	,	,	PUNCT
ejpam-3248	323	33	we	we	PRON
ejpam-3248	323	34	get	get	VERB
ejpam-3248	323	35	[	[	X
ejpam-3248	323	36	y[d(z)xd(z	y[d(z)xd(z	NOUN
ejpam-3248	323	37	)	)	PUNCT
ejpam-3248	323	38	,	,	PUNCT
ejpam-3248	324	1	z	z	X
ejpam-3248	324	2	]	]	X
ejpam-3248	324	3	,	,	PUNCT
ejpam-3248	324	4	z	z	X
ejpam-3248	324	5	]	]	X
ejpam-3248	324	6	=	=	SYM
ejpam-3248	324	7	0	0	NUM
ejpam-3248	324	8	for	for	ADP
ejpam-3248	324	9	all	all	DET
ejpam-3248	324	10	x	x	NOUN
ejpam-3248	324	11	,	,	PUNCT
ejpam-3248	324	12	y	y	PROPN
ejpam-3248	324	13	,	,	PUNCT
ejpam-3248	324	14	z	z	PROPN
ejpam-3248	324	15	∈	∈	PROPN
ejpam-3248	324	16	i.	i.	NOUN
ejpam-3248	324	17	(	(	PUNCT
ejpam-3248	324	18	3.58	3.58	NUM
ejpam-3248	324	19	)	)	PUNCT
ejpam-3248	324	20	this	this	PRON
ejpam-3248	324	21	is	be	AUX
ejpam-3248	324	22	the	the	DET
ejpam-3248	324	23	same	same	ADJ
ejpam-3248	324	24	as	as	ADP
ejpam-3248	324	25	(	(	PUNCT
ejpam-3248	324	26	3.19	3.19	NUM
ejpam-3248	324	27	)	)	PUNCT
ejpam-3248	324	28	in	in	ADP
ejpam-3248	324	29	theorem	theorem	NOUN
ejpam-3248	324	30	3.2	3.2	NUM
ejpam-3248	324	31	.	.	PUNCT
ejpam-3248	325	1	we	we	PRON
ejpam-3248	325	2	can	can	AUX
ejpam-3248	325	3	complete	complete	VERB
ejpam-3248	325	4	the	the	DET
ejpam-3248	325	5	proof	proof	NOUN
ejpam-3248	325	6	by	by	ADP
ejpam-3248	325	7	using	use	VERB
ejpam-3248	325	8	similar	similar	ADJ
ejpam-3248	325	9	technique	technique	NOUN
ejpam-3248	325	10	as	as	SCONJ
ejpam-3248	325	11	we	we	PRON
ejpam-3248	325	12	have	have	AUX
ejpam-3248	325	13	used	use	VERB
ejpam-3248	325	14	in	in	ADP
ejpam-3248	325	15	theorem	theorem	ADJ
ejpam-3248	325	16	3.2	3.2	NUM
ejpam-3248	325	17	.	.	PUNCT
ejpam-3248	326	1	in	in	ADP
ejpam-3248	326	2	the	the	DET
ejpam-3248	326	3	similar	similar	ADJ
ejpam-3248	326	4	manner	manner	NOUN
ejpam-3248	326	5	the	the	DET
ejpam-3248	326	6	conclusion	conclusion	NOUN
ejpam-3248	326	7	can	can	AUX
ejpam-3248	326	8	be	be	AUX
ejpam-3248	326	9	obtained	obtain	VERB
ejpam-3248	326	10	for	for	ADP
ejpam-3248	326	11	[	[	X
ejpam-3248	326	12	f	f	X
ejpam-3248	326	13	(	(	PUNCT
ejpam-3248	326	14	x	x	NOUN
ejpam-3248	326	15	)	)	PUNCT
ejpam-3248	326	16	,	,	PUNCT
ejpam-3248	326	17	y]−	y]−	NOUN
ejpam-3248	326	18	xy	xy	PROPN
ejpam-3248	326	19	∈	∈	PROPN
ejpam-3248	326	20	z(r	z(r	PROPN
ejpam-3248	326	21	)	)	PUNCT
ejpam-3248	326	22	for	for	ADP
ejpam-3248	326	23	all	all	DET
ejpam-3248	326	24	x	x	NOUN
ejpam-3248	326	25	,	,	PUNCT
ejpam-3248	326	26	y	y	PROPN
ejpam-3248	326	27	∈	∈	PROPN
ejpam-3248	326	28	i.	i.	NOUN
ejpam-3248	326	29	using	use	VERB
ejpam-3248	326	30	similar	similar	ADJ
ejpam-3248	326	31	technique	technique	NOUN
ejpam-3248	326	32	with	with	ADP
ejpam-3248	326	33	some	some	DET
ejpam-3248	326	34	necessary	necessary	ADJ
ejpam-3248	326	35	variations	variation	NOUN
ejpam-3248	326	36	,	,	PUNCT
ejpam-3248	326	37	we	we	PRON
ejpam-3248	326	38	can	can	AUX
ejpam-3248	326	39	prove	prove	VERB
ejpam-3248	326	40	the	the	DET
ejpam-3248	326	41	following	following	NOUN
ejpam-3248	326	42	:	:	PUNCT
ejpam-3248	326	43	a.	a.	PROPN
ejpam-3248	326	44	ali	ali	PROPN
ejpam-3248	326	45	,	,	PUNCT
ejpam-3248	326	46	a.	a.	PROPN
ejpam-3248	326	47	bano	bano	PROPN
ejpam-3248	326	48	/	/	SYM
ejpam-3248	326	49	eur	eur	PROPN
ejpam-3248	326	50	.	.	PUNCT
ejpam-3248	327	1	j.	j.	PROPN
ejpam-3248	327	2	pure	pure	PROPN
ejpam-3248	327	3	appl	appl	PROPN
ejpam-3248	327	4	.	.	PROPN
ejpam-3248	327	5	math	math	PROPN
ejpam-3248	327	6	,	,	PUNCT
ejpam-3248	327	7	11	11	NUM
ejpam-3248	327	8	(	(	PUNCT
ejpam-3248	327	9	3	3	NUM
ejpam-3248	327	10	)	)	PUNCT
ejpam-3248	327	11	(	(	PUNCT
ejpam-3248	327	12	2018	2018	NUM
ejpam-3248	327	13	)	)	PUNCT
ejpam-3248	327	14	,	,	PUNCT
ejpam-3248	327	15	717	717	NUM
ejpam-3248	327	16	-	-	SYM
ejpam-3248	327	17	729	729	NUM
ejpam-3248	327	18	727	727	NUM
ejpam-3248	327	19	theorem	theorem	VERB
ejpam-3248	327	20	3.7	3.7	NUM
ejpam-3248	327	21	.	.	PUNCT
ejpam-3248	328	1	let	let	VERB
ejpam-3248	328	2	r	r	PRON
ejpam-3248	328	3	be	be	AUX
ejpam-3248	328	4	a	a	DET
ejpam-3248	328	5	semiprime	semiprime	NOUN
ejpam-3248	328	6	ring	ring	NOUN
ejpam-3248	328	7	and	and	CCONJ
ejpam-3248	328	8	f	f	PROPN
ejpam-3248	328	9	be	be	AUX
ejpam-3248	328	10	a	a	DET
ejpam-3248	328	11	non	non	ADJ
ejpam-3248	328	12	-	-	ADJ
ejpam-3248	328	13	zero	zero	ADJ
ejpam-3248	328	14	multiplicative	multiplicative	ADJ
ejpam-3248	328	15	(	(	PUNCT
ejpam-3248	328	16	generalized	generalized	ADJ
ejpam-3248	328	17	)	)	PUNCT
ejpam-3248	328	18	reverse	reverse	ADJ
ejpam-3248	328	19	derivation	derivation	NOUN
ejpam-3248	328	20	associated	associate	VERB
ejpam-3248	328	21	with	with	ADP
ejpam-3248	328	22	a	a	DET
ejpam-3248	328	23	map	map	NOUN
ejpam-3248	329	1	d	d	NOUN
ejpam-3248	329	2	,	,	PUNCT
ejpam-3248	329	3	i	i	PRON
ejpam-3248	329	4	be	be	VERB
ejpam-3248	329	5	a	a	DET
ejpam-3248	329	6	non	non	ADJ
ejpam-3248	329	7	-	-	ADJ
ejpam-3248	329	8	zero	zero	NUM
ejpam-3248	329	9	ideal	ideal	NOUN
ejpam-3248	329	10	of	of	ADP
ejpam-3248	329	11	r.	r.	PROPN
ejpam-3248	329	12	if	if	SCONJ
ejpam-3248	329	13	f	f	PROPN
ejpam-3248	329	14	(	(	PUNCT
ejpam-3248	329	15	x	x	X
ejpam-3248	329	16	)	)	PUNCT
ejpam-3248	329	17	◦	◦	NOUN
ejpam-3248	329	18	y±	y±	PROPN
ejpam-3248	329	19	xy	xy	PROPN
ejpam-3248	330	1	∈	∈	PROPN
ejpam-3248	331	1	z(r	z(r	PROPN
ejpam-3248	331	2	)	)	PUNCT
ejpam-3248	331	3	for	for	ADP
ejpam-3248	331	4	all	all	DET
ejpam-3248	331	5	x	x	NOUN
ejpam-3248	331	6	,	,	PUNCT
ejpam-3248	331	7	y	y	PROPN
ejpam-3248	331	8	∈	∈	PROPN
ejpam-3248	332	1	i	i	PRON
ejpam-3248	332	2	,	,	PUNCT
ejpam-3248	332	3	then	then	ADV
ejpam-3248	332	4	[	[	X
ejpam-3248	332	5	d(x	d(x	NOUN
ejpam-3248	332	6	)	)	PUNCT
ejpam-3248	332	7	,	,	PUNCT
ejpam-3248	332	8	x	x	X
ejpam-3248	332	9	]	]	X
ejpam-3248	332	10	=	=	SYM
ejpam-3248	332	11	0	0	NUM
ejpam-3248	332	12	for	for	ADP
ejpam-3248	332	13	all	all	PRON
