id	sid	tid	token	lemma	pos
ejpam-3496	1	1	european	european	PROPN
ejpam-3496	1	2	journal	journal	PROPN
ejpam-3496	1	3	of	of	ADP
ejpam-3496	1	4	pure	pure	ADJ
ejpam-3496	1	5	and	and	CCONJ
ejpam-3496	1	6	applied	apply	VERB
ejpam-3496	1	7	mathematics	mathematic	NOUN
ejpam-3496	1	8	vol	vol	NOUN
ejpam-3496	1	9	.	.	PROPN
ejpam-3496	2	1	12	12	NUM
ejpam-3496	2	2	,	,	PUNCT
ejpam-3496	2	3	no	no	INTJ
ejpam-3496	2	4	.	.	NOUN
ejpam-3496	2	5	3	3	NUM
ejpam-3496	2	6	,	,	PUNCT
ejpam-3496	2	7	2019	2019	NUM
ejpam-3496	2	8	,	,	PUNCT
ejpam-3496	2	9	1138	1138	NUM
ejpam-3496	2	10	-	-	SYM
ejpam-3496	2	11	1148	1148	NUM
ejpam-3496	2	12	issn	issn	PROPN
ejpam-3496	2	13	1307	1307	NUM
ejpam-3496	2	14	-	-	SYM
ejpam-3496	2	15	5543	5543	NUM
ejpam-3496	2	16	–	–	PUNCT
ejpam-3496	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3496	2	18	published	publish	VERB
ejpam-3496	2	19	by	by	ADP
ejpam-3496	2	20	new	new	PROPN
ejpam-3496	2	21	york	york	PROPN
ejpam-3496	2	22	business	business	PROPN
ejpam-3496	3	1	global	global	PROPN
ejpam-3496	3	2	a	a	DET
ejpam-3496	3	3	characterization	characterization	NOUN
ejpam-3496	3	4	of	of	ADP
ejpam-3496	3	5	derivations	derivation	NOUN
ejpam-3496	3	6	in	in	ADP
ejpam-3496	3	7	prime	prime	ADJ
ejpam-3496	3	8	rings	ring	NOUN
ejpam-3496	3	9	with	with	ADP
ejpam-3496	3	10	involution	involution	NOUN
ejpam-3496	3	11	shakir	shakir	PROPN
ejpam-3496	3	12	ali1,∗	ali1,∗	PROPN
ejpam-3496	3	13	,	,	PUNCT
ejpam-3496	3	14	m.	m.	NOUN
ejpam-3496	3	15	rahman	rahman	PROPN
ejpam-3496	3	16	mozumder1	mozumder1	PROPN
ejpam-3496	3	17	,	,	PUNCT
ejpam-3496	3	18	adnan	adnan	PROPN
ejpam-3496	3	19	abbasi1	abbasi1	PROPN
ejpam-3496	3	20	,	,	PUNCT
ejpam-3496	3	21	m.	m.	NOUN
ejpam-3496	3	22	salahuddin	salahuddin	NOUN
ejpam-3496	3	23	khan2	khan2	PROPN
ejpam-3496	3	24	1	1	NUM
ejpam-3496	3	25	department	department	NOUN
ejpam-3496	3	26	of	of	ADP
ejpam-3496	3	27	mathematics	mathematic	NOUN
ejpam-3496	3	28	,	,	PUNCT
ejpam-3496	3	29	faculty	faculty	NOUN
ejpam-3496	3	30	of	of	ADP
ejpam-3496	3	31	science	science	NOUN
ejpam-3496	3	32	,	,	PUNCT
ejpam-3496	3	33	aligarh	aligarh	PROPN
ejpam-3496	3	34	muslim	muslim	PROPN
ejpam-3496	3	35	university	university	PROPN
ejpam-3496	3	36	,	,	PUNCT
ejpam-3496	3	37	aligarh-202002	aligarh-202002	NOUN
ejpam-3496	3	38	,	,	PUNCT
ejpam-3496	3	39	india	india	PROPN
ejpam-3496	3	40	2	2	NUM
ejpam-3496	3	41	department	department	NOUN
ejpam-3496	3	42	of	of	ADP
ejpam-3496	3	43	applied	apply	VERB
ejpam-3496	3	44	mathematics	mathematic	NOUN
ejpam-3496	3	45	,	,	PUNCT
ejpam-3496	3	46	faculty	faculty	NOUN
ejpam-3496	3	47	of	of	ADP
ejpam-3496	3	48	engineering	engineering	PROPN
ejpam-3496	3	49	,	,	PUNCT
ejpam-3496	3	50	aligarh	aligarh	PROPN
ejpam-3496	3	51	muslim	muslim	PROPN
ejpam-3496	3	52	university	university	PROPN
ejpam-3496	3	53	,	,	PUNCT
ejpam-3496	3	54	aligarh-202002	aligarh-202002	NOUN
ejpam-3496	3	55	,	,	PUNCT
ejpam-3496	3	56	india	india	PROPN
ejpam-3496	3	57	abstract	abstract	NOUN
ejpam-3496	3	58	.	.	PUNCT
ejpam-3496	4	1	the	the	DET
ejpam-3496	4	2	purpose	purpose	NOUN
ejpam-3496	4	3	of	of	ADP
ejpam-3496	4	4	this	this	DET
ejpam-3496	4	5	paper	paper	NOUN
ejpam-3496	4	6	is	be	AUX
ejpam-3496	4	7	to	to	PART
ejpam-3496	4	8	investigate	investigate	VERB
ejpam-3496	4	9	∗-differential	∗-differential	ADJ
ejpam-3496	4	10	identities	identity	NOUN
ejpam-3496	4	11	satisfied	satisfy	VERB
ejpam-3496	4	12	by	by	ADP
ejpam-3496	4	13	pair	pair	NOUN
ejpam-3496	4	14	of	of	ADP
ejpam-3496	4	15	derivations	derivation	NOUN
ejpam-3496	4	16	on	on	ADP
ejpam-3496	4	17	prime	prime	ADJ
ejpam-3496	4	18	rings	ring	NOUN
ejpam-3496	4	19	with	with	ADP
ejpam-3496	4	20	involution	involution	NOUN
ejpam-3496	4	21	.	.	PUNCT
ejpam-3496	5	1	in	in	ADP
ejpam-3496	5	2	particular	particular	ADJ
ejpam-3496	5	3	,	,	PUNCT
ejpam-3496	5	4	we	we	PRON
ejpam-3496	5	5	prove	prove	VERB
ejpam-3496	5	6	that	that	SCONJ
ejpam-3496	5	7	if	if	SCONJ
ejpam-3496	5	8	a	a	DET
ejpam-3496	5	9	2	2	NUM
ejpam-3496	5	10	-	-	PUNCT
ejpam-3496	5	11	torsion	torsion	NOUN
ejpam-3496	5	12	free	free	ADJ
ejpam-3496	5	13	noncommutative	noncommutative	ADJ
ejpam-3496	5	14	ring	ring	NOUN
ejpam-3496	5	15	r	r	NOUN
ejpam-3496	5	16	admit	admit	VERB
ejpam-3496	5	17	nonzero	nonzero	NOUN
ejpam-3496	5	18	derivations	derivation	NOUN
ejpam-3496	5	19	d1	d1	PROPN
ejpam-3496	5	20	,	,	PUNCT
ejpam-3496	5	21	d2	d2	VERB
ejpam-3496	5	22	such	such	ADJ
ejpam-3496	5	23	that	that	SCONJ
ejpam-3496	6	1	[	[	X
ejpam-3496	6	2	d1(x	d1(x	NOUN
ejpam-3496	6	3	)	)	PUNCT
ejpam-3496	6	4	,	,	PUNCT
ejpam-3496	6	5	d2(x∗	d2(x∗	PROPN
ejpam-3496	6	6	)	)	PUNCT
ejpam-3496	6	7	]	]	PUNCT
ejpam-3496	7	1	=	=	PUNCT
ejpam-3496	7	2	0	0	PUNCT
ejpam-3496	7	3	for	for	ADP
ejpam-3496	7	4	all	all	DET
ejpam-3496	7	5	x	x	SYM
ejpam-3496	7	6	∈	∈	PROPN
ejpam-3496	7	7	r	r	NOUN
ejpam-3496	7	8	,	,	PUNCT
ejpam-3496	7	9	then	then	ADV
ejpam-3496	7	10	d1	d1	PROPN
ejpam-3496	7	11	=	=	SYM
ejpam-3496	7	12	λd2	λd2	PROPN
ejpam-3496	7	13	,	,	PUNCT
ejpam-3496	7	14	where	where	SCONJ
ejpam-3496	7	15	λ	λ	PROPN
ejpam-3496	7	16	∈	∈	PROPN
ejpam-3496	7	17	c.	c.	NOUN
ejpam-3496	7	18	finally	finally	ADV
ejpam-3496	7	19	,	,	PUNCT
ejpam-3496	7	20	we	we	PRON
ejpam-3496	7	21	provide	provide	VERB
ejpam-3496	7	22	an	an	DET
ejpam-3496	7	23	example	example	NOUN
ejpam-3496	7	24	to	to	PART
ejpam-3496	7	25	show	show	VERB
ejpam-3496	7	26	that	that	SCONJ
ejpam-3496	7	27	the	the	DET
ejpam-3496	7	28	condition	condition	NOUN
ejpam-3496	7	29	imposed	impose	VERB
ejpam-3496	7	30	in	in	ADP
ejpam-3496	7	31	the	the	DET
ejpam-3496	7	32	hypothesis	hypothesis	NOUN
ejpam-3496	7	33	of	of	ADP
ejpam-3496	7	34	our	our	PRON