ejpam-3248	332	14	x	x	SYM
ejpam-3248	332	15	∈	∈	PROPN
ejpam-3248	332	16	i.	i.	NOUN
ejpam-3248	332	17	theorem	theorem	VERB
ejpam-3248	332	18	3.8	3.8	NUM
ejpam-3248	332	19	.	.	PUNCT
ejpam-3248	333	1	let	let	VERB
ejpam-3248	333	2	r	r	PRON
ejpam-3248	333	3	be	be	AUX
ejpam-3248	333	4	a	a	DET
ejpam-3248	333	5	semiprime	semiprime	NOUN
ejpam-3248	333	6	ring	ring	NOUN
ejpam-3248	333	7	and	and	CCONJ
ejpam-3248	333	8	f	f	PROPN
ejpam-3248	333	9	be	be	AUX
ejpam-3248	333	10	a	a	DET
ejpam-3248	333	11	non	non	ADJ
ejpam-3248	333	12	-	-	ADJ
ejpam-3248	333	13	zero	zero	ADJ
ejpam-3248	333	14	multiplicative	multiplicative	ADJ
ejpam-3248	333	15	(	(	PUNCT
ejpam-3248	333	16	generalized	generalized	ADJ
ejpam-3248	333	17	)	)	PUNCT
ejpam-3248	333	18	reverse	reverse	ADJ
ejpam-3248	333	19	derivation	derivation	NOUN
ejpam-3248	333	20	associated	associate	VERB
ejpam-3248	333	21	with	with	ADP
ejpam-3248	333	22	a	a	DET
ejpam-3248	333	23	map	map	NOUN
ejpam-3248	334	1	d	d	NOUN
ejpam-3248	334	2	,	,	PUNCT
ejpam-3248	334	3	i	i	PRON
ejpam-3248	334	4	be	be	VERB
ejpam-3248	334	5	a	a	DET
ejpam-3248	334	6	non	non	ADJ
ejpam-3248	334	7	-	-	ADJ
ejpam-3248	334	8	zero	zero	NUM
ejpam-3248	334	9	ideal	ideal	NOUN
ejpam-3248	334	10	of	of	ADP
ejpam-3248	334	11	r.	r.	PROPN
ejpam-3248	334	12	if	if	SCONJ
ejpam-3248	334	13	[	[	X
ejpam-3248	334	14	f	f	X
ejpam-3248	334	15	(	(	PUNCT
ejpam-3248	334	16	x	x	NOUN
ejpam-3248	334	17	)	)	PUNCT
ejpam-3248	334	18	,	,	PUNCT
ejpam-3248	334	19	y]±	y]±	PROPN
ejpam-3248	334	20	yx	yx	PROPN
ejpam-3248	334	21	∈	∈	PROPN
ejpam-3248	334	22	z(r	z(r	PROPN
ejpam-3248	334	23	)	)	PUNCT
ejpam-3248	334	24	for	for	ADP
ejpam-3248	334	25	all	all	DET
ejpam-3248	334	26	x	x	NOUN
ejpam-3248	334	27	,	,	PUNCT
ejpam-3248	334	28	y	y	PROPN
ejpam-3248	334	29	∈	∈	PROPN
ejpam-3248	334	30	i	i	PRON
ejpam-3248	334	31	,	,	PUNCT
ejpam-3248	334	32	then	then	ADV
ejpam-3248	334	33	[	[	X
ejpam-3248	334	34	f	f	X
ejpam-3248	334	35	(	(	PUNCT
ejpam-3248	334	36	x	x	NOUN
ejpam-3248	334	37	)	)	PUNCT
ejpam-3248	334	38	,	,	PUNCT
ejpam-3248	334	39	x]2x	x]2x	PUNCT
ejpam-3248	335	1	=	=	SYM
ejpam-3248	335	2	0	0	NUM
ejpam-3248	335	3	and	and	CCONJ
ejpam-3248	335	4	x[d(x	x[d(x	NOUN
ejpam-3248	335	5	)	)	PUNCT
ejpam-3248	335	6	,	,	PUNCT
ejpam-3248	335	7	x]2	x]2	PUNCT
ejpam-3248	336	1	=	=	SYM
ejpam-3248	336	2	0	0	PROPN
ejpam-3248	336	3	for	for	ADP
ejpam-3248	336	4	all	all	DET
ejpam-3248	336	5	x	x	SYM
ejpam-3248	336	6	∈	∈	NOUN
ejpam-3248	336	7	i.	i.	NOUN
ejpam-3248	336	8	proof	proof	NOUN
ejpam-3248	336	9	we	we	PRON
ejpam-3248	336	10	begin	begin	VERB
ejpam-3248	336	11	with	with	ADP
ejpam-3248	336	12	the	the	DET
ejpam-3248	336	13	situation	situation	NOUN
ejpam-3248	337	1	[	[	X
ejpam-3248	337	2	f	f	X
ejpam-3248	337	3	(	(	PUNCT
ejpam-3248	337	4	x	x	NOUN
ejpam-3248	337	5	)	)	PUNCT
ejpam-3248	337	6	,	,	PUNCT
ejpam-3248	337	7	y	y	PROPN
ejpam-3248	337	8	]	]	X
ejpam-3248	337	9	+	+	CCONJ
ejpam-3248	337	10	yx	yx	X
ejpam-3248	337	11	∈	∈	PROPN
ejpam-3248	337	12	z(r	z(r	PROPN
ejpam-3248	337	13	)	)	PUNCT
ejpam-3248	337	14	for	for	ADP
ejpam-3248	337	15	all	all	DET
ejpam-3248	337	16	x	x	NOUN
ejpam-3248	337	17	,	,	PUNCT
ejpam-3248	337	18	y	y	PROPN
ejpam-3248	337	19	∈	∈	PROPN
ejpam-3248	337	20	i.	i.	NOUN
ejpam-3248	337	21	(	(	PUNCT
ejpam-3248	337	22	3.59	3.59	NUM
ejpam-3248	337	23	)	)	PUNCT
ejpam-3248	337	24	replacing	replace	VERB
ejpam-3248	337	25	y	y	PRON
ejpam-3248	337	26	by	by	ADP
ejpam-3248	337	27	yz	yz	PROPN
ejpam-3248	337	28	in	in	ADP
ejpam-3248	337	29	(	(	PUNCT
ejpam-3248	337	30	3.59	3.59	NUM
ejpam-3248	337	31	)	)	PUNCT
ejpam-3248	337	32	,	,	PUNCT
ejpam-3248	337	33	we	we	PRON
ejpam-3248	337	34	get	get	VERB
ejpam-3248	337	35	y[f	y[f	NOUN
ejpam-3248	337	36	(	(	PUNCT
ejpam-3248	337	37	x	x	NOUN
ejpam-3248	337	38	)	)	PUNCT
ejpam-3248	337	39	,	,	PUNCT
ejpam-3248	338	1	z	z	X
ejpam-3248	338	2	]	]	X
ejpam-3248	339	1	+	+	CCONJ
ejpam-3248	339	2	[	[	X
ejpam-3248	339	3	f	f	X
ejpam-3248	339	4	(	(	PUNCT
ejpam-3248	339	5	x	x	NOUN
ejpam-3248	339	6	)	)	PUNCT
ejpam-3248	339	7	,	,	PUNCT
ejpam-3248	339	8	y]z	y]z	NOUN
ejpam-3248	339	9	+	+	CCONJ
ejpam-3248	339	10	yzx	yzx	PROPN
ejpam-3248	339	11	+	+	X
ejpam-3248	339	12	yxz	yxz	PROPN
ejpam-3248	339	13	−	−	PROPN
ejpam-3248	339	14	yxz	yxz	NOUN
ejpam-3248	339	15	∈	∈	PROPN
ejpam-3248	339	16	z(r	z(r	NOUN
ejpam-3248	339	17	)	)	PUNCT
ejpam-3248	339	18	for	for	ADP
ejpam-3248	339	19	all	all	DET
ejpam-3248	339	20	x	x	NOUN
ejpam-3248	339	21	,	,	PUNCT
ejpam-3248	339	22	y	y	PROPN
ejpam-3248	339	23	,	,	PUNCT
ejpam-3248	339	24	z	z	PROPN
ejpam-3248	339	25	∈	∈	PROPN
ejpam-3248	339	26	i.	i.	NOUN
ejpam-3248	339	27	this	this	PRON
ejpam-3248	339	28	implies	imply	VERB
ejpam-3248	339	29	that	that	SCONJ
ejpam-3248	339	30	(	(	PUNCT
ejpam-3248	339	31	[	[	X
ejpam-3248	339	32	f	f	X
ejpam-3248	339	33	(	(	PUNCT
ejpam-3248	339	34	x	x	NOUN
ejpam-3248	339	35	)	)	PUNCT
ejpam-3248	339	36	,	,	PUNCT
ejpam-3248	339	37	y	y	PROPN
ejpam-3248	339	38	]	]	X
ejpam-3248	340	1	+	+	NUM
ejpam-3248	340	2	yx)z	yx)z	PROPN
ejpam-3248	340	3	+	+	NUM
ejpam-3248	340	4	y[f	y[f	NOUN
ejpam-3248	340	5	(	(	PUNCT
ejpam-3248	340	6	x	x	NOUN
ejpam-3248	340	7	)	)	PUNCT
ejpam-3248	340	8	,	,	PUNCT
ejpam-3248	340	9	z	z	X
ejpam-3248	340	10	]	]	X
ejpam-3248	340	11	+	+	CCONJ
ejpam-3248	340	12	y[z	y[z	NUM
ejpam-3248	340	13	,	,	PUNCT
ejpam-3248	340	14	x	x	X
ejpam-3248	340	15	]	]	X
ejpam-3248	340	16	∈	∈	PROPN
ejpam-3248	340	17	z(r	z(r	PROPN
ejpam-3248	340	18	)	)	PUNCT
ejpam-3248	340	19	.	.	PUNCT
ejpam-3248	341	1	(	(	PUNCT
ejpam-3248	341	2	3.60	3.60	NUM
ejpam-3248	341	3	)	)	PUNCT
ejpam-3248	341	4	commuting	commuting	NOUN
ejpam-3248	341	5	(	(	PUNCT
ejpam-3248	341	6	3.60	3.60	NUM
ejpam-3248	341	7	)	)	PUNCT
ejpam-3248	341	8	with	with	ADP
ejpam-3248	341	9	z	z	NOUN
ejpam-3248	341	10	and	and	CCONJ
ejpam-3248	341	11	applying	apply	VERB
ejpam-3248	341	12	(	(	PUNCT
ejpam-3248	341	13	3.59	3.59	NUM
ejpam-3248	341	14	)	)	PUNCT
ejpam-3248	341	15	,	,	PUNCT
ejpam-3248	341	16	we	we	PRON
ejpam-3248	341	17	obtain	obtain	VERB
ejpam-3248	341	18	[	[	X
ejpam-3248	341	19	y[f	y[f	NOUN
ejpam-3248	341	20	(	(	PUNCT
ejpam-3248	341	21	x	x	NOUN
ejpam-3248	341	22	)	)	PUNCT
ejpam-3248	341	23	,	,	PUNCT
ejpam-3248	341	24	z	z	X
ejpam-3248	341	25	]	]	X
ejpam-3248	341	26	,	,	PUNCT
ejpam-3248	341	27	z	z	X
ejpam-3248	341	28	]	]	X
ejpam-3248	342	1	+	+	CCONJ
ejpam-3248	343	1	[	[	X
ejpam-3248	343	2	y[z	y[z	X
ejpam-3248	343	3	,	,	PUNCT
ejpam-3248	343	4	x	x	NOUN
ejpam-3248	343	5	]	]	X
ejpam-3248	343	6	,	,	PUNCT
ejpam-3248	343	7	z	z	X
ejpam-3248	343	8	]	]	X
ejpam-3248	343	9	=	=	SYM
ejpam-3248	343	10	0	0	NUM
ejpam-3248	343	11	for	for	ADP
ejpam-3248	343	12	all	all	DET
ejpam-3248	343	13	x	x	NOUN
ejpam-3248	343	14	,	,	PUNCT
ejpam-3248	343	15	y	y	PROPN
ejpam-3248	343	16	,	,	PUNCT
ejpam-3248	343	17	z	z	PROPN
ejpam-3248	343	18	∈	∈	PROPN
ejpam-3248	343	19	i.	i.	NOUN
ejpam-3248	343	20	(	(	PUNCT
ejpam-3248	343	21	3.61	3.61	NUM
ejpam-3248	343	22	)	)	PUNCT
ejpam-3248	343	23	substituting	substitute	VERB
ejpam-3248	343	24	zx	zx	NUM
ejpam-3248	343	25	for	for	ADP
ejpam-3248	343	26	x	x	SYM
ejpam-3248	343	27	in	in	ADP
ejpam-3248	343	28	(	(	PUNCT
ejpam-3248	343	29	3.61	3.61	NUM
ejpam-3248	343	30	)	)	PUNCT
ejpam-3248	343	31	,	,	PUNCT
ejpam-3248	343	32	we	we	PRON
ejpam-3248	343	33	obtain	obtain	VERB
ejpam-3248	343	34	[	[	X
ejpam-3248	343	35	y[f	y[f	NOUN
ejpam-3248	343	36	(	(	PUNCT
ejpam-3248	343	37	x)z	x)z	PUNCT
ejpam-3248	343	38	+	+	NUM
ejpam-3248	343	39	xd(z	xd(z	NUM
ejpam-3248	343	40	)	)	PUNCT
ejpam-3248	343	41	,	,	PUNCT
ejpam-3248	344	1	z	z	X
ejpam-3248	344	2	]	]	X
ejpam-3248	344	3	,	,	PUNCT
ejpam-3248	344	4	z	z	X
ejpam-3248	344	5	]	]	X
ejpam-3248	345	1	+	+	CCONJ
ejpam-3248	345	2	[	[	X
ejpam-3248	345	3	yz[z	yz[z	NOUN
ejpam-3248	345	4	,	,	PUNCT
ejpam-3248	345	5	x	x	X
ejpam-3248	345	6	]	]	X
ejpam-3248	345	7	,	,	PUNCT
ejpam-3248	345	8	z	z	X
ejpam-3248	345	9	]	]	X
ejpam-3248	345	10	=	=	SYM
ejpam-3248	345	11	0	0	NUM
ejpam-3248	345	12	for	for	ADP
ejpam-3248	345	13	all	all	DET
ejpam-3248	345	14	x	x	NOUN
ejpam-3248	345	15	,	,	PUNCT
ejpam-3248	345	16	y	y	PROPN
ejpam-3248	345	17	,	,	PUNCT
ejpam-3248	345	18	z	z	PROPN
ejpam-3248	345	19	∈	∈	PROPN
ejpam-3248	345	20	i.	i.	NOUN
ejpam-3248	345	21	this	this	PRON
ejpam-3248	345	22	gives	give	VERB
ejpam-3248	345	23	that	that	SCONJ
ejpam-3248	345	24	[	[	X
ejpam-3248	345	25	y[f	y[f	NOUN
ejpam-3248	345	26	(	(	PUNCT
ejpam-3248	345	27	x	x	NOUN
ejpam-3248	345	28	)	)	PUNCT
ejpam-3248	345	29	,	,	PUNCT
ejpam-3248	345	30	z	z	X
ejpam-3248	345	31	]	]	X
ejpam-3248	345	32	,	,	PUNCT
ejpam-3248	345	33	z]z	z]z	NOUN
ejpam-3248	345	34	+	+	X
ejpam-3248	346	1	[	[	X
ejpam-3248	346	2	y[xd(z	y[xd(z	PROPN
ejpam-3248	346	3	)	)	PUNCT
ejpam-3248	346	4	,	,	PUNCT
ejpam-3248	347	1	z	z	X
ejpam-3248	347	2	]	]	X
ejpam-3248	347	3	,	,	PUNCT
ejpam-3248	347	4	z	z	X
ejpam-3248	347	5	]	]	X
ejpam-3248	348	1	+	+	CCONJ
ejpam-3248	348	2	[	[	X
ejpam-3248	348	3	yz[z	yz[z	NOUN
ejpam-3248	348	4	,	,	PUNCT
ejpam-3248	348	5	x	x	X
ejpam-3248	348	6	]	]	X
ejpam-3248	348	7	,	,	PUNCT
ejpam-3248	348	8	z	z	X
ejpam-3248	348	9	]	]	X
ejpam-3248	348	10	=	=	SYM
ejpam-3248	348	11	0	0	X
ejpam-3248	348	12	.	.	PUNCT
ejpam-3248	349	1	(	(	PUNCT
ejpam-3248	349	2	3.62	3.62	NUM
ejpam-3248	349	3	)	)	PUNCT
ejpam-3248	349	4	replacing	replace	VERB
ejpam-3248	349	5	y	y	PRON
ejpam-3248	349	6	by	by	ADP
ejpam-3248	349	7	ry	ry	INTJ
ejpam-3248	349	8	in	in	ADP
ejpam-3248	349	9	(	(	PUNCT
ejpam-3248	349	10	3.62	3.62	NUM
ejpam-3248	349	11	)	)	PUNCT
ejpam-3248	349	12	,	,	PUNCT
ejpam-3248	349	13	we	we	PRON
ejpam-3248	349	14	obtain	obtain	VERB
ejpam-3248	349	15	r[y[f	r[y[f	NOUN
ejpam-3248	349	16	(	(	PUNCT
ejpam-3248	349	17	x	x	NOUN
ejpam-3248	349	18	)	)	PUNCT
ejpam-3248	349	19	,	,	PUNCT
ejpam-3248	350	1	z	z	X
ejpam-3248	350	2	]	]	X
ejpam-3248	350	3	,	,	PUNCT
ejpam-3248	350	4	z]z	z]z	NOUN
ejpam-3248	350	5	+	+	X
ejpam-3248	351	1	[	[	X
ejpam-3248	351	2	r	r	X
ejpam-3248	351	3	,	,	PUNCT
ejpam-3248	351	4	z]y[f	z]y[f	NOUN
ejpam-3248	351	5	(	(	PUNCT
ejpam-3248	351	6	x	x	NOUN
ejpam-3248	351	7	)	)	PUNCT
ejpam-3248	351	8	,	,	PUNCT
ejpam-3248	351	9	z]z	z]z	NOUN
ejpam-3248	351	10	+	+	CCONJ
ejpam-3248	351	11	r[y[xd(z	r[y[xd(z	NOUN
ejpam-3248	351	12	)	)	PUNCT
ejpam-3248	351	13	,	,	PUNCT
ejpam-3248	351	14	z	z	X
ejpam-3248	351	15	]	]	X
ejpam-3248	351	16	,	,	PUNCT
ejpam-3248	351	17	z	z	X
ejpam-3248	351	18	]	]	X
ejpam-3248	352	1	+	+	PROPN
ejpam-3248	352	2	[	[	X
ejpam-3248	352	3	r	r	X
ejpam-3248	352	4	,	,	PUNCT
ejpam-3248	352	5	z]y[xd(z	z]y[xd(z	NUM
ejpam-3248	352	6	)	)	PUNCT
ejpam-3248	352	7	,	,	PUNCT
ejpam-3248	352	8	z	z	X
ejpam-3248	352	9	]	]	X
ejpam-3248	352	10	+	+	CCONJ
ejpam-3248	352	11	r[yz[z	r[yz[z	NOUN
ejpam-3248	352	12	,	,	PUNCT
ejpam-3248	352	13	x	x	X
ejpam-3248	352	14	]	]	X
ejpam-3248	352	15	,	,	PUNCT
ejpam-3248	353	1	z	z	X
ejpam-3248	353	2	]	]	X
ejpam-3248	354	1	+	+	CCONJ
ejpam-3248	354	2	[	[	X
ejpam-3248	354	3	r	r	X
ejpam-3248	354	4	,	,	PUNCT
ejpam-3248	354	5	z]yz[z	z]yz[z	NOUN
ejpam-3248	354	6	,	,	PUNCT
ejpam-3248	354	7	x	x	X
ejpam-3248	354	8	]	]	X
ejpam-3248	354	9	=	=	SYM
ejpam-3248	354	10	0	0	X
ejpam-3248	354	11	.	.	PUNCT
ejpam-3248	355	1	(	(	PUNCT
ejpam-3248	355	2	3.63	3.63	NUM
ejpam-3248	355	3	)	)	PUNCT
ejpam-3248	355	4	left	leave	VERB
ejpam-3248	355	5	multiplying	multiplying	NOUN
ejpam-3248	355	6	(	(	PUNCT
ejpam-3248	355	7	3.62	3.62	NUM
ejpam-3248	355	8	)	)	PUNCT
ejpam-3248	355	9	by	by	ADP
ejpam-3248	355	10	r	r	NOUN
ejpam-3248	355	11	and	and	CCONJ
ejpam-3248	355	12	subtracting	subtracting	NOUN
ejpam-3248	355	13	from	from	ADP
ejpam-3248	355	14	(	(	PUNCT
ejpam-3248	355	15	3.63	3.63	NUM
ejpam-3248	355	16	)	)	PUNCT