ejpam-3496	7	35	results	result	NOUN
ejpam-3496	7	36	are	be	AUX
ejpam-3496	7	37	necessary	necessary	ADJ
ejpam-3496	7	38	.	.	PUNCT
ejpam-3496	8	1	2010	2010	NUM
ejpam-3496	8	2	mathematics	mathematic	NOUN
ejpam-3496	8	3	subject	subject	NOUN
ejpam-3496	8	4	classifications	classification	NOUN
ejpam-3496	8	5	:	:	PUNCT
ejpam-3496	8	6	16w10	16w10	NUM
ejpam-3496	8	7	,	,	PUNCT
ejpam-3496	8	8	16n60	16n60	NUM
ejpam-3496	8	9	,	,	PUNCT
ejpam-3496	8	10	16w25	16w25	NUM
ejpam-3496	8	11	key	key	ADJ
ejpam-3496	8	12	words	word	NOUN
ejpam-3496	8	13	and	and	CCONJ
ejpam-3496	8	14	phrases	phrase	NOUN
ejpam-3496	8	15	:	:	PUNCT
ejpam-3496	8	16	prime	prime	ADJ
ejpam-3496	8	17	ring	ring	NOUN
ejpam-3496	8	18	,	,	PUNCT
ejpam-3496	8	19	derivation	derivation	NOUN
ejpam-3496	8	20	,	,	PUNCT
ejpam-3496	8	21	involution	involution	NOUN
ejpam-3496	8	22	,	,	PUNCT
ejpam-3496	8	23	∗-differential	∗-differential	ADJ
ejpam-3496	8	24	identity	identity	NOUN
ejpam-3496	8	25	1	1	NUM
ejpam-3496	8	26	.	.	PUNCT
ejpam-3496	9	1	introduction	introduction	NOUN
ejpam-3496	9	2	in	in	ADP
ejpam-3496	9	3	all	all	PRON
ejpam-3496	9	4	that	that	PRON
ejpam-3496	9	5	follows	follow	VERB
ejpam-3496	9	6	,	,	PUNCT
ejpam-3496	9	7	r	r	NOUN
ejpam-3496	9	8	will	will	AUX
ejpam-3496	9	9	represent	represent	VERB
ejpam-3496	9	10	an	an	DET
ejpam-3496	9	11	associative	associative	ADJ
ejpam-3496	9	12	ring	ring	NOUN
ejpam-3496	9	13	with	with	ADP
ejpam-3496	9	14	center	center	NOUN
ejpam-3496	9	15	z(r	z(r	NOUN
ejpam-3496	9	16	)	)	PUNCT
ejpam-3496	9	17	.	.	PUNCT
ejpam-3496	10	1	we	we	PRON
ejpam-3496	10	2	denote	denote	VERB
ejpam-3496	10	3	by	by	ADP
ejpam-3496	10	4	q	q	PROPN
ejpam-3496	10	5	and	and	CCONJ
ejpam-3496	10	6	c	c	X
ejpam-3496	10	7	the	the	DET
ejpam-3496	10	8	maximal	maximal	ADJ
ejpam-3496	10	9	ring	ring	NOUN
ejpam-3496	10	10	of	of	ADP
ejpam-3496	10	11	quotient	quotient	NOUN
ejpam-3496	10	12	and	and	CCONJ
ejpam-3496	10	13	the	the	DET
ejpam-3496	10	14	extended	extended	ADJ
ejpam-3496	10	15	centroid	centroid	NOUN
ejpam-3496	10	16	of	of	ADP
ejpam-3496	10	17	a	a	DET
ejpam-3496	10	18	prime	prime	ADJ
ejpam-3496	10	19	ring	ring	NOUN
ejpam-3496	10	20	,	,	PUNCT
ejpam-3496	10	21	respectively	respectively	ADV
ejpam-3496	10	22	.	.	PUNCT
ejpam-3496	11	1	for	for	ADP
ejpam-3496	11	2	the	the	DET
ejpam-3496	11	3	explanation	explanation	NOUN
ejpam-3496	11	4	of	of	ADP
ejpam-3496	11	5	q	q	PROPN
ejpam-3496	11	6	and	and	CCONJ
ejpam-3496	11	7	c	c	AUX
ejpam-3496	11	8	we	we	PRON
ejpam-3496	11	9	refer	refer	VERB
ejpam-3496	11	10	the	the	DET
ejpam-3496	11	11	reader	reader	NOUN
ejpam-3496	11	12	to	to	ADP
ejpam-3496	11	13	[	[	X
ejpam-3496	11	14	4	4	NUM
ejpam-3496	11	15	]	]	PUNCT
ejpam-3496	11	16	.	.	PUNCT
ejpam-3496	12	1	we	we	PRON
ejpam-3496	12	2	denote	denote	VERB
ejpam-3496	12	3	[	[	X
ejpam-3496	12	4	x	x	X
ejpam-3496	12	5	,	,	PUNCT
ejpam-3496	12	6	y	y	PROPN
ejpam-3496	12	7	]	]	X
ejpam-3496	13	1	=	=	PUNCT
ejpam-3496	14	1	xy	xy	PROPN
ejpam-3496	14	2	−	−	PROPN
ejpam-3496	14	3	yx	yx	PROPN
ejpam-3496	14	4	,	,	PUNCT
ejpam-3496	14	5	the	the	DET
ejpam-3496	14	6	commutator	commutator	NOUN
ejpam-3496	14	7	of	of	ADP
ejpam-3496	14	8	x	x	PROPN
ejpam-3496	14	9	and	and	CCONJ
ejpam-3496	14	10	y	y	PROPN
ejpam-3496	14	11	and	and	CCONJ
ejpam-3496	14	12	x	x	PUNCT
ejpam-3496	14	13	◦	◦	NOUN
ejpam-3496	14	14	y	y	NOUN
ejpam-3496	14	15	=	=	PUNCT
ejpam-3496	14	16	xy	xy	PROPN
ejpam-3496	15	1	+	+	CCONJ
ejpam-3496	15	2	yx	yx	PROPN
ejpam-3496	15	3	,	,	PUNCT
ejpam-3496	15	4	the	the	DET
ejpam-3496	15	5	anti	anti	NOUN
ejpam-3496	15	6	-	-	NOUN
ejpam-3496	15	7	commutator	commutator	NOUN
ejpam-3496	15	8	of	of	ADP
ejpam-3496	15	9	x	x	PUNCT
ejpam-3496	15	10	and	and	CCONJ
ejpam-3496	15	11	y.	y.	PROPN
ejpam-3496	15	12	a	a	DET
ejpam-3496	15	13	ring	ring	NOUN
ejpam-3496	15	14	is	be	AUX
ejpam-3496	15	15	said	say	VERB
ejpam-3496	15	16	to	to	ADP
ejpam-3496	15	17	2	2	NUM
ejpam-3496	15	18	-	-	PUNCT
ejpam-3496	15	19	torsion	torsion	NOUN
ejpam-3496	15	20	free	free	ADJ
ejpam-3496	15	21	if	if	SCONJ
ejpam-3496	15	22	2x	2x	NUM
ejpam-3496	15	23	=	=	SYM
ejpam-3496	15	24	0	0	PUNCT
ejpam-3496	16	1	(	(	PUNCT
ejpam-3496	16	2	where	where	SCONJ
ejpam-3496	16	3	x	x	SYM
ejpam-3496	16	4	∈	∈	PROPN
ejpam-3496	16	5	r	r	NOUN
ejpam-3496	16	6	)	)	PUNCT
ejpam-3496	16	7	implies	imply	VERB
ejpam-3496	16	8	x	x	PUNCT
ejpam-3496	16	9	=	=	SYM
ejpam-3496	16	10	0	0	NUM
ejpam-3496	16	11	.	.	PUNCT
ejpam-3496	17	1	a	a	DET
ejpam-3496	17	2	ring	ring	NOUN
ejpam-3496	17	3	r	r	NOUN
ejpam-3496	17	4	is	be	AUX
ejpam-3496	17	5	said	say	VERB
ejpam-3496	17	6	to	to	PART
ejpam-3496	17	7	be	be	AUX
ejpam-3496	17	8	prime	prime	ADJ
ejpam-3496	17	9	if	if	SCONJ
ejpam-3496	17	10	arb	arb	NOUN
ejpam-3496	17	11	=	=	SYM
ejpam-3496	17	12	(	(	PUNCT
ejpam-3496	17	13	0	0	NUM
ejpam-3496	17	14	)	)	PUNCT
ejpam-3496	17	15	(	(	PUNCT
ejpam-3496	17	16	where	where	SCONJ
ejpam-3496	17	17	a	a	PRON
ejpam-3496	17	18	,	,	PUNCT
ejpam-3496	17	19	b	b	X
ejpam-3496	17	20	∈	∈	PROPN
ejpam-3496	17	21	r	r	NOUN
ejpam-3496	17	22	)	)	PUNCT
ejpam-3496	17	23	implies	imply	VERB
ejpam-3496	17	24	either	either	CCONJ
ejpam-3496	17	25	a	a	PRON
ejpam-3496	17	26	=	=	SYM
ejpam-3496	17	27	0	0	NUM
ejpam-3496	17	28	or	or	CCONJ
ejpam-3496	17	29	b	b	NOUN
ejpam-3496	17	30	=	=	SYM
ejpam-3496	17	31	0	0	NUM
ejpam-3496	17	32	,	,	PUNCT
ejpam-3496	17	33	and	and	CCONJ
ejpam-3496	17	34	is	be	AUX
ejpam-3496	17	35	called	call	VERB
ejpam-3496	17	36	semiprime	semiprime	NOUN
ejpam-3496	17	37	ring	ring	NOUN
ejpam-3496	17	38	if	if	SCONJ
ejpam-3496	17	39	ara	ara	PROPN
ejpam-3496	17	40	=	=	SYM
ejpam-3496	17	41	(	(	PUNCT
ejpam-3496	17	42	0	0	NUM
ejpam-3496	17	43	)	)	PUNCT