ejpam-3248	355	17	,	,	PUNCT
ejpam-3248	355	18	we	we	PRON
ejpam-3248	355	19	get	get	VERB
ejpam-3248	355	20	[	[	X
ejpam-3248	355	21	r	r	NOUN
ejpam-3248	355	22	,	,	PUNCT
ejpam-3248	355	23	z]y{[f	z]y{[f	NOUN
ejpam-3248	355	24	(	(	PUNCT
ejpam-3248	355	25	x	x	NOUN
ejpam-3248	355	26	)	)	PUNCT
ejpam-3248	355	27	,	,	PUNCT
ejpam-3248	355	28	z]z	z]z	NOUN
ejpam-3248	356	1	+	+	CCONJ
ejpam-3248	357	1	[	[	X
ejpam-3248	357	2	xd(z	xd(z	NOUN
ejpam-3248	357	3	)	)	PUNCT
ejpam-3248	357	4	,	,	PUNCT
ejpam-3248	358	1	z	z	X
ejpam-3248	358	2	]	]	X
ejpam-3248	358	3	+	+	CCONJ
ejpam-3248	358	4	z[z	z[z	NUM
ejpam-3248	358	5	,	,	PUNCT
ejpam-3248	358	6	x	x	NOUN
ejpam-3248	358	7	]	]	X
ejpam-3248	358	8	}	}	PUNCT
ejpam-3248	358	9	=	=	SYM
ejpam-3248	358	10	0	0	NUM
ejpam-3248	358	11	for	for	ADP
ejpam-3248	358	12	all	all	DET
ejpam-3248	358	13	x	x	NOUN
ejpam-3248	358	14	,	,	PUNCT
ejpam-3248	358	15	y	y	PROPN
ejpam-3248	358	16	,	,	PUNCT
ejpam-3248	358	17	z	z	PROPN
ejpam-3248	358	18	∈	∈	PROPN
ejpam-3248	359	1	i	i	PRON
ejpam-3248	359	2	and	and	CCONJ
ejpam-3248	359	3	r	r	PROPN
ejpam-3248	359	4	∈	∈	PROPN
ejpam-3248	359	5	r.	r.	NOUN
ejpam-3248	359	6	(	(	PUNCT
ejpam-3248	359	7	3.64	3.64	NUM
ejpam-3248	359	8	)	)	PUNCT
ejpam-3248	359	9	in	in	ADP
ejpam-3248	359	10	particular	particular	ADJ
ejpam-3248	359	11	take	take	VERB
ejpam-3248	359	12	x	x	NOUN
ejpam-3248	359	13	=	=	NOUN
ejpam-3248	359	14	z	z	NOUN
ejpam-3248	359	15	in	in	ADP
ejpam-3248	359	16	(	(	PUNCT
ejpam-3248	359	17	3.64	3.64	NUM
ejpam-3248	359	18	)	)	PUNCT
ejpam-3248	359	19	,	,	PUNCT
ejpam-3248	359	20	we	we	PRON
ejpam-3248	359	21	obtain	obtain	VERB
ejpam-3248	359	22	[	[	X
ejpam-3248	359	23	r	r	NOUN
ejpam-3248	359	24	,	,	PUNCT
ejpam-3248	359	25	z]y{[f	z]y{[f	NOUN
ejpam-3248	360	1	(	(	PUNCT
ejpam-3248	360	2	z	z	NOUN
ejpam-3248	360	3	)	)	PUNCT
ejpam-3248	360	4	,	,	PUNCT
ejpam-3248	360	5	z]z	z]z	NOUN
ejpam-3248	360	6	+	+	CCONJ
ejpam-3248	360	7	z[d(z	z[d(z	NOUN
ejpam-3248	360	8	)	)	PUNCT
ejpam-3248	360	9	,	,	PUNCT
ejpam-3248	361	1	z	z	X
ejpam-3248	361	2	]	]	X
ejpam-3248	361	3	}	}	PUNCT
ejpam-3248	361	4	=	=	SYM
ejpam-3248	361	5	0	0	NUM
ejpam-3248	361	6	for	for	ADP
ejpam-3248	361	7	all	all	DET
ejpam-3248	361	8	y	y	PROPN
ejpam-3248	361	9	,	,	PUNCT
ejpam-3248	361	10	z	z	NOUN
ejpam-3248	361	11	∈	∈	PROPN
ejpam-3248	362	1	i	i	PRON
ejpam-3248	362	2	and	and	CCONJ
ejpam-3248	362	3	r	r	PROPN
ejpam-3248	362	4	∈	∈	PROPN
ejpam-3248	362	5	r.	r.	NOUN
ejpam-3248	362	6	this	this	PRON
ejpam-3248	362	7	implies	imply	VERB
ejpam-3248	362	8	that	that	SCONJ
ejpam-3248	362	9	[	[	X
ejpam-3248	362	10	r	r	NOUN
ejpam-3248	362	11	,	,	PUNCT
ejpam-3248	362	12	z]y[f	z]y[f	NOUN
ejpam-3248	362	13	(	(	PUNCT
ejpam-3248	362	14	z)z	z)z	X
ejpam-3248	362	15	+	+	NUM
ejpam-3248	362	16	zd(z	zd(z	NOUN
ejpam-3248	362	17	)	)	PUNCT
ejpam-3248	362	18	,	,	PUNCT
ejpam-3248	362	19	z	z	X
ejpam-3248	362	20	]	]	X
ejpam-3248	362	21	=	=	SYM
ejpam-3248	362	22	0	0	NUM
ejpam-3248	362	23	for	for	ADP
ejpam-3248	362	24	all	all	DET
ejpam-3248	362	25	y	y	PROPN
ejpam-3248	362	26	,	,	PUNCT
ejpam-3248	362	27	z	z	NOUN
ejpam-3248	362	28	∈	∈	PROPN
ejpam-3248	363	1	i	i	PRON
ejpam-3248	363	2	and	and	CCONJ
ejpam-3248	363	3	r	r	PROPN
ejpam-3248	363	4	∈	∈	PROPN
ejpam-3248	363	5	r.	r.	NOUN
ejpam-3248	363	6	references	reference	NOUN
ejpam-3248	363	7	728	728	NUM
ejpam-3248	363	8	since	since	SCONJ
ejpam-3248	363	9	f	f	PROPN
ejpam-3248	363	10	is	be	AUX
ejpam-3248	363	11	a	a	DET
ejpam-3248	363	12	multiplicative	multiplicative	ADJ
ejpam-3248	363	13	(	(	PUNCT
ejpam-3248	363	14	generalized	generalized	ADJ
ejpam-3248	363	15	)	)	PUNCT
ejpam-3248	363	16	reverse	reverse	ADJ
ejpam-3248	363	17	derivation	derivation	NOUN
ejpam-3248	363	18	,	,	PUNCT
ejpam-3248	363	19	we	we	PRON
ejpam-3248	363	20	conclude	conclude	VERB
ejpam-3248	363	21	that	that	SCONJ
ejpam-3248	364	1	[	[	X
ejpam-3248	364	2	r	r	NOUN
ejpam-3248	364	3	,	,	PUNCT
ejpam-3248	364	4	z]y[f	z]y[f	NOUN
ejpam-3248	364	5	(	(	PUNCT
ejpam-3248	364	6	z2	z2	PROPN
ejpam-3248	364	7	)	)	PUNCT
ejpam-3248	364	8	,	,	PUNCT
ejpam-3248	364	9	z	z	X
ejpam-3248	364	10	]	]	X
ejpam-3248	364	11	=	=	SYM
ejpam-3248	364	12	0	0	NUM
ejpam-3248	364	13	for	for	ADP
ejpam-3248	364	14	all	all	DET
ejpam-3248	364	15	y	y	PROPN
ejpam-3248	364	16	,	,	PUNCT
ejpam-3248	364	17	z	z	NOUN
ejpam-3248	364	18	∈	∈	PROPN
ejpam-3248	365	1	i	i	PRON
ejpam-3248	365	2	and	and	CCONJ
ejpam-3248	365	3	r	r	PROPN
ejpam-3248	365	4	∈	∈	PROPN
ejpam-3248	365	5	r.	r.	NOUN
ejpam-3248	365	6	(	(	PUNCT
ejpam-3248	365	7	3.65	3.65	NUM
ejpam-3248	365	8	)	)	PUNCT
ejpam-3248	365	9	putting	put	VERB
ejpam-3248	365	10	r	r	NOUN
ejpam-3248	365	11	=	=	SYM
ejpam-3248	365	12	f	f	PROPN
ejpam-3248	365	13	(	(	PUNCT
ejpam-3248	365	14	z2	z2	PROPN
ejpam-3248	365	15	)	)	PUNCT
ejpam-3248	365	16	and	and	CCONJ
ejpam-3248	365	17	using	use	VERB
ejpam-3248	365	18	semiprimeness	semiprimeness	NOUN
ejpam-3248	365	19	of	of	ADP
ejpam-3248	365	20	r	r	NOUN
ejpam-3248	365	21	,	,	PUNCT
ejpam-3248	365	22	we	we	PRON
ejpam-3248	365	23	have	have	VERB
ejpam-3248	365	24	[	[	X
ejpam-3248	365	25	f	f	X
ejpam-3248	365	26	(	(	PUNCT
ejpam-3248	365	27	z2	z2	PROPN
ejpam-3248	365	28	)	)	PUNCT
ejpam-3248	365	29	,	,	PUNCT
ejpam-3248	365	30	z	z	X
ejpam-3248	365	31	]	]	X
ejpam-3248	365	32	=	=	SYM
ejpam-3248	365	33	0	0	NUM
ejpam-3248	366	1	for	for	ADP
ejpam-3248	366	2	all	all	DET
ejpam-3248	366	3	z	z	NOUN
ejpam-3248	366	4	∈	∈	PROPN
ejpam-3248	366	5	i.	i.	NOUN
ejpam-3248	366	6	replacing	replace	VERB
ejpam-3248	366	7	yx	yx	NOUN
ejpam-3248	366	8	in	in	ADP
ejpam-3248	366	9	place	place	NOUN
ejpam-3248	366	10	of	of	ADP
ejpam-3248	366	11	x	x	PUNCT
ejpam-3248	366	12	in	in	ADP
ejpam-3248	366	13	(	(	PUNCT
ejpam-3248	366	14	3.59	3.59	NUM
ejpam-3248	366	15	)	)	PUNCT
ejpam-3248	366	16	,	,	PUNCT
ejpam-3248	366	17	we	we	PRON
ejpam-3248	366	18	have	have	VERB
ejpam-3248	366	19	[	[	X
ejpam-3248	366	20	f	f	X
ejpam-3248	366	21	(	(	PUNCT
ejpam-3248	366	22	x)y	x)y	PUNCT
ejpam-3248	366	23	+	+	NUM
ejpam-3248	366	24	xd(y	xd(y	NUM
ejpam-3248	366	25	)	)	PUNCT
ejpam-3248	366	26	,	,	PUNCT
ejpam-3248	366	27	y	y	PROPN
ejpam-3248	366	28	]	]	X
ejpam-3248	367	1	+	+	PROPN
ejpam-3248	367	2	y2x	y2x	PROPN
ejpam-3248	367	3	∈	∈	PROPN
ejpam-3248	367	4	z(r	z(r	PROPN
ejpam-3248	367	5	)	)	PUNCT
ejpam-3248	367	6	for	for	ADP
ejpam-3248	367	7	all	all	DET
ejpam-3248	367	8	x	x	NOUN
ejpam-3248	367	9	,	,	PUNCT
ejpam-3248	367	10	y	y	PROPN
ejpam-3248	367	11	∈	∈	PROPN
ejpam-3248	367	12	i.	i.	NOUN
ejpam-3248	367	13	that	that	PRON
ejpam-3248	367	14	is	be	AUX
ejpam-3248	367	15	(	(	PUNCT
ejpam-3248	367	16	[	[	X
ejpam-3248	367	17	f	f	X
ejpam-3248	367	18	(	(	PUNCT
ejpam-3248	367	19	x	x	NOUN
ejpam-3248	367	20	)	)	PUNCT
ejpam-3248	367	21	,	,	PUNCT
ejpam-3248	367	22	y	y	PROPN
ejpam-3248	367	23	]	]	X
ejpam-3248	368	1	+	+	CCONJ
ejpam-3248	368	2	yx)y	yx)y	PROPN
ejpam-3248	368	3	+	+	NUM
ejpam-3248	368	4	[	[	X
ejpam-3248	368	5	xd(y	xd(y	NUM
ejpam-3248	368	6	)	)	PUNCT
ejpam-3248	368	7	,	,	PUNCT
ejpam-3248	368	8	y	y	PROPN
ejpam-3248	368	9	]	]	X
ejpam-3248	368	10	+	+	X
ejpam-3248	368	11	y[y	y[y	ADJ
ejpam-3248	368	12	,	,	PUNCT
ejpam-3248	368	13	x	x	X
ejpam-3248	368	14	]	]	X
ejpam-3248	368	15	∈	∈	PROPN
ejpam-3248	368	16	z(r	z(r	PROPN
ejpam-3248	368	17	)	)	PUNCT
ejpam-3248	368	18	for	for	ADP
ejpam-3248	368	19	all	all	DET
ejpam-3248	368	20	x	x	NOUN
ejpam-3248	368	21	,	,	PUNCT
ejpam-3248	368	22	y	y	PROPN
ejpam-3248	368	23	∈	∈	PROPN
ejpam-3248	368	24	i.	i.	NOUN
ejpam-3248	368	25	(	(	PUNCT
ejpam-3248	368	26	3.66	3.66	NUM
ejpam-3248	368	27	)	)	PUNCT
ejpam-3248	368	28	commuting	commuting	NOUN
ejpam-3248	368	29	(	(	PUNCT
ejpam-3248	368	30	3.66	3.66	NUM
ejpam-3248	368	31	)	)	PUNCT
ejpam-3248	368	32	with	with	ADP
ejpam-3248	368	33	y	y	PROPN
ejpam-3248	368	34	and	and	CCONJ
ejpam-3248	368	35	using	use	VERB
ejpam-3248	368	36	(	(	PUNCT
ejpam-3248	368	37	3.59	3.59	NUM
ejpam-3248	368	38	)	)	PUNCT
ejpam-3248	368	39	,	,	PUNCT
ejpam-3248	368	40	we	we	PRON
ejpam-3248	368	41	have	have	VERB
ejpam-3248	368	42	[	[	X
ejpam-3248	368	43	[	[	X
ejpam-3248	368	44	xd(y	xd(y	NOUN
ejpam-3248	368	45	)	)	PUNCT
ejpam-3248	368	46	,	,	PUNCT
ejpam-3248	368	47	y	y	PROPN
ejpam-3248	368	48	]	]	X
ejpam-3248	368	49	,	,	PUNCT
ejpam-3248	368	50	y	y	X
ejpam-3248	368	51	]	]	X
ejpam-3248	369	1	+	+	CCONJ
ejpam-3248	369	2	y[[y	y[[y	PROPN
ejpam-3248	369	3	,	,	PUNCT
ejpam-3248	369	4	x	x	X
ejpam-3248	369	5	]	]	X
ejpam-3248	369	6	,	,	PUNCT
ejpam-3248	369	7	y	y	X
ejpam-3248	369	8	]	]	X
ejpam-3248	369	9	=	=	SYM
ejpam-3248	369	10	0	0	NUM
ejpam-3248	369	11	for	for	ADP
ejpam-3248	369	12	all	all	DET
ejpam-3248	369	13	x	x	NOUN
ejpam-3248	369	14	,	,	PUNCT
ejpam-3248	369	15	y	y	PROPN
ejpam-3248	369	16	∈	∈	PROPN
ejpam-3248	369	17	i.	i.	NOUN
ejpam-3248	369	18	(	(	PUNCT
ejpam-3248	369	19	3.67	3.67	NUM
ejpam-3248	369	20	)	)	PUNCT
ejpam-3248	369	21	in	in	ADP
ejpam-3248	369	22	particular	particular	ADJ
ejpam-3248	369	23	for	for	ADP
ejpam-3248	369	24	y	y	PROPN
ejpam-3248	369	25	=	=	PUNCT
ejpam-3248	369	26	x	x	PROPN
ejpam-3248	369	27	in	in	ADP
ejpam-3248	369	28	(	(	PUNCT
ejpam-3248	369	29	3.67	3.67	NUM
ejpam-3248	369	30	)	)	PUNCT
ejpam-3248	369	31	,	,	PUNCT
ejpam-3248	369	32	we	we	PRON
ejpam-3248	369	33	have	have	VERB
ejpam-3248	369	34	x[d(x	x[d(x	NOUN
ejpam-3248	369	35	)	)	PUNCT
ejpam-3248	369	36	,	,	PUNCT
ejpam-3248	369	37	x]2	x]2	PUNCT
ejpam-3248	370	1	=	=	SYM
ejpam-3248	370	2	0	0	PROPN
ejpam-3248	370	3	for	for	ADP
ejpam-3248	370	4	all	all	DET
ejpam-3248	370	5	x	x	SYM
ejpam-3248	370	6	∈	∈	PROPN
ejpam-3248	370	7	i.	i.	NOUN
ejpam-3248	370	8	since	since	SCONJ
ejpam-3248	370	9	[	[	X
ejpam-3248	370	10	f	f	X
ejpam-3248	370	11	(	(	PUNCT
ejpam-3248	370	12	x2	x2	PROPN
ejpam-3248	370	13	)	)	PUNCT
ejpam-3248	370	14	,	,	PUNCT
ejpam-3248	370	15	x	x	X
ejpam-3248	370	16	]	]	X
ejpam-3248	370	17	=	=	SYM
ejpam-3248	370	18	0	0	X
ejpam-3248	370	19	.	.	PUNCT
ejpam-3248	371	1	it	it	PRON
ejpam-3248	371	2	implies	imply	VERB
ejpam-3248	371	3	that	that	SCONJ
ejpam-3248	371	4	[	[	X
ejpam-3248	371	5	f	f	X
ejpam-3248	371	6	(	(	PUNCT
ejpam-3248	371	7	x	x	NOUN
ejpam-3248	371	8	)	)	PUNCT
ejpam-3248	371	9	,	,	PUNCT
ejpam-3248	371	10	x]x	x]x	VERB
ejpam-3248	372	1	+	+	CCONJ
ejpam-3248	372	2	x[d(x	x[d(x	NUM
ejpam-3248	372	3	)	)	PUNCT
ejpam-3248	372	4	,	,	PUNCT
ejpam-3248	372	5	x	x	X
ejpam-3248	372	6	]	]	X
ejpam-3248	372	7	=	=	SYM
ejpam-3248	372	8	0	0	NUM
ejpam-3248	372	9	for	for	ADP
ejpam-3248	372	10	all	all	DET
ejpam-3248	372	11	x	x	SYM
ejpam-3248	372	12	∈	∈	PROPN
ejpam-3248	372	13	i.	i.	NOUN
ejpam-3248	372	14	(	(	PUNCT
ejpam-3248	372	15	3.68	3.68	NUM
ejpam-3248	372	16	)	)	PUNCT
ejpam-3248	372	17	this	this	PRON
ejpam-3248	372	18	can	can	AUX
ejpam-3248	372	19	be	be	AUX
ejpam-3248	372	20	written	write	VERB
ejpam-3248	372	21	as	as	ADP
ejpam-3248	372	22	[	[	X
ejpam-3248	372	23	f	f	X
ejpam-3248	372	24	(	(	PUNCT
ejpam-3248	372	25	x	x	NOUN
ejpam-3248	372	26	)	)	PUNCT
ejpam-3248	372	27	,	,	PUNCT
ejpam-3248	372	28	x]2x+x[d(x	x]2x+x[d(x	PUNCT
ejpam-3248	372	29	)	)	PUNCT
ejpam-3248	372	30	,	,	PUNCT
ejpam-3248	372	31	x]2	x]2	PUNCT
ejpam-3248	373	1	=	=	SYM
ejpam-3248	373	2	0	0	PROPN
ejpam-3248	373	3	for	for	ADP
ejpam-3248	373	4	all	all	DET
ejpam-3248	373	5	x	x	SYM
ejpam-3248	373	6	∈	∈	PROPN
ejpam-3248	373	7	i.	i.	NOUN
ejpam-3248	373	8	by	by	ADP
ejpam-3248	373	9	using	use	VERB
ejpam-3248	373	10	x[d(x	x[d(x	NOUN
ejpam-3248	373	11	)	)	PUNCT
ejpam-3248	373	12	,	,	PUNCT
ejpam-3248	373	13	x]2	x]2	PUNCT
ejpam-3248	374	1	=	=	SYM
ejpam-3248	374	2	0	0	X
ejpam-3248	374	3	.	.	PUNCT
ejpam-3248	375	1	this	this	PRON
ejpam-3248	375	2	implies	imply	VERB
ejpam-3248	375	3	that	that	SCONJ
ejpam-3248	376	1	[	[	X
ejpam-3248	376	2	f	f	X