ejpam-3496	17	44	(	(	PUNCT
ejpam-3496	17	45	where	where	SCONJ
ejpam-3496	17	46	a	a	DET
ejpam-3496	17	47	∈	∈	PROPN
ejpam-3496	17	48	r	r	NOUN
ejpam-3496	17	49	)	)	PUNCT
ejpam-3496	17	50	implies	imply	VERB
ejpam-3496	17	51	a	a	DET
ejpam-3496	17	52	=	=	NOUN
ejpam-3496	17	53	0	0	NUM
ejpam-3496	17	54	.	.	PUNCT
ejpam-3496	18	1	an	an	DET
ejpam-3496	18	2	additive	additive	ADJ
ejpam-3496	18	3	mapping	mapping	NOUN
ejpam-3496	18	4	∗	∗	NOUN
ejpam-3496	18	5	:	:	PUNCT
ejpam-3496	18	6	r	r	NOUN
ejpam-3496	18	7	→	→	SYM
ejpam-3496	18	8	r	r	NOUN
ejpam-3496	18	9	is	be	AUX
ejpam-3496	18	10	called	call	VERB
ejpam-3496	18	11	an	an	DET
ejpam-3496	18	12	involution	involution	NOUN
ejpam-3496	18	13	if	if	SCONJ
ejpam-3496	18	14	∗	∗	NOUN
ejpam-3496	18	15	is	be	AUX
ejpam-3496	18	16	an	an	DET
ejpam-3496	18	17	anti	anti	ADJ
ejpam-3496	18	18	-	-	ADJ
ejpam-3496	18	19	automorphism	automorphism	NOUN
ejpam-3496	18	20	of	of	ADP
ejpam-3496	18	21	order	order	NOUN
ejpam-3496	18	22	2	2	NUM
ejpam-3496	18	23	;	;	PUNCT
ejpam-3496	18	24	that	that	PRON
ejpam-3496	18	25	is	is	ADV
ejpam-3496	18	26	,	,	PUNCT
ejpam-3496	18	27	(	(	PUNCT
ejpam-3496	18	28	x∗)∗	x∗)∗	PROPN
ejpam-3496	18	29	=	=	SYM
ejpam-3496	18	30	x	x	PROPN
ejpam-3496	18	31	for	for	ADP
ejpam-3496	18	32	all	all	DET
ejpam-3496	18	33	x	x	PROPN
ejpam-3496	18	34	∈	∈	PROPN
ejpam-3496	18	35	r.	r.	NOUN
ejpam-3496	18	36	an	an	DET
ejpam-3496	18	37	element	element	NOUN
ejpam-3496	18	38	x	x	PUNCT
ejpam-3496	18	39	in	in	ADP
ejpam-3496	18	40	a	a	DET
ejpam-3496	18	41	ring	ring	NOUN
ejpam-3496	18	42	with	with	ADP
ejpam-3496	18	43	involution	involution	NOUN
ejpam-3496	18	44	is	be	AUX
ejpam-3496	18	45	said	say	VERB
ejpam-3496	18	46	to	to	PART
ejpam-3496	18	47	be	be	AUX
ejpam-3496	18	48	hermitian	hermitian	ADJ
ejpam-3496	18	49	if	if	SCONJ
ejpam-3496	18	50	x∗	x∗	PROPN
ejpam-3496	18	51	=	=	SYM
ejpam-3496	18	52	x	x	PUNCT
ejpam-3496	18	53	and	and	CCONJ
ejpam-3496	18	54	skew	skew	NOUN
ejpam-3496	18	55	-	-	PUNCT
ejpam-3496	18	56	hermitian	hermitian	ADJ
ejpam-3496	18	57	if	if	SCONJ
ejpam-3496	18	58	x∗	x∗	PROPN
ejpam-3496	18	59	=	=	SYM
ejpam-3496	18	60	−x	−x	NOUN
ejpam-3496	18	61	.	.	PUNCT
ejpam-3496	19	1	the	the	DET
ejpam-3496	19	2	sets	set	NOUN
ejpam-3496	19	3	of	of	ADP
ejpam-3496	19	4	all	all	DET
ejpam-3496	19	5	hermitian	hermitian	ADJ
ejpam-3496	19	6	and	and	CCONJ
ejpam-3496	19	7	skew	skew	ADJ
ejpam-3496	19	8	-	-	PUNCT
ejpam-3496	19	9	hermitian	hermitian	ADJ
ejpam-3496	19	10	elements	element	NOUN
ejpam-3496	19	11	of	of	ADP
ejpam-3496	19	12	r	r	NOUN
ejpam-3496	19	13	will	will	AUX
ejpam-3496	19	14	be	be	AUX
ejpam-3496	19	15	denoted	denote	VERB
ejpam-3496	19	16	by	by	ADP
ejpam-3496	19	17	h(r	h(r	NOUN
ejpam-3496	19	18	)	)	PUNCT
ejpam-3496	19	19	and	and	CCONJ
ejpam-3496	19	20	s(r	s(r	NOUN
ejpam-3496	19	21	)	)	PUNCT
ejpam-3496	19	22	,	,	PUNCT
ejpam-3496	19	23	respectively	respectively	ADV
ejpam-3496	19	24	.	.	PUNCT
ejpam-3496	20	1	a	a	DET
ejpam-3496	20	2	ring	ring	NOUN
ejpam-3496	20	3	equipped	equip	VERB
ejpam-3496	20	4	with	with	ADP
ejpam-3496	20	5	an	an	DET
ejpam-3496	20	6	involution	involution	NOUN
ejpam-3496	20	7	is	be	AUX
ejpam-3496	20	8	known	know	VERB
ejpam-3496	20	9	as	as	ADP
ejpam-3496	20	10	ring	ring	NOUN
ejpam-3496	20	11	with	with	ADP
ejpam-3496	20	12	involution	involution	NOUN
ejpam-3496	20	13	or	or	CCONJ
ejpam-3496	20	14	∗-ring	∗-ring	NOUN
ejpam-3496	20	15	.	.	PUNCT
ejpam-3496	21	1	the	the	DET
ejpam-3496	21	2	involution	involution	NOUN
ejpam-3496	21	3	is	be	AUX
ejpam-3496	21	4	said	say	VERB
ejpam-3496	21	5	to	to	PART
ejpam-3496	21	6	be	be	AUX
ejpam-3496	21	7	of	of	ADP
ejpam-3496	21	8	the	the	DET
ejpam-3496	21	9	first	first	ADJ
ejpam-3496	21	10	kind	kind	NOUN
ejpam-3496	21	11	if	if	SCONJ
ejpam-3496	21	12	z(r	z(r	NOUN
ejpam-3496	21	13	)	)	PUNCT
ejpam-3496	21	14	⊆	⊆	NUM
ejpam-3496	21	15	h(r	h(r	NOUN
ejpam-3496	21	16	)	)	PUNCT
ejpam-3496	21	17	,	,	PUNCT
ejpam-3496	21	18	otherwise	otherwise	ADV
ejpam-3496	21	19	it	it	PRON
ejpam-3496	21	20	is	be	AUX
ejpam-3496	21	21	said	say	VERB
ejpam-3496	21	22	to	to	PART
ejpam-3496	21	23	be	be	AUX
ejpam-3496	21	24	of	of	ADP
ejpam-3496	21	25	the	the	DET
ejpam-3496	21	26	second	second	ADJ
ejpam-3496	21	27	kind	kind	NOUN
ejpam-3496	21	28	.	.	PUNCT
ejpam-3496	22	1	in	in	ADP
ejpam-3496	22	2	the	the	DET
ejpam-3496	22	3	later	later	ADJ
ejpam-3496	22	4	case	case	NOUN
ejpam-3496	22	5	,	,	PUNCT
ejpam-3496	22	6	∗corresponding	∗corresponde	VERB
ejpam-3496	22	7	author	author	NOUN
ejpam-3496	22	8	.	.	PUNCT
ejpam-3496	23	1	doi	doi	NOUN
ejpam-3496	23	2	:	:	PUNCT
ejpam-3496	23	3	https://doi.org/10.29020/nybg.ejpam.v12i3.3496	https://doi.org/10.29020/nybg.ejpam.v12i3.3496	PART
ejpam-3496	23	4	email	email	NOUN
ejpam-3496	23	5	addresses	address	NOUN
ejpam-3496	23	6	:	:	PUNCT
ejpam-3496	23	7	shakir.ali.mm@amu.ac.in	shakir.ali.mm@amu.ac.in	PROPN
ejpam-3496	23	8	(	(	PUNCT
ejpam-3496	23	9	s.	s.	PROPN
ejpam-3496	23	10	ali	ali	PROPN
ejpam-3496	23	11	)	)	PUNCT
ejpam-3496	23	12	,	,	PUNCT
ejpam-3496	23	13	muzibamu81@gmail.com	muzibamu81@gmail.com	PROPN
ejpam-3496	23	14	(	(	PUNCT
ejpam-3496	23	15	m.	m.	PROPN
ejpam-3496	23	16	r.	r.	PROPN
ejpam-3496	23	17	mozumder	mozumder	PROPN
ejpam-3496	23	18	)	)	PUNCT
ejpam-3496	23	19	,	,	PUNCT
ejpam-3496	23	20	adnan.abbasi001@gmail.com	adnan.abbasi001@gmail.com	PROPN
ejpam-3496	23	21	(	(	PUNCT
ejpam-3496	23	22	a.	a.	PROPN
ejpam-3496	23	23	abbasi	abbasi	PROPN
ejpam-3496	23	24	)	)	PUNCT
ejpam-3496	23	25	,	,	PUNCT
ejpam-3496	23	26	salahuddinkhan50@gmail.com	salahuddinkhan50@gmail.com	PROPN
ejpam-3496	23	27	(	(	PUNCT
ejpam-3496	23	28	m.	m.	PROPN
ejpam-3496	23	29	s.	s.	PROPN