ejpam-3248	376	3	(	(	PUNCT
ejpam-3248	376	4	x	x	NOUN
ejpam-3248	376	5	)	)	PUNCT
ejpam-3248	376	6	,	,	PUNCT
ejpam-3248	376	7	x]2x	x]2x	PUNCT
ejpam-3248	376	8	=	=	SYM
ejpam-3248	376	9	0	0	PROPN
ejpam-3248	376	10	for	for	ADP
ejpam-3248	376	11	all	all	DET
ejpam-3248	376	12	x	x	SYM
ejpam-3248	376	13	∈	∈	PROPN
ejpam-3248	376	14	i	i	PRON
ejpam-3248	376	15	,	,	PUNCT
ejpam-3248	376	16	which	which	PRON
ejpam-3248	376	17	is	be	AUX
ejpam-3248	376	18	our	our	PRON
ejpam-3248	376	19	desired	desire	VERB
ejpam-3248	376	20	result	result	NOUN
ejpam-3248	376	21	.	.	PUNCT
ejpam-3248	377	1	in	in	ADP
ejpam-3248	377	2	the	the	DET
ejpam-3248	377	3	similar	similar	ADJ
ejpam-3248	377	4	manner	manner	NOUN
ejpam-3248	377	5	the	the	DET
ejpam-3248	377	6	conclusion	conclusion	NOUN
ejpam-3248	377	7	can	can	AUX
ejpam-3248	377	8	be	be	AUX
ejpam-3248	377	9	obtained	obtain	VERB
ejpam-3248	377	10	for	for	ADP
ejpam-3248	377	11	the	the	DET
ejpam-3248	377	12	case	case	NOUN
ejpam-3248	377	13	[	[	X
ejpam-3248	377	14	f	f	X
ejpam-3248	377	15	(	(	PUNCT
ejpam-3248	377	16	x	x	NOUN
ejpam-3248	377	17	)	)	PUNCT
ejpam-3248	377	18	,	,	PUNCT
ejpam-3248	377	19	y]−	y]−	NOUN
ejpam-3248	377	20	yx	yx	ADP
ejpam-3248	377	21	∈	∈	PROPN
ejpam-3248	377	22	z(r	z(r	PROPN
ejpam-3248	377	23	)	)	PUNCT
ejpam-3248	377	24	for	for	ADP
ejpam-3248	377	25	all	all	DET
ejpam-3248	377	26	x	x	NOUN
ejpam-3248	377	27	,	,	PUNCT
ejpam-3248	377	28	y	y	PROPN
ejpam-3248	377	29	∈	∈	PROPN
ejpam-3248	377	30	i.	i.	NOUN
ejpam-3248	377	31	using	use	VERB
ejpam-3248	377	32	similar	similar	ADJ
ejpam-3248	377	33	technique	technique	NOUN
ejpam-3248	377	34	with	with	ADP
ejpam-3248	377	35	some	some	DET
ejpam-3248	377	36	necessary	necessary	ADJ
ejpam-3248	377	37	variations	variation	NOUN
ejpam-3248	377	38	,	,	PUNCT
ejpam-3248	377	39	we	we	PRON
ejpam-3248	377	40	can	can	AUX
ejpam-3248	377	41	prove	prove	VERB
ejpam-3248	377	42	the	the	DET
ejpam-3248	377	43	following	following	NOUN
ejpam-3248	377	44	:	:	PUNCT
ejpam-3248	377	45	theorem	theorem	VERB
ejpam-3248	377	46	3.9	3.9	NUM
ejpam-3248	377	47	.	.	PUNCT
ejpam-3248	378	1	let	let	VERB
ejpam-3248	378	2	r	r	PRON
ejpam-3248	378	3	be	be	AUX
ejpam-3248	378	4	a	a	DET
ejpam-3248	378	5	semiprime	semiprime	NOUN
ejpam-3248	378	6	ring	ring	NOUN
ejpam-3248	378	7	and	and	CCONJ
ejpam-3248	378	8	f	f	PROPN
ejpam-3248	378	9	be	be	AUX
ejpam-3248	378	10	a	a	DET
ejpam-3248	378	11	non	non	ADJ
ejpam-3248	378	12	-	-	ADJ
ejpam-3248	378	13	zero	zero	ADJ
ejpam-3248	378	14	multiplicative	multiplicative	ADJ
ejpam-3248	378	15	(	(	PUNCT
ejpam-3248	378	16	generalized	generalized	ADJ
ejpam-3248	378	17	)	)	PUNCT
ejpam-3248	378	18	reverse	reverse	ADJ
ejpam-3248	378	19	derivation	derivation	NOUN
ejpam-3248	378	20	associated	associate	VERB
ejpam-3248	378	21	with	with	ADP
ejpam-3248	378	22	a	a	DET
ejpam-3248	378	23	map	map	NOUN
ejpam-3248	379	1	d	d	NOUN
ejpam-3248	379	2	,	,	PUNCT
ejpam-3248	379	3	i	i	PRON
ejpam-3248	379	4	be	be	VERB
ejpam-3248	379	5	a	a	DET
ejpam-3248	379	6	non	non	ADJ
ejpam-3248	379	7	-	-	ADJ
ejpam-3248	379	8	zero	zero	NUM
ejpam-3248	379	9	ideal	ideal	NOUN
ejpam-3248	379	10	of	of	ADP
ejpam-3248	379	11	r.	r.	PROPN
ejpam-3248	379	12	if	if	SCONJ
ejpam-3248	379	13	f	f	PROPN
ejpam-3248	379	14	(	(	PUNCT
ejpam-3248	379	15	x	x	X
ejpam-3248	379	16	)	)	PUNCT
ejpam-3248	379	17	◦	◦	NOUN
ejpam-3248	379	18	y±	y±	PROPN
ejpam-3248	379	19	yx	yx	PROPN
ejpam-3248	379	20	∈	∈	PROPN
ejpam-3248	379	21	z(r	z(r	PROPN
ejpam-3248	379	22	)	)	PUNCT
ejpam-3248	379	23	for	for	ADP
ejpam-3248	379	24	all	all	DET
ejpam-3248	379	25	x	x	NOUN
ejpam-3248	379	26	,	,	PUNCT
ejpam-3248	379	27	y	y	PROPN
ejpam-3248	379	28	∈	∈	PROPN
ejpam-3248	380	1	i	i	PRON
ejpam-3248	380	2	,	,	PUNCT
ejpam-3248	380	3	then	then	ADV
ejpam-3248	380	4	[	[	X
ejpam-3248	380	5	f	f	X
ejpam-3248	380	6	(	(	PUNCT
ejpam-3248	380	7	x	x	NOUN
ejpam-3248	380	8	)	)	PUNCT
ejpam-3248	380	9	,	,	PUNCT
ejpam-3248	380	10	x]2x	x]2x	PUNCT
ejpam-3248	380	11	=	=	SYM
ejpam-3248	380	12	0	0	NUM
ejpam-3248	380	13	and	and	CCONJ
ejpam-3248	380	14	x[d(x	x[d(x	NOUN
ejpam-3248	380	15	)	)	PUNCT
ejpam-3248	380	16	,	,	PUNCT
ejpam-3248	380	17	x]2	x]2	PUNCT
ejpam-3248	381	1	=	=	SYM
ejpam-3248	381	2	0	0	PROPN
ejpam-3248	381	3	for	for	ADP
ejpam-3248	381	4	all	all	DET
ejpam-3248	381	5	x	x	SYM
ejpam-3248	381	6	∈	∈	PROPN
ejpam-3248	381	7	i.	i.	NOUN
ejpam-3248	381	8	acknowledgements	acknowledgement	VERB
ejpam-3248	381	9	the	the	DET
ejpam-3248	381	10	authors	author	NOUN
ejpam-3248	381	11	are	be	AUX
ejpam-3248	381	12	thankful	thankful	ADJ
ejpam-3248	381	13	to	to	ADP
ejpam-3248	381	14	the	the	DET
ejpam-3248	381	15	referee	referee	NOUN
ejpam-3248	381	16	for	for	ADP
ejpam-3248	381	17	the	the	DET
ejpam-3248	381	18	valuable	valuable	ADJ
ejpam-3248	381	19	comments	comment	NOUN
ejpam-3248	381	20	and	and	CCONJ
ejpam-3248	381	21	suggestions	suggestion	NOUN
ejpam-3248	381	22	.	.	PUNCT
ejpam-3248	382	1	references	reference	NOUN
ejpam-3248	382	2	[	[	X
ejpam-3248	382	3	1	1	NUM
ejpam-3248	382	4	]	]	PUNCT
ejpam-3248	382	5	aboubakr	aboubakr	NOUN
ejpam-3248	382	6	,	,	PUNCT
ejpam-3248	382	7	a.	a.	PROPN
ejpam-3248	382	8	and	and	CCONJ
ejpam-3248	382	9	gonzalez	gonzalez	PROPN
ejpam-3248	382	10	,	,	PUNCT
ejpam-3248	382	11	s.	s.	PROPN
ejpam-3248	382	12	,	,	PUNCT
ejpam-3248	382	13	generalized	generalize	VERB
ejpam-3248	382	14	reverse	reverse	ADJ
ejpam-3248	382	15	derivations	derivation	NOUN
ejpam-3248	382	16	on	on	ADP
ejpam-3248	382	17	semiprime	semiprime	NOUN
ejpam-3248	382	18	rings	ring	NOUN
ejpam-3248	382	19	,	,	PUNCT
ejpam-3248	382	20	siberian	siberian	ADJ
ejpam-3248	382	21	math	math	NOUN
ejpam-3248	382	22	.	.	PUNCT
ejpam-3248	383	1	j.	j.	PROPN
ejpam-3248	383	2	56(2	56(2	PROPN
ejpam-3248	383	3	)	)	PUNCT
ejpam-3248	383	4	(	(	PUNCT
ejpam-3248	383	5	2015	2015	NUM
ejpam-3248	383	6	)	)	PUNCT