ejpam-3496	23	30	khan	khan	PROPN
ejpam-3496	23	31	)	)	PUNCT
ejpam-3496	23	32	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3496	23	33	1138	1138	NUM
ejpam-3496	24	1	c	c	X
ejpam-3496	24	2	©	©	PROPN
ejpam-3496	24	3	2019	2019	NUM
ejpam-3496	24	4	ejpam	ejpam	NOUN
ejpam-3496	24	5	all	all	DET
ejpam-3496	24	6	rights	right	NOUN
ejpam-3496	24	7	reserved	reserve	VERB
ejpam-3496	24	8	.	.	PUNCT
ejpam-3496	25	1	s.	s.	PROPN
ejpam-3496	25	2	ali	ali	PROPN
ejpam-3496	25	3	et	et	PROPN
ejpam-3496	25	4	al	al	PROPN
ejpam-3496	25	5	.	.	PUNCT
ejpam-3496	25	6	/	/	SYM
ejpam-3496	25	7	eur	eur	PROPN
ejpam-3496	25	8	.	.	PUNCT
ejpam-3496	26	1	j.	j.	PROPN
ejpam-3496	26	2	pure	pure	PROPN
ejpam-3496	26	3	appl	appl	PROPN
ejpam-3496	26	4	.	.	PROPN
ejpam-3496	26	5	math	math	PROPN
ejpam-3496	26	6	,	,	PUNCT
ejpam-3496	26	7	12	12	NUM
ejpam-3496	26	8	(	(	PUNCT
ejpam-3496	26	9	3	3	NUM
ejpam-3496	26	10	)	)	PUNCT
ejpam-3496	26	11	(	(	PUNCT
ejpam-3496	26	12	2019	2019	NUM
ejpam-3496	26	13	)	)	PUNCT
ejpam-3496	26	14	,	,	PUNCT
ejpam-3496	26	15	1138	1138	NUM
ejpam-3496	26	16	-	-	SYM
ejpam-3496	26	17	1148	1148	NUM
ejpam-3496	26	18	1139	1139	NUM
ejpam-3496	26	19	s(r)∩z(r	s(r)∩z(r	PUNCT
ejpam-3496	26	20	)	)	PUNCT
ejpam-3496	26	21	6=	6=	PUNCT
ejpam-3496	26	22	(	(	PUNCT
ejpam-3496	26	23	0	0	NUM
ejpam-3496	26	24	)	)	PUNCT
ejpam-3496	26	25	.	.	PUNCT
ejpam-3496	27	1	if	if	SCONJ
ejpam-3496	27	2	r	r	NOUN
ejpam-3496	27	3	is	be	AUX
ejpam-3496	27	4	2	2	NUM
ejpam-3496	27	5	-	-	PUNCT
ejpam-3496	27	6	torsion	torsion	NOUN
ejpam-3496	27	7	free	free	ADJ
ejpam-3496	27	8	then	then	ADV
ejpam-3496	27	9	every	every	DET
ejpam-3496	27	10	x	x	SYM
ejpam-3496	27	11	∈	∈	NOUN
ejpam-3496	27	12	r	r	NOUN
ejpam-3496	27	13	can	can	AUX
ejpam-3496	27	14	be	be	AUX
ejpam-3496	27	15	uniquely	uniquely	ADV
ejpam-3496	27	16	represented	represent	VERB
ejpam-3496	27	17	in	in	ADP
ejpam-3496	27	18	the	the	DET
ejpam-3496	27	19	form	form	NOUN
ejpam-3496	27	20	2x	2x	NUM
ejpam-3496	28	1	=	=	SYM
ejpam-3496	28	2	h	h	NOUN
ejpam-3496	29	1	+	+	CCONJ
ejpam-3496	30	1	k	k	ADJ
ejpam-3496	30	2	,	,	PUNCT
ejpam-3496	30	3	where	where	SCONJ
ejpam-3496	30	4	h	h	PROPN
ejpam-3496	30	5	∈	∈	PROPN
ejpam-3496	30	6	h(r	h(r	NOUN
ejpam-3496	30	7	)	)	PUNCT
ejpam-3496	30	8	and	and	CCONJ
ejpam-3496	30	9	k	k	PROPN
ejpam-3496	30	10	∈	∈	PROPN
ejpam-3496	30	11	s(r	s(r	PROPN
ejpam-3496	30	12	)	)	PUNCT
ejpam-3496	30	13	.	.	PUNCT
ejpam-3496	31	1	note	note	VERB
ejpam-3496	31	2	that	that	SCONJ
ejpam-3496	31	3	in	in	ADP
ejpam-3496	31	4	this	this	DET
ejpam-3496	31	5	case	case	NOUN
ejpam-3496	31	6	x	x	NOUN
ejpam-3496	31	7	is	be	AUX
ejpam-3496	31	8	normal	normal	ADJ
ejpam-3496	31	9	i.e.	i.e.	X
ejpam-3496	31	10	,	,	PUNCT
ejpam-3496	31	11	xx∗	xx∗	NOUN
ejpam-3496	31	12	=	=	PUNCT
ejpam-3496	31	13	x∗x	x∗x	ADJ
ejpam-3496	31	14	,	,	PUNCT
ejpam-3496	31	15	if	if	SCONJ
ejpam-3496	31	16	and	and	CCONJ
ejpam-3496	31	17	only	only	ADV
ejpam-3496	31	18	if	if	SCONJ
ejpam-3496	31	19	h	h	PROPN
ejpam-3496	31	20	and	and	CCONJ
ejpam-3496	31	21	k	k	PROPN
ejpam-3496	31	22	commute	commute	NOUN
ejpam-3496	31	23	.	.	PUNCT
ejpam-3496	32	1	if	if	SCONJ
ejpam-3496	32	2	all	all	DET
ejpam-3496	32	3	elements	element	NOUN
ejpam-3496	32	4	in	in	ADP
ejpam-3496	32	5	r	r	NOUN
ejpam-3496	32	6	are	be	AUX
ejpam-3496	32	7	normal	normal	ADJ
ejpam-3496	32	8	,	,	PUNCT
ejpam-3496	32	9	then	then	ADV
ejpam-3496	32	10	r	r	NOUN
ejpam-3496	32	11	is	be	AUX
ejpam-3496	32	12	called	call	VERB
ejpam-3496	32	13	a	a	DET
ejpam-3496	32	14	normal	normal	ADJ
ejpam-3496	32	15	ring	ring	NOUN
ejpam-3496	32	16	.	.	PUNCT
ejpam-3496	33	1	an	an	DET
ejpam-3496	33	2	example	example	NOUN
ejpam-3496	33	3	is	be	AUX
ejpam-3496	33	4	the	the	DET
ejpam-3496	33	5	ring	ring	NOUN
ejpam-3496	33	6	of	of	ADP
ejpam-3496	33	7	quaternions	quaternion	NOUN
ejpam-3496	33	8	.	.	PUNCT
ejpam-3496	34	1	a	a	DET
ejpam-3496	34	2	description	description	NOUN
ejpam-3496	34	3	of	of	ADP
ejpam-3496	34	4	such	such	ADJ
ejpam-3496	34	5	rings	ring	NOUN
ejpam-3496	34	6	can	can	AUX
ejpam-3496	34	7	be	be	AUX
ejpam-3496	34	8	found	find	VERB
ejpam-3496	34	9	in	in	ADP
ejpam-3496	34	10	[	[	X
ejpam-3496	34	11	14	14	NUM
ejpam-3496	34	12	]	]	PUNCT
ejpam-3496	34	13	,	,	PUNCT
ejpam-3496	34	14	where	where	SCONJ
ejpam-3496	34	15	further	further	ADJ
ejpam-3496	34	16	references	reference	NOUN
ejpam-3496	34	17	can	can	AUX
ejpam-3496	34	18	be	be	AUX
ejpam-3496	34	19	found	find	VERB
ejpam-3496	34	20	.	.	PUNCT
ejpam-3496	35	1	a	a	DET
ejpam-3496	35	2	derivation	derivation	NOUN
ejpam-3496	35	3	on	on	ADP
ejpam-3496	35	4	r	r	NOUN
ejpam-3496	35	5	is	be	AUX
ejpam-3496	35	6	an	an	DET
ejpam-3496	35	7	additive	additive	ADJ
ejpam-3496	35	8	mapping	mapping	NOUN
ejpam-3496	36	1	d	d	NOUN
ejpam-3496	36	2	:	:	PUNCT
ejpam-3496	36	3	r→	r→	PRON
ejpam-3496	36	4	r	r	NOUN
ejpam-3496	36	5	such	such	ADJ
ejpam-3496	36	6	that	that	DET
ejpam-3496	36	7	d(xy	d(xy	NOUN
ejpam-3496	36	8	)	)	PUNCT
ejpam-3496	36	9	=	=	SYM
ejpam-3496	36	10	d(x)y+xd(y	d(x)y+xd(y	PROPN
ejpam-3496	36	11	)	)	PUNCT
ejpam-3496	36	12	for	for	ADP
ejpam-3496	36	13	all	all	DET
ejpam-3496	36	14	x	x	NOUN
ejpam-3496	36	15	,	,	PUNCT
ejpam-3496	36	16	y	y	PROPN
ejpam-3496	36	17	∈	∈	PROPN
ejpam-3496	36	18	r.	r.	NOUN
ejpam-3496	36	19	a	a	DET
ejpam-3496	36	20	derivation	derivation	NOUN
ejpam-3496	36	21	d	d	NOUN
ejpam-3496	36	22	is	be	AUX
ejpam-3496	36	23	said	say	VERB
ejpam-3496	36	24	to	to	PART
ejpam-3496	36	25	be	be	AUX
ejpam-3496	36	26	inner	inner	ADJ
ejpam-3496	36	27	if	if	SCONJ
ejpam-3496	36	28	there	there	PRON
ejpam-3496	36	29	exists	exist	VERB
ejpam-3496	36	30	a	a	DET
ejpam-3496	36	31	∈	∈	NOUN
ejpam-3496	36	32	r	r	NOUN
ejpam-3496	36	33	such	such	ADJ
ejpam-3496	36	34	that	that	DET
ejpam-3496	36	35	d(x	d(x	NOUN
ejpam-3496	36	36	)	)	PUNCT
ejpam-3496	37	1	=	=	PUNCT
ejpam-3496	37	2	ax−xa	ax−xa	PROPN
ejpam-3496	37	3	for	for	ADP
ejpam-3496	37	4	all	all	DET
ejpam-3496	37	5	x	x	PROPN
ejpam-3496	37	6	∈	∈	PROPN
ejpam-3496	37	7	r.	r.	PROPN
ejpam-3496	37	8	over	over	ADP
ejpam-3496	37	9	the	the	DET
ejpam-3496	37	10	last	last	ADJ
ejpam-3496	37	11	30	30	NUM
ejpam-3496	37	12	years	year	NOUN
ejpam-3496	37	13	,	,	PUNCT
ejpam-3496	37	14	several	several	ADJ
ejpam-3496	37	15	authors	author	NOUN
ejpam-3496	37	16	have	have	AUX
ejpam-3496	37	17	investigated	investigate	VERB
ejpam-3496	37	18	the	the	DET
ejpam-3496	37	19	relationship	relationship	NOUN
ejpam-3496	37	20	between	between	ADP
ejpam-3496	37	21	commutativity	commutativity	NOUN
ejpam-3496	37	22	of	of	ADP
ejpam-3496	37	23	the	the	DET
ejpam-3496	37	24	ring	ring	NOUN
ejpam-3496	37	25	r	r	NOUN
ejpam-3496	37	26	and	and	CCONJ
ejpam-3496	37	27	certain	certain	ADJ
ejpam-3496	37	28	special	special	ADJ
ejpam-3496	37	29	types	type	NOUN
ejpam-3496	37	30	of	of	ADP
ejpam-3496	37	31	maps	map	NOUN
ejpam-3496	37	32	on	on	ADP
ejpam-3496	37	33	r.	r.	PROPN
ejpam-3496	37	34	the	the	DET
ejpam-3496	37	35	first	first	ADJ
ejpam-3496	37	36	result	result	NOUN
ejpam-3496	37	37	in	in	ADP
ejpam-3496	37	38	this	this	DET
ejpam-3496	37	39	direction	direction	NOUN
ejpam-3496	37	40	is	be	AUX
ejpam-3496	37	41	due	due	ADJ
ejpam-3496	37	42	to	to	ADP
ejpam-3496	37	43	divinsky	divinsky	NOUN
ejpam-3496	37	44	[	[	X
ejpam-3496	37	45	12	12	NUM
ejpam-3496	37	46	]	]	PUNCT
ejpam-3496	37	47	,	,	PUNCT
ejpam-3496	37	48	who	who	PRON
ejpam-3496	37	49	proved	prove	VERB
ejpam-3496	37	50	that	that	SCONJ
ejpam-3496	37	51	a	a	DET
ejpam-3496	37	52	simple	simple	ADJ
ejpam-3496	37	53	artinian	artinian	ADJ
ejpam-3496	37	54	ring	ring	NOUN
ejpam-3496	37	55	is	be	AUX
ejpam-3496	37	56	commutative	commutative	ADJ
ejpam-3496	37	57	if	if	SCONJ
ejpam-3496	37	58	it	it	PRON
ejpam-3496	37	59	has	have	VERB
ejpam-3496	37	60	a	a	DET
ejpam-3496	37	61	commuting	commuting	ADJ
ejpam-3496	37	62	non	non	ADJ
ejpam-3496	37	63	-	-	ADJ
ejpam-3496	37	64	trivial	trivial	ADJ
ejpam-3496	37	65	automorphism	automorphism	NOUN
ejpam-3496	37	66	.	.	PUNCT
ejpam-3496	38	1	two	two	NUM
ejpam-3496	38	2	years	year	NOUN
ejpam-3496	38	3	later	later	ADV
ejpam-3496	38	4	,	,	PUNCT
ejpam-3496	38	5	posner	posner	NOUN
ejpam-3496	38	6	[	[	X
ejpam-3496	38	7	18	18	NUM
ejpam-3496	38	8	]	]	PUNCT
ejpam-3496	38	9	proved	prove	VERB
ejpam-3496	38	10	that	that	SCONJ
ejpam-3496	38	11	the	the	DET
ejpam-3496	38	12	existence	existence	NOUN
ejpam-3496	38	13	of	of	ADP
ejpam-3496	38	14	a	a	DET
ejpam-3496	38	15	nonzero	nonzero	NOUN
ejpam-3496	38	16	centralizing	centralize	VERB
ejpam-3496	38	17	derivation	derivation	NOUN
ejpam-3496	38	18	on	on	ADP
ejpam-3496	38	19	a	a	DET
ejpam-3496	38	20	prime	prime	ADJ
ejpam-3496	38	21	ring	ring	NOUN
ejpam-3496	38	22	forces	force	VERB
ejpam-3496	38	23	the	the	DET
ejpam-3496	38	24	ring	ring	NOUN
ejpam-3496	38	25	to	to	PART
ejpam-3496	38	26	be	be	AUX
ejpam-3496	38	27	commutative	commutative	ADJ
ejpam-3496	38	28	.	.	PUNCT
ejpam-3496	39	1	over	over	ADP
ejpam-3496	39	2	the	the	DET
ejpam-3496	39	3	last	last	ADJ
ejpam-3496	39	4	few	few	ADJ
ejpam-3496	39	5	decades	decade	NOUN
ejpam-3496	39	6	,	,	PUNCT
ejpam-3496	39	7	many	many	ADJ
ejpam-3496	39	8	authors	author	NOUN
ejpam-3496	39	9	have	have	AUX
ejpam-3496	39	10	refined	refine	VERB
ejpam-3496	39	11	and	and	CCONJ
ejpam-3496	39	12	extended	extend	VERB
ejpam-3496	39	13	these	these	DET
ejpam-3496	39	14	results	result	NOUN
ejpam-3496	39	15	in	in	ADP
ejpam-3496	39	16	various	various	ADJ
ejpam-3496	39	17	directions	direction	NOUN
ejpam-3496	39	18	(	(	PUNCT
ejpam-3496	39	19	see	see	VERB
ejpam-3496	39	20	for	for	ADP
ejpam-3496	39	21	example	example	NOUN
ejpam-3496	39	22	[	[	X
ejpam-3496	39	23	3	3	NUM
ejpam-3496	39	24	,	,	PUNCT
ejpam-3496	39	25	5–7	5–7	NUM
ejpam-3496	39	26	,	,	PUNCT
ejpam-3496	39	27	9	9	NUM
ejpam-3496	39	28	]	]	PUNCT
ejpam-3496	39	29	where	where	SCONJ
ejpam-3496	39	30	further	further	ADJ
ejpam-3496	39	31	references	reference	NOUN
ejpam-3496	39	32	can	can	AUX
ejpam-3496	39	33	be	be	AUX
ejpam-3496	39	34	looked	look	VERB
ejpam-3496	39	35	)	)	PUNCT
ejpam-3496	39	36	.	.	PUNCT
ejpam-3496	40	1	in	in	ADP
ejpam-3496	40	2	[	[	X
ejpam-3496	40	3	13	13	NUM
ejpam-3496	40	4	]	]	PUNCT
ejpam-3496	40	5	,	,	PUNCT
ejpam-3496	40	6	herstein	herstein	PROPN
ejpam-3496	40	7	proved	prove	VERB
ejpam-3496	40	8	that	that	SCONJ
ejpam-3496	40	9	if	if	SCONJ
ejpam-3496	40	10	r	r	NOUN
ejpam-3496	40	11	is	be	AUX
ejpam-3496	40	12	a	a	DET
ejpam-3496	40	13	prime	prime	ADJ
ejpam-3496	40	14	ring	ring	NOUN
ejpam-3496	40	15	of	of	ADP
ejpam-3496	40	16	characteristic	characteristic	ADJ
ejpam-3496	40	17	not	not	PART
ejpam-3496	40	18	two	two	NUM
ejpam-3496	40	19	admitting	admit	VERB
ejpam-3496	40	20	a	a	DET
ejpam-3496	40	21	nonzero	nonzero	NOUN
ejpam-3496	40	22	derivation	derivation	NOUN
ejpam-3496	40	23	d	d	ADP
ejpam-3496	40	24	such	such	ADJ
ejpam-3496	40	25	that	that	SCONJ
ejpam-3496	41	1	[	[	X
ejpam-3496	41	2	d(x	d(x	NOUN
ejpam-3496	41	3	)	)	PUNCT
ejpam-3496	41	4	,	,	PUNCT
ejpam-3496	41	5	d(y	d(y	NOUN
ejpam-3496	41	6	)	)	PUNCT
ejpam-3496	41	7	]	]	PUNCT
ejpam-3496	42	1	=	=	PUNCT
ejpam-3496	42	2	0	0	NUM
ejpam-3496	42	3	for	for	ADP
ejpam-3496	42	4	all	all	DET
ejpam-3496	42	5	x	x	NOUN
ejpam-3496	42	6	,	,	PUNCT
ejpam-3496	42	7	y	y	PROPN
ejpam-3496	42	8	∈	∈	PROPN
ejpam-3496	42	9	r	r	NOUN
ejpam-3496	42	10	,	,	PUNCT
ejpam-3496	42	11	then	then	ADV
ejpam-3496	42	12	r	r	NOUN