ejpam-3248	383	7	,	,	PUNCT
ejpam-3248	383	8	199	199	NUM
ejpam-3248	383	9	-	-	SYM
ejpam-3248	383	10	205	205	NUM
ejpam-3248	383	11	.	.	PUNCT
ejpam-3248	384	1	[	[	X
ejpam-3248	384	2	2	2	NUM
ejpam-3248	384	3	]	]	PUNCT
ejpam-3248	384	4	bresar	bresar	VERB
ejpam-3248	384	5	,	,	PUNCT
ejpam-3248	384	6	m.	m.	NOUN
ejpam-3248	384	7	,	,	PUNCT
ejpam-3248	384	8	on	on	ADP
ejpam-3248	384	9	the	the	DET
ejpam-3248	384	10	distance	distance	NOUN
ejpam-3248	384	11	of	of	ADP
ejpam-3248	384	12	the	the	DET
ejpam-3248	384	13	composition	composition	NOUN
ejpam-3248	384	14	of	of	ADP
ejpam-3248	384	15	two	two	NUM
ejpam-3248	384	16	derivations	derivation	NOUN
ejpam-3248	384	17	to	to	ADP
ejpam-3248	384	18	the	the	DET
ejpam-3248	384	19	generalized	generalized	ADJ
ejpam-3248	384	20	derivations	derivation	NOUN
ejpam-3248	384	21	,	,	PUNCT
ejpam-3248	384	22	glasgow	glasgow	PROPN
ejpam-3248	384	23	math	math	NOUN
ejpam-3248	384	24	.	.	PUNCT
ejpam-3248	385	1	j.	j.	PROPN
ejpam-3248	385	2	33(1	33(1	PROPN
ejpam-3248	385	3	)	)	PUNCT
ejpam-3248	385	4	(	(	PUNCT
ejpam-3248	385	5	1991	1991	NUM
ejpam-3248	385	6	)	)	PUNCT
ejpam-3248	385	7	,	,	PUNCT
ejpam-3248	385	8	89	89	NUM
ejpam-3248	385	9	-	-	SYM
ejpam-3248	385	10	93	93	NUM
ejpam-3248	385	11	.	.	PUNCT
ejpam-3248	386	1	[	[	X
ejpam-3248	386	2	3	3	NUM
ejpam-3248	386	3	]	]	X
ejpam-3248	386	4	bresar	bresar	VERB
ejpam-3248	386	5	,	,	PUNCT
ejpam-3248	386	6	m.	m.	NOUN
ejpam-3248	386	7	and	and	CCONJ
ejpam-3248	386	8	vukman	vukman	NOUN
ejpam-3248	386	9	,	,	PUNCT
ejpam-3248	386	10	j.	j.	PROPN
ejpam-3248	386	11	,	,	PUNCT
ejpam-3248	386	12	on	on	ADP
ejpam-3248	386	13	some	some	DET
ejpam-3248	386	14	additive	additive	ADJ
ejpam-3248	386	15	mappings	mapping	NOUN
ejpam-3248	386	16	in	in	ADP
ejpam-3248	386	17	rings	ring	NOUN
ejpam-3248	386	18	with	with	ADP
ejpam-3248	386	19	involution	involution	NOUN
ejpam-3248	386	20	,	,	PUNCT
ejpam-3248	386	21	aequat	aequat	PROPN
ejpam-3248	386	22	.	.	PUNCT
ejpam-3248	386	23	math	math	NOUN
ejpam-3248	386	24	.	.	PUNCT
ejpam-3248	387	1	38	38	NUM
ejpam-3248	387	2	(	(	PUNCT
ejpam-3248	387	3	1989	1989	NUM
ejpam-3248	387	4	)	)	PUNCT
ejpam-3248	387	5	,	,	PUNCT
ejpam-3248	387	6	178	178	NUM
ejpam-3248	387	7	-	-	SYM
ejpam-3248	387	8	185	185	NUM
ejpam-3248	387	9	.	.	PUNCT
ejpam-3248	388	1	references	reference	NOUN
ejpam-3248	388	2	729	729	NUM
ejpam-3248	388	3	[	[	X
ejpam-3248	388	4	4	4	NUM
ejpam-3248	388	5	]	]	PUNCT
ejpam-3248	388	6	m.	m.	NOUN
ejpam-3248	388	7	n.	n.	PROPN
ejpam-3248	388	8	daif	daif	PROPN
ejpam-3248	388	9	,	,	PUNCT
ejpam-3248	388	10	when	when	SCONJ
ejpam-3248	388	11	is	be	AUX
ejpam-3248	388	12	a	a	DET
ejpam-3248	388	13	multiplicative	multiplicative	ADJ
ejpam-3248	388	14	derivation	derivation	NOUN
ejpam-3248	388	15	additive	additive	NOUN
ejpam-3248	388	16	,	,	PUNCT
ejpam-3248	388	17	int	int	NOUN
ejpam-3248	388	18	.	.	PUNCT
ejpam-3248	389	1	j.	j.	PROPN
ejpam-3248	389	2	math	math	PROPN
ejpam-3248	389	3	.	.	PUNCT
ejpam-3248	390	1	math	math	NOUN
ejpam-3248	390	2	.	.	PUNCT
ejpam-3248	391	1	sci	sci	PROPN
ejpam-3248	391	2	.	.	PUNCT
ejpam-3248	391	3	14(3	14(3	NUM
ejpam-3248	391	4	)	)	PUNCT
ejpam-3248	391	5	(	(	PUNCT
ejpam-3248	391	6	1991	1991	NUM
ejpam-3248	391	7	)	)	PUNCT
ejpam-3248	391	8	,	,	PUNCT
ejpam-3248	391	9	615	615	NUM
ejpam-3248	391	10	-	-	SYM
ejpam-3248	391	11	618	618	NUM
ejpam-3248	391	12	.	.	PUNCT
ejpam-3248	392	1	[	[	X
ejpam-3248	392	2	5	5	NUM
ejpam-3248	392	3	]	]	X
ejpam-3248	392	4	daif	daif	NOUN
ejpam-3248	392	5	,	,	PUNCT
ejpam-3248	392	6	m.n	m.n	PROPN
ejpam-3248	392	7	.	.	PROPN
ejpam-3248	392	8	,	,	PUNCT
ejpam-3248	392	9	and	and	CCONJ
ejpam-3248	392	10	tammam	tammam	NOUN
ejpam-3248	392	11	el	el	PROPN
ejpam-3248	392	12	-	-	PUNCT
ejpam-3248	392	13	sayiad	sayiad	PROPN
ejpam-3248	392	14	,	,	PUNCT
ejpam-3248	392	15	m.s	m.s	PROPN
ejpam-3248	392	16	.	.	PROPN
ejpam-3248	392	17	,	,	PUNCT
ejpam-3248	392	18	multiplicative	multiplicative	VERB
ejpam-3248	392	19	generalized	generalized	ADJ
ejpam-3248	392	20	derivations	derivation	NOUN
ejpam-3248	392	21	which	which	PRON
ejpam-3248	392	22	are	be	AUX
ejpam-3248	392	23	additive	additive	ADJ
ejpam-3248	392	24	,	,	PUNCT
ejpam-3248	392	25	east	east	NOUN
ejpam-3248	392	26	-	-	PUNCT
ejpam-3248	392	27	west	west	PROPN
ejpam-3248	392	28	j.	j.	PROPN
ejpam-3248	392	29	math	math	PROPN
ejpam-3248	392	30	.	.	PUNCT
ejpam-3248	393	1	9(1	9(1	NUM
ejpam-3248	393	2	)	)	PUNCT
ejpam-3248	393	3	(	(	PUNCT
ejpam-3248	393	4	1997	1997	NUM
ejpam-3248	393	5	)	)	PUNCT
ejpam-3248	393	6	,	,	PUNCT
ejpam-3248	393	7	31	31	NUM
ejpam-3248	393	8	-	-	SYM
ejpam-3248	393	9	37	37	NUM
ejpam-3248	393	10	.	.	PUNCT
ejpam-3248	394	1	[	[	X
ejpam-3248	394	2	6	6	NUM
ejpam-3248	394	3	]	]	X
ejpam-3248	394	4	dhara	dhara	PROPN
ejpam-3248	394	5	,	,	PUNCT
ejpam-3248	394	6	b.	b.	PROPN
ejpam-3248	394	7	and	and	CCONJ
ejpam-3248	394	8	ali	ali	PROPN
ejpam-3248	394	9	,	,	PUNCT
ejpam-3248	394	10	s.	s.	PROPN
ejpam-3248	394	11	,	,	PUNCT
ejpam-3248	394	12	on	on	ADP
ejpam-3248	394	13	n	n	CCONJ
ejpam-3248	394	14	-	-	PUNCT
ejpam-3248	394	15	centralizing	centralize	VERB
ejpam-3248	394	16	generalized	generalized	ADJ
ejpam-3248	394	17	derivations	derivation	NOUN
ejpam-3248	394	18	in	in	ADP
ejpam-3248	394	19	semiprime	semiprime	NOUN
ejpam-3248	394	20	rings	ring	NOUN
ejpam-3248	394	21	with	with	ADP
ejpam-3248	394	22	applications	application	NOUN
ejpam-3248	394	23	to	to	ADP
ejpam-3248	394	24	c∗-algebras	c∗-algebra	NOUN
ejpam-3248	394	25	,	,	PUNCT
ejpam-3248	394	26	j.	j.	PROPN
ejpam-3248	394	27	algebra	algebra	PROPN
ejpam-3248	394	28	and	and	CCONJ
ejpam-3248	394	29	its	its	PRON
ejpam-3248	394	30	applications	application	NOUN
ejpam-3248	394	31	11(6	11(6	NUM
ejpam-3248	394	32	)	)	PUNCT
ejpam-3248	394	33	(	(	PUNCT
ejpam-3248	394	34	2012	2012	NUM
ejpam-3248	394	35	)	)	PUNCT