ejpam-3496	42	13	is	be	AUX
ejpam-3496	42	14	commutative	commutative	ADJ
ejpam-3496	42	15	.	.	PUNCT
ejpam-3496	43	1	further	far	ADV
ejpam-3496	43	2	,	,	PUNCT
ejpam-3496	43	3	daif	daif	VERB
ejpam-3496	43	4	[	[	X
ejpam-3496	43	5	10	10	NUM
ejpam-3496	43	6	]	]	PUNCT
ejpam-3496	43	7	showed	show	VERB
ejpam-3496	43	8	that	that	SCONJ
ejpam-3496	43	9	a	a	DET
ejpam-3496	43	10	2	2	NUM
ejpam-3496	43	11	-	-	PUNCT
ejpam-3496	43	12	torsion	torsion	NOUN
ejpam-3496	43	13	free	free	ADJ
ejpam-3496	43	14	semiprime	semiprime	NOUN
ejpam-3496	43	15	ring	ring	NOUN
ejpam-3496	43	16	r	r	NOUN
ejpam-3496	43	17	admits	admit	VERB
ejpam-3496	43	18	a	a	DET
ejpam-3496	43	19	nonzero	nonzero	ADJ
ejpam-3496	43	20	derivation	derivation	NOUN
ejpam-3496	43	21	d	d	ADP
ejpam-3496	43	22	such	such	ADJ
ejpam-3496	43	23	that	that	SCONJ
ejpam-3496	43	24	[	[	X
ejpam-3496	43	25	d(x	d(x	NOUN
ejpam-3496	43	26	)	)	PUNCT
ejpam-3496	43	27	,	,	PUNCT
ejpam-3496	43	28	d(y	d(y	NOUN
ejpam-3496	43	29	)	)	PUNCT
ejpam-3496	43	30	]	]	PUNCT
ejpam-3496	44	1	=	=	PUNCT
ejpam-3496	44	2	0	0	NUM
ejpam-3496	44	3	for	for	ADP
ejpam-3496	44	4	all	all	DET
ejpam-3496	44	5	x	x	NOUN
ejpam-3496	44	6	,	,	PUNCT
ejpam-3496	44	7	y	y	PROPN
ejpam-3496	44	8	∈	∈	PROPN
ejpam-3496	45	1	i	i	PRON
ejpam-3496	45	2	,	,	PUNCT
ejpam-3496	45	3	where	where	SCONJ
ejpam-3496	45	4	i	i	PRON
ejpam-3496	45	5	is	be	AUX
ejpam-3496	45	6	a	a	DET
ejpam-3496	45	7	nonzero	nonzero	ADJ
ejpam-3496	45	8	ideal	ideal	NOUN
ejpam-3496	45	9	of	of	ADP
ejpam-3496	45	10	r	r	NOUN
ejpam-3496	45	11	,	,	PUNCT
ejpam-3496	45	12	then	then	ADV
ejpam-3496	45	13	r	r	NOUN
ejpam-3496	45	14	contains	contain	VERB
ejpam-3496	45	15	a	a	DET
ejpam-3496	45	16	nonzero	nonzero	ADJ
ejpam-3496	45	17	central	central	ADJ
ejpam-3496	45	18	ideal	ideal	NOUN
ejpam-3496	45	19	.	.	PUNCT
ejpam-3496	46	1	in	in	ADP
ejpam-3496	46	2	[	[	X
ejpam-3496	46	3	15	15	NUM
ejpam-3496	46	4	]	]	PUNCT
ejpam-3496	46	5	,	,	PUNCT
ejpam-3496	46	6	lanski	lanski	NOUN
ejpam-3496	46	7	prove	prove	VERB
ejpam-3496	46	8	that	that	SCONJ
ejpam-3496	46	9	if	if	SCONJ
ejpam-3496	46	10	l	l	NOUN
ejpam-3496	46	11	is	be	AUX
ejpam-3496	46	12	a	a	DET
ejpam-3496	46	13	noncommutative	noncommutative	ADJ
ejpam-3496	46	14	lie	lie	NOUN
ejpam-3496	46	15	ideal	ideal	NOUN
ejpam-3496	46	16	of	of	ADP
ejpam-3496	46	17	a	a	DET
ejpam-3496	46	18	2	2	NUM
ejpam-3496	46	19	-	-	PUNCT
ejpam-3496	46	20	torsion	torsion	NOUN
ejpam-3496	46	21	free	free	ADJ
ejpam-3496	46	22	prime	prime	NOUN
ejpam-3496	46	23	ring	ring	NOUN
ejpam-3496	46	24	r	r	NOUN
ejpam-3496	46	25	and	and	CCONJ
ejpam-3496	46	26	d	d	NOUN
ejpam-3496	46	27	,	,	PUNCT
ejpam-3496	46	28	h	h	PROPN
ejpam-3496	46	29	are	be	AUX
ejpam-3496	46	30	nonzero	nonzero	NOUN
ejpam-3496	46	31	derivations	derivation	NOUN
ejpam-3496	46	32	of	of	ADP
ejpam-3496	46	33	r	r	NOUN
ejpam-3496	46	34	such	such	ADJ
ejpam-3496	46	35	that	that	SCONJ
ejpam-3496	47	1	[	[	X
ejpam-3496	47	2	d(x	d(x	NOUN
ejpam-3496	47	3	)	)	PUNCT
ejpam-3496	47	4	,	,	PUNCT
ejpam-3496	47	5	h(x	h(x	PROPN
ejpam-3496	47	6	)	)	PUNCT
ejpam-3496	47	7	]	]	PUNCT
ejpam-3496	48	1	∈	∈	PROPN
ejpam-3496	48	2	c	c	NOUN
ejpam-3496	48	3	for	for	ADP
ejpam-3496	48	4	all	all	DET
ejpam-3496	48	5	x	x	SYM
ejpam-3496	48	6	∈	∈	PROPN
ejpam-3496	48	7	l	l	NOUN
ejpam-3496	48	8	,	,	PUNCT
ejpam-3496	48	9	then	then	ADV
ejpam-3496	48	10	h	h	NOUN
ejpam-3496	48	11	=	=	SYM
ejpam-3496	48	12	λd	λd	NOUN
ejpam-3496	48	13	,	,	PUNCT
ejpam-3496	48	14	where	where	SCONJ
ejpam-3496	48	15	λ	λ	PROPN
ejpam-3496	48	16	∈	∈	PROPN
ejpam-3496	48	17	c.	c.	PROPN
ejpam-3496	48	18	very	very	ADV
ejpam-3496	48	19	recently	recently	ADV
ejpam-3496	48	20	,	,	PUNCT
ejpam-3496	48	21	the	the	DET
ejpam-3496	48	22	first	first	ADJ
ejpam-3496	48	23	author	author	NOUN
ejpam-3496	48	24	together	together	ADV
ejpam-3496	48	25	with	with	ADP
ejpam-3496	48	26	dar	dar	PROPN
ejpam-3496	49	1	[	[	X
ejpam-3496	49	2	11	11	NUM
ejpam-3496	49	3	]	]	PUNCT
ejpam-3496	49	4	proved	prove	VERB
ejpam-3496	49	5	the	the	DET
ejpam-3496	49	6	following	follow	VERB
ejpam-3496	49	7	result	result	NOUN
ejpam-3496	49	8	:	:	PUNCT
ejpam-3496	49	9	let	let	VERB
ejpam-3496	49	10	r	r	PRON
ejpam-3496	49	11	be	be	AUX
ejpam-3496	49	12	a	a	DET
ejpam-3496	49	13	prime	prime	ADJ
ejpam-3496	49	14	ring	ring	NOUN
ejpam-3496	49	15	with	with	ADP
ejpam-3496	49	16	involution	involution	NOUN
ejpam-3496	49	17	∗	∗	NOUN
ejpam-3496	49	18	of	of	ADP
ejpam-3496	49	19	the	the	DET
ejpam-3496	49	20	second	second	ADJ
ejpam-3496	49	21	kind	kind	NOUN
ejpam-3496	49	22	such	such	ADJ
ejpam-3496	49	23	that	that	DET
ejpam-3496	49	24	char(r	char(r	NOUN
ejpam-3496	49	25	)	)	PUNCT
ejpam-3496	49	26	6=	6=	ADP
ejpam-3496	50	1	2	2	X
ejpam-3496	50	2	.	.	PUNCT
ejpam-3496	51	1	if	if	SCONJ
ejpam-3496	51	2	r	r	NOUN
ejpam-3496	51	3	admits	admit	VERB
ejpam-3496	51	4	a	a	DET
ejpam-3496	51	5	nonzero	nonzero	ADJ
ejpam-3496	51	6	derivation	derivation	NOUN
ejpam-3496	51	7	d	d	ADP
ejpam-3496	51	8	such	such	ADJ
ejpam-3496	51	9	that	that	SCONJ
ejpam-3496	51	10	[	[	X
ejpam-3496	51	11	d(x	d(x	NOUN
ejpam-3496	51	12	)	)	PUNCT
ejpam-3496	51	13	,	,	PUNCT
ejpam-3496	51	14	d(x∗	d(x∗	NOUN
ejpam-3496	51	15	)	)	PUNCT
ejpam-3496	51	16	]	]	PUNCT
ejpam-3496	52	1	=	=	PUNCT
ejpam-3496	52	2	0	0	PUNCT
ejpam-3496	52	3	for	for	ADP
ejpam-3496	52	4	all	all	DET
ejpam-3496	52	5	x	x	SYM
ejpam-3496	52	6	∈	∈	PROPN
ejpam-3496	52	7	r	r	NOUN
ejpam-3496	52	8	,	,	PUNCT
ejpam-3496	52	9	then	then	ADV
ejpam-3496	52	10	r	r	NOUN
ejpam-3496	52	11	is	be	AUX
ejpam-3496	52	12	commutative	commutative	ADJ
ejpam-3496	52	13	.	.	PUNCT
ejpam-3496	53	1	in	in	ADP
ejpam-3496	53	2	the	the	DET
ejpam-3496	53	3	last	last	ADJ
ejpam-3496	53	4	three	three	NUM
ejpam-3496	53	5	decades	decade	NOUN
ejpam-3496	53	6	many	many	ADJ
ejpam-3496	53	7	authors	author	NOUN
ejpam-3496	53	8	have	have	AUX
ejpam-3496	53	9	generalized	generalize	VERB
ejpam-3496	53	10	the	the	DET
ejpam-3496	53	11	above	above	ADJ
ejpam-3496	53	12	mention	mention	NOUN
ejpam-3496	53	13	result	result	NOUN
ejpam-3496	53	14	in	in	ADP
ejpam-3496	53	15	several	several	ADJ
ejpam-3496	53	16	ways	way	NOUN
ejpam-3496	53	17	(	(	PUNCT
ejpam-3496	53	18	viz	viz	PROPN
ejpam-3496	53	19	.	.	PUNCT
ejpam-3496	53	20	;	;	PUNCT
ejpam-3496	54	1	[	[	X
ejpam-3496	54	2	1	1	NUM
ejpam-3496	54	3	,	,	PUNCT
ejpam-3496	54	4	2	2	NUM
ejpam-3496	54	5	,	,	PUNCT
ejpam-3496	54	6	8	8	NUM
ejpam-3496	54	7	,	,	PUNCT
ejpam-3496	54	8	11	11	NUM
ejpam-3496	54	9	,	,	PUNCT
ejpam-3496	54	10	15	15	NUM
ejpam-3496	54	11	,	,	PUNCT
ejpam-3496	54	12	17	17	NUM
ejpam-3496	54	13	,	,	PUNCT
ejpam-3496	54	14	19	19	NUM
ejpam-3496	54	15	]	]	PUNCT
ejpam-3496	54	16	where	where	SCONJ
ejpam-3496	54	17	further	further	ADJ
ejpam-3496	54	18	references	reference	NOUN
ejpam-3496	54	19	can	can	AUX
ejpam-3496	54	20	be	be	AUX
ejpam-3496	54	21	found	find	VERB
ejpam-3496	54	22	)	)	PUNCT
ejpam-3496	54	23	.	.	PUNCT
ejpam-3496	55	1	motivated	motivate	VERB
ejpam-3496	55	2	by	by	ADP
ejpam-3496	55	3	the	the	DET
ejpam-3496	55	4	above	above	ADJ
ejpam-3496	55	5	results	result	NOUN
ejpam-3496	55	6	,	,	PUNCT
ejpam-3496	55	7	here	here	ADV
ejpam-3496	55	8	we	we	PRON
ejpam-3496	55	9	continue	continue	VERB
ejpam-3496	55	10	this	this	DET
ejpam-3496	55	11	line	line	NOUN
ejpam-3496	55	12	of	of	ADP
ejpam-3496	55	13	investigation	investigation	NOUN
ejpam-3496	55	14	by	by	ADP
ejpam-3496	55	15	considering	consider	VERB
ejpam-3496	55	16	more	more	ADJ
ejpam-3496	55	17	general	general	ADJ
ejpam-3496	55	18	situations	situation	NOUN
ejpam-3496	55	19	.	.	PUNCT
ejpam-3496	56	1	besides	besides	SCONJ
ejpam-3496	56	2	proving	prove	VERB
ejpam-3496	56	3	some	some	DET
ejpam-3496	56	4	other	other	ADJ
ejpam-3496	56	5	results	result	NOUN
ejpam-3496	56	6	,	,	PUNCT
ejpam-3496	56	7	the	the	DET
ejpam-3496	56	8	main	main	ADJ
ejpam-3496	56	9	result	result	NOUN
ejpam-3496	56	10	is	be	AUX
ejpam-3496	56	11	the	the	DET
ejpam-3496	56	12	following	follow	VERB
ejpam-3496	56	13	theorem	theorem	ADJ
ejpam-3496	56	14	.	.	PUNCT
ejpam-3496	56	15	main	main	ADJ
ejpam-3496	56	16	theorem	theorem	NOUN
ejpam-3496	56	17	.	.	PUNCT
ejpam-3496	57	1	let	let	VERB
ejpam-3496	57	2	r	r	PRON
ejpam-3496	57	3	be	be	AUX
ejpam-3496	57	4	a	a	DET
ejpam-3496	57	5	2	2	NUM
ejpam-3496	57	6	-	-	PUNCT
ejpam-3496	57	7	torsion	torsion	NOUN
ejpam-3496	57	8	free	free	ADJ
ejpam-3496	57	9	noncommutative	noncommutative	ADJ
ejpam-3496	57	10	prime	prime	ADJ
ejpam-3496	57	11	ring	ring	NOUN
ejpam-3496	57	12	with	with	ADP
ejpam-3496	57	13	involution	involution	NOUN
ejpam-3496	57	14	∗	∗	NOUN
ejpam-3496	57	15	of	of	ADP
ejpam-3496	57	16	the	the	DET
ejpam-3496	57	17	second	second	ADJ
ejpam-3496	57	18	kind	kind	NOUN
ejpam-3496	57	19	and	and	CCONJ
ejpam-3496	57	20	d1	d1	PROPN
ejpam-3496	57	21	,	,	PUNCT
ejpam-3496	57	22	d2	d2	PROPN
ejpam-3496	57	23	be	be	AUX
ejpam-3496	57	24	two	two	NUM
ejpam-3496	57	25	nonzero	nonzero	ADJ
ejpam-3496	57	26	derivations	derivation	NOUN
ejpam-3496	57	27	on	on	ADP
ejpam-3496	57	28	r	r	NOUN
ejpam-3496	58	1	such	such	ADJ
ejpam-3496	58	2	that	that	SCONJ
ejpam-3496	58	3	[	[	X
ejpam-3496	58	4	d1(x	d1(x	NOUN
ejpam-3496	58	5	)	)	PUNCT
ejpam-3496	58	6	,	,	PUNCT
ejpam-3496	58	7	d2(x	d2(x	NOUN
ejpam-3496	58	8	∗	∗	NOUN
ejpam-3496	58	9	)	)	PUNCT
ejpam-3496	58	10	]	]	PUNCT
ejpam-3496	59	1	=	=	PUNCT
ejpam-3496	59	2	0	0	PUNCT
ejpam-3496	59	3	for	for	ADP
ejpam-3496	59	4	all	all	DET
ejpam-3496	59	5	x	x	SYM
ejpam-3496	59	6	∈	∈	PROPN
ejpam-3496	59	7	r.	r.	NOUN
ejpam-3496	59	8	then	then	ADV
ejpam-3496	59	9	d1	d1	PROPN
ejpam-3496	59	10	=	=	SYM
ejpam-3496	59	11	λd2	λd2	PROPN
ejpam-3496	59	12	,	,	PUNCT
ejpam-3496	59	13	where	where	SCONJ
ejpam-3496	59	14	λ	λ	PROPN
ejpam-3496	59	15	∈	∈	PROPN
ejpam-3496	59	16	c.	c.	PROPN
ejpam-3496	59	17	2	2	NUM
ejpam-3496	59	18	.	.	PUNCT
ejpam-3496	59	19	main	main	ADJ
ejpam-3496	59	20	results	result	NOUN
ejpam-3496	59	21	in	in	ADP
ejpam-3496	59	22	order	order	NOUN
ejpam-3496	59	23	to	to	PART
ejpam-3496	59	24	prove	prove	VERB
ejpam-3496	59	25	our	our	PRON
ejpam-3496	59	26	results	result	NOUN
ejpam-3496	59	27	,	,	PUNCT
ejpam-3496	59	28	we	we	PRON
ejpam-3496	59	29	need	need	VERB
ejpam-3496	59	30	the	the	DET
ejpam-3496	59	31	following	follow	VERB
ejpam-3496	59	32	lemma	lemma	PROPN
ejpam-3496	59	33	.	.	PUNCT
ejpam-3496	60	1	s.	s.	PROPN
ejpam-3496	60	2	ali	ali	PROPN
ejpam-3496	60	3	et	et	PROPN
ejpam-3496	60	4	al	al	PROPN
ejpam-3496	60	5	.	.	PUNCT
ejpam-3496	60	6	/	/	SYM
ejpam-3496	60	7	eur	eur	PROPN
ejpam-3496	60	8	.	.	PUNCT
ejpam-3496	61	1	j.	j.	PROPN
ejpam-3496	61	2	pure	pure	PROPN
ejpam-3496	61	3	appl	appl	PROPN
ejpam-3496	61	4	.	.	PROPN
ejpam-3496	61	5	math	math	PROPN
ejpam-3496	61	6	,	,	PUNCT
ejpam-3496	61	7	12	12	NUM
ejpam-3496	61	8	(	(	PUNCT
ejpam-3496	61	9	3	3	NUM
ejpam-3496	61	10	)	)	PUNCT
ejpam-3496	61	11	(	(	PUNCT
ejpam-3496	61	12	2019	2019	NUM
ejpam-3496	61	13	)	)	PUNCT
ejpam-3496	61	14	,	,	PUNCT
ejpam-3496	61	15	1138	1138	NUM
ejpam-3496	61	16	-	-	SYM
ejpam-3496	61	17	1148	1148	NUM
ejpam-3496	61	18	1140	1140	NUM
ejpam-3496	61	19	lemma	lemma	PROPN
ejpam-3496	61	20	1	1	NUM
ejpam-3496	61	21	.	.	PUNCT
ejpam-3496	62	1	let	let	VERB
ejpam-3496	62	2	r	r	PRON
ejpam-3496	62	3	be	be	AUX
ejpam-3496	62	4	a	a	DET
ejpam-3496	62	5	2	2	NUM
ejpam-3496	62	6	-	-	PUNCT
ejpam-3496	62	7	torsion	torsion	NOUN
ejpam-3496	62	8	free	free	ADJ