ejpam-3248	394	36	paper	paper	NOUN
ejpam-3248	394	37	no-1250111	no-1250111	NOUN
ejpam-3248	394	38	,	,	PUNCT
ejpam-3248	394	39	(	(	PUNCT
ejpam-3248	394	40	11	11	NUM
ejpam-3248	394	41	pages	page	NOUN
ejpam-3248	394	42	)	)	PUNCT
ejpam-3248	394	43	.	.	PUNCT
ejpam-3248	395	1	[	[	X
ejpam-3248	395	2	7	7	NUM
ejpam-3248	395	3	]	]	X
ejpam-3248	395	4	dhara	dhara	PROPN
ejpam-3248	395	5	,	,	PUNCT
ejpam-3248	395	6	b.	b.	PROPN
ejpam-3248	395	7	and	and	CCONJ
ejpam-3248	395	8	ali	ali	PROPN
ejpam-3248	395	9	,	,	PUNCT
ejpam-3248	395	10	s.	s.	PROPN
ejpam-3248	395	11	,	,	PUNCT
ejpam-3248	395	12	on	on	ADP
ejpam-3248	395	13	multiplicative	multiplicative	ADJ
ejpam-3248	395	14	(	(	PUNCT
ejpam-3248	395	15	generalized)-derivations	generalized)-derivation	NOUN
ejpam-3248	395	16	in	in	ADP
ejpam-3248	395	17	prime	prime	ADJ
ejpam-3248	395	18	and	and	CCONJ
ejpam-3248	395	19	semiprime	semiprime	NOUN
ejpam-3248	395	20	rings	ring	NOUN
ejpam-3248	395	21	,	,	PUNCT
ejpam-3248	395	22	aequat	aequat	PROPN
ejpam-3248	395	23	.	.	PUNCT
ejpam-3248	395	24	math	math	NOUN
ejpam-3248	395	25	.	.	PUNCT
ejpam-3248	396	1	86	86	NUM
ejpam-3248	396	2	(	(	PUNCT
ejpam-3248	396	3	1	1	NUM
ejpam-3248	396	4	-	-	SYM
ejpam-3248	396	5	2	2	NUM
ejpam-3248	396	6	)	)	PUNCT
ejpam-3248	396	7	(	(	PUNCT
ejpam-3248	396	8	2013	2013	NUM
ejpam-3248	396	9	)	)	PUNCT
ejpam-3248	396	10	,	,	PUNCT
ejpam-3248	396	11	65	65	NUM
ejpam-3248	396	12	-	-	SYM
ejpam-3248	396	13	79	79	NUM
ejpam-3248	396	14	.	.	PUNCT
ejpam-3248	397	1	[	[	X
ejpam-3248	397	2	8	8	NUM
ejpam-3248	397	3	]	]	X
ejpam-3248	397	4	herstein	herstein	NOUN
ejpam-3248	397	5	,	,	PUNCT
ejpam-3248	397	6	i.n	i.n	PROPN
ejpam-3248	397	7	.	.	PROPN
ejpam-3248	397	8	,	,	PUNCT
ejpam-3248	397	9	jordan	jordan	PROPN
ejpam-3248	397	10	derivations	derivation	NOUN
ejpam-3248	397	11	of	of	ADP
ejpam-3248	397	12	prime	prime	ADJ
ejpam-3248	397	13	rings	ring	NOUN
ejpam-3248	397	14	,	,	PUNCT
ejpam-3248	397	15	proc	proc	NOUN
ejpam-3248	397	16	.	.	PUNCT
ejpam-3248	398	1	amer	amer	PROPN
ejpam-3248	398	2	.	.	PUNCT
ejpam-3248	398	3	math	math	PROPN
ejpam-3248	398	4	.	.	PUNCT
ejpam-3248	399	1	soc	soc	PROPN
ejpam-3248	399	2	.	.	PUNCT
ejpam-3248	400	1	8	8	NUM
ejpam-3248	400	2	(	(	PUNCT
ejpam-3248	400	3	1957	1957	NUM
ejpam-3248	400	4	)	)	PUNCT
ejpam-3248	400	5	,	,	PUNCT
ejpam-3248	400	6	1104	1104	NUM
ejpam-3248	400	7	-	-	SYM
ejpam-3248	400	8	1110	1110	NUM
ejpam-3248	400	9	.	.	PUNCT
ejpam-3248	401	1	[	[	X
ejpam-3248	401	2	9	9	NUM
ejpam-3248	401	3	]	]	SYM
ejpam-3248	401	4	herstein	herstein	NOUN
ejpam-3248	401	5	,	,	PUNCT
ejpam-3248	401	6	i.	i.	PROPN
ejpam-3248	401	7	n.	n.	PROPN
ejpam-3248	401	8	,	,	PUNCT
ejpam-3248	401	9	rings	ring	NOUN
ejpam-3248	401	10	with	with	ADP
ejpam-3248	401	11	involution	involution	NOUN
ejpam-3248	401	12	,	,	PUNCT
ejpam-3248	401	13	chicago	chicago	PROPN
ejpam-3248	401	14	lectures	lecture	VERB
ejpam-3248	401	15	in	in	ADP
ejpam-3248	401	16	mathematics	mathematic	NOUN
ejpam-3248	401	17	,	,	PUNCT
ejpam-3248	401	18	university	university	NOUN
ejpam-3248	401	19	of	of	ADP
ejpam-3248	401	20	chicago	chicago	PROPN
ejpam-3248	401	21	press	press	PROPN
ejpam-3248	401	22	,	,	PUNCT
ejpam-3248	401	23	chicago	chicago	PROPN
ejpam-3248	401	24	iii	iii	PROPN
ejpam-3248	401	25	usa	usa	PROPN
ejpam-3248	401	26	(	(	PUNCT
ejpam-3248	401	27	1976	1976	NUM
ejpam-3248	401	28	)	)	PUNCT
ejpam-3248	401	29	.	.	PUNCT
ejpam-3248	402	1	[	[	X
ejpam-3248	402	2	10	10	NUM
ejpam-3248	402	3	]	]	X
ejpam-3248	402	4	koc	koc	PROPN
ejpam-3248	402	5	,	,	PUNCT
ejpam-3248	402	6	e.	e.	PROPN
ejpam-3248	402	7	,	,	PUNCT
ejpam-3248	402	8	some	some	DET
ejpam-3248	402	9	results	result	NOUN
ejpam-3248	402	10	in	in	ADP
ejpam-3248	402	11	semiprime	semiprime	NOUN
ejpam-3248	402	12	rings	ring	NOUN
ejpam-3248	402	13	with	with	ADP
ejpam-3248	402	14	derivation	derivation	NOUN
ejpam-3248	402	15	,	,	PUNCT
ejpam-3248	402	16	commun	commun	PROPN
ejpam-3248	402	17	.	.	PUNCT
ejpam-3248	403	1	fac	fac	PROPN
ejpam-3248	403	2	.	.	PUNCT
ejpam-3248	403	3	sci	sci	PROPN
ejpam-3248	403	4	.	.	PROPN
ejpam-3248	403	5	univ	univ	PROPN
ejpam-3248	403	6	.	.	PUNCT
ejpam-3248	404	1	ank	ank	PROPN
ejpam-3248	404	2	.	.	PROPN
ejpam-3248	404	3	series	series	PROPN
ejpam-3248	404	4	62(1	62(1	PROPN
ejpam-3248	404	5	)	)	PUNCT
ejpam-3248	404	6	(	(	PUNCT
ejpam-3248	404	7	2013	2013	NUM
ejpam-3248	404	8	)	)	PUNCT
ejpam-3248	404	9	,	,	PUNCT
ejpam-3248	404	10	11	11	NUM
ejpam-3248	404	11	-	-	SYM
ejpam-3248	404	12	20	20	NUM
ejpam-3248	404	13	.	.	PUNCT
ejpam-3248	405	1	[	[	X
ejpam-3248	405	2	11	11	NUM
ejpam-3248	405	3	]	]	SYM
ejpam-3248	405	4	tiwari	tiwari	PROPN
ejpam-3248	405	5	,	,	PUNCT
ejpam-3248	405	6	s.k	s.k	PROPN
ejpam-3248	405	7	.	.	PROPN
ejpam-3248	405	8	,	,	PUNCT
ejpam-3248	405	9	sharma	sharma	PROPN
ejpam-3248	405	10	,	,	PUNCT
ejpam-3248	405	11	r.k	r.k	PROPN
ejpam-3248	405	12	.	.	PROPN
ejpam-3248	405	13	and	and	CCONJ
ejpam-3248	405	14	dhara	dhara	PROPN
ejpam-3248	405	15	,	,	PUNCT
ejpam-3248	405	16	b.	b.	PROPN
ejpam-3248	405	17	,	,	PUNCT
ejpam-3248	405	18	some	some	DET
ejpam-3248	405	19	theorems	theorem	NOUN
ejpam-3248	405	20	of	of	ADP
ejpam-3248	405	21	commutativity	commutativity	NOUN
ejpam-3248	405	22	on	on	ADP
ejpam-3248	405	23	semiprime	semiprime	NOUN
ejpam-3248	405	24	rings	ring	NOUN
ejpam-3248	405	25	with	with	ADP
ejpam-3248	405	26	mappings	mapping	NOUN
ejpam-3248	405	27	,	,	PUNCT
ejpam-3248	405	28	southeast	southeast	ADJ
ejpam-3248	405	29	asian	asian	ADJ
ejpam-3248	405	30	bull	bull	NOUN
ejpam-3248	405	31	.	.	PUNCT
ejpam-3248	406	1	math	math	NOUN
ejpam-3248	406	2	.	.	PUNCT
ejpam-3248	407	1	42	42	NUM
ejpam-3248	407	2	(	(	PUNCT
ejpam-3248	407	3	2018	2018	NUM
ejpam-3248	407	4	)	)	PUNCT
ejpam-3248	407	5	,	,	PUNCT
ejpam-3248	407	6	579	579	NUM
ejpam-3248	407	7	-	-	SYM
ejpam-3248	407	8	592	592	NUM
ejpam-3248	407	9	.	.	PUNCT