ejpam-3496	62	9	noncommutative	noncommutative	ADJ
ejpam-3496	62	10	prime	prime	ADJ
ejpam-3496	62	11	ring	ring	NOUN
ejpam-3496	62	12	with	with	ADP
ejpam-3496	62	13	involution	involution	NOUN
ejpam-3496	62	14	∗	∗	NOUN
ejpam-3496	62	15	of	of	ADP
ejpam-3496	62	16	the	the	DET
ejpam-3496	62	17	second	second	ADJ
ejpam-3496	62	18	kind	kind	NOUN
ejpam-3496	62	19	and	and	CCONJ
ejpam-3496	62	20	d1	d1	PROPN
ejpam-3496	62	21	,	,	PUNCT
ejpam-3496	62	22	d2	d2	PROPN
ejpam-3496	62	23	be	be	AUX
ejpam-3496	62	24	two	two	NUM
ejpam-3496	62	25	nonzero	nonzero	ADJ
ejpam-3496	62	26	derivations	derivation	NOUN
ejpam-3496	62	27	on	on	ADP
ejpam-3496	62	28	r.	r.	PROPN
ejpam-3496	62	29	if	if	SCONJ
ejpam-3496	62	30	one	one	NUM
ejpam-3496	62	31	of	of	ADP
ejpam-3496	62	32	the	the	DET
ejpam-3496	62	33	following	follow	VERB
ejpam-3496	62	34	conditions	condition	NOUN
ejpam-3496	62	35	holds	hold	VERB
ejpam-3496	62	36	:	:	PUNCT
ejpam-3496	62	37	(	(	PUNCT
ejpam-3496	62	38	i	i	NOUN
ejpam-3496	62	39	)	)	PUNCT
ejpam-3496	63	1	[	[	X
ejpam-3496	63	2	d1(x	d1(x	NOUN
ejpam-3496	63	3	)	)	PUNCT
ejpam-3496	63	4	,	,	PUNCT
ejpam-3496	63	5	d2(y	d2(y	PROPN
ejpam-3496	63	6	)	)	PUNCT
ejpam-3496	63	7	]	]	PUNCT
ejpam-3496	64	1	=	=	PUNCT
ejpam-3496	64	2	x	x	PUNCT
ejpam-3496	64	3	◦	◦	VERB
ejpam-3496	64	4	y	y	NOUN
ejpam-3496	64	5	for	for	ADP
ejpam-3496	64	6	all	all	DET
ejpam-3496	64	7	x	x	NOUN
ejpam-3496	64	8	,	,	PUNCT
ejpam-3496	64	9	y	y	PROPN
ejpam-3496	64	10	∈	∈	PROPN
ejpam-3496	64	11	r	r	PROPN
ejpam-3496	64	12	,	,	PUNCT
ejpam-3496	64	13	(	(	PUNCT
ejpam-3496	64	14	ii	ii	NOUN
ejpam-3496	64	15	)	)	PUNCT
ejpam-3496	65	1	[	[	X
ejpam-3496	65	2	d1(x	d1(x	NOUN
ejpam-3496	65	3	)	)	PUNCT
ejpam-3496	65	4	,	,	PUNCT
ejpam-3496	65	5	d2(y	d2(y	PROPN
ejpam-3496	65	6	)	)	PUNCT
ejpam-3496	65	7	]	]	PUNCT
ejpam-3496	66	1	=	=	PUNCT
ejpam-3496	66	2	−x	−x	PRON
ejpam-3496	66	3	◦	◦	VERB
ejpam-3496	66	4	y	y	NOUN
ejpam-3496	66	5	for	for	ADP
ejpam-3496	66	6	all	all	DET
ejpam-3496	66	7	x	x	NOUN
ejpam-3496	66	8	,	,	PUNCT
ejpam-3496	67	1	y	y	PROPN
ejpam-3496	67	2	∈	∈	PROPN
ejpam-3496	67	3	r	r	NOUN
ejpam-3496	67	4	,	,	PUNCT
ejpam-3496	67	5	then	then	ADV
ejpam-3496	67	6	d1	d1	PROPN
ejpam-3496	67	7	=	=	SYM
ejpam-3496	67	8	λd2	λd2	PROPN
ejpam-3496	67	9	,	,	PUNCT
ejpam-3496	67	10	where	where	SCONJ
ejpam-3496	67	11	λ	λ	PROPN
ejpam-3496	67	12	∈	∈	PROPN
ejpam-3496	67	13	c.	c.	NOUN
ejpam-3496	67	14	proof	proof	NOUN
ejpam-3496	67	15	.	.	PUNCT
ejpam-3496	68	1	(	(	PUNCT
ejpam-3496	68	2	i	i	NOUN
ejpam-3496	68	3	)	)	PUNCT
ejpam-3496	68	4	we	we	PRON
ejpam-3496	68	5	consider	consider	VERB
ejpam-3496	68	6	the	the	DET
ejpam-3496	68	7	case	case	NOUN
ejpam-3496	68	8	[	[	X
ejpam-3496	68	9	d1(x	d1(x	NOUN
ejpam-3496	68	10	)	)	PUNCT
ejpam-3496	68	11	,	,	PUNCT
ejpam-3496	68	12	d2(y	d2(y	PROPN
ejpam-3496	68	13	)	)	PUNCT
ejpam-3496	68	14	]	]	PUNCT
ejpam-3496	69	1	=	=	PUNCT
ejpam-3496	69	2	x	x	PUNCT
ejpam-3496	69	3	◦	◦	VERB
ejpam-3496	69	4	y	y	NOUN
ejpam-3496	69	5	for	for	ADP
ejpam-3496	69	6	all	all	DET
ejpam-3496	69	7	x	x	NOUN
ejpam-3496	69	8	,	,	PUNCT
ejpam-3496	69	9	y	y	PROPN
ejpam-3496	69	10	∈	∈	PROPN
ejpam-3496	69	11	r.	r.	PROPN
ejpam-3496	69	12	(	(	PUNCT
ejpam-3496	69	13	1	1	X
ejpam-3496	69	14	)	)	PUNCT
ejpam-3496	69	15	substituting	substitute	VERB
ejpam-3496	69	16	yh	yh	NOUN
ejpam-3496	69	17	for	for	ADP
ejpam-3496	69	18	y	y	PROPN
ejpam-3496	69	19	,	,	PUNCT
ejpam-3496	69	20	where	where	SCONJ
ejpam-3496	69	21	h	h	PROPN
ejpam-3496	69	22	∈	∈	PROPN
ejpam-3496	69	23	h(r	h(r	NOUN
ejpam-3496	69	24	)	)	PUNCT
ejpam-3496	69	25	∩	∩	NOUN
ejpam-3496	69	26	z(r	z(r	NOUN
ejpam-3496	69	27	)	)	PUNCT
ejpam-3496	69	28	,	,	PUNCT
ejpam-3496	69	29	we	we	PRON
ejpam-3496	69	30	get	get	VERB
ejpam-3496	69	31	[	[	X
ejpam-3496	69	32	d1(x	d1(x	NOUN
ejpam-3496	69	33	)	)	PUNCT
ejpam-3496	69	34	,	,	PUNCT
ejpam-3496	69	35	y]d2(h	y]d2(h	NOUN
ejpam-3496	69	36	)	)	PUNCT
ejpam-3496	69	37	=	=	SYM
ejpam-3496	69	38	0	0	NUM
ejpam-3496	69	39	for	for	ADP
ejpam-3496	69	40	all	all	DET
ejpam-3496	69	41	x	x	NOUN
ejpam-3496	69	42	,	,	PUNCT
ejpam-3496	69	43	y	y	PROPN
ejpam-3496	69	44	∈	∈	PROPN
ejpam-3496	69	45	r.	r.	PROPN
ejpam-3496	69	46	(	(	PUNCT
ejpam-3496	69	47	2	2	X
ejpam-3496	69	48	)	)	PUNCT
ejpam-3496	69	49	using	use	VERB
ejpam-3496	69	50	the	the	DET
ejpam-3496	69	51	primeness	primeness	NOUN
ejpam-3496	69	52	of	of	ADP
ejpam-3496	69	53	r	r	NOUN
ejpam-3496	69	54	we	we	PRON
ejpam-3496	69	55	have	have	VERB
ejpam-3496	69	56	either	either	PRON
ejpam-3496	69	57	d2(h	d2(h	PROPN
ejpam-3496	69	58	)	)	PUNCT
ejpam-3496	69	59	=	=	SYM
ejpam-3496	69	60	0	0	NUM
ejpam-3496	69	61	for	for	ADP
ejpam-3496	69	62	all	all	DET
ejpam-3496	69	63	h	h	NOUN
ejpam-3496	69	64	∈	∈	PROPN
ejpam-3496	69	65	h(r)∩z(r	h(r)∩z(r	NOUN
ejpam-3496	69	66	)	)	PUNCT
ejpam-3496	69	67	or	or	CCONJ
ejpam-3496	69	68	[	[	X
ejpam-3496	69	69	d1(x	d1(x	NOUN
ejpam-3496	69	70	)	)	PUNCT
ejpam-3496	69	71	,	,	PUNCT
ejpam-3496	69	72	y	y	PROPN
ejpam-3496	69	73	]	]	X
ejpam-3496	69	74	=	=	SYM
ejpam-3496	69	75	0	0	NUM
ejpam-3496	69	76	for	for	ADP
ejpam-3496	69	77	all	all	DET
ejpam-3496	69	78	x	x	NOUN
ejpam-3496	69	79	,	,	PUNCT
ejpam-3496	69	80	y	y	PROPN
ejpam-3496	69	81	∈	∈	PROPN
ejpam-3496	69	82	r.	r.	NOUN
ejpam-3496	69	83	if	if	SCONJ
ejpam-3496	69	84	[	[	X
ejpam-3496	69	85	d1(x	d1(x	NOUN
ejpam-3496	69	86	)	)	PUNCT
ejpam-3496	69	87	,	,	PUNCT
ejpam-3496	69	88	y	y	PROPN
ejpam-3496	69	89	]	]	X
ejpam-3496	69	90	=	=	SYM
ejpam-3496	69	91	0	0	NUM
ejpam-3496	69	92	for	for	ADP
ejpam-3496	69	93	all	all	DET
ejpam-3496	69	94	x	x	NOUN
ejpam-3496	69	95	,	,	PUNCT
ejpam-3496	69	96	y	y	PROPN
ejpam-3496	69	97	∈	∈	PROPN
ejpam-3496	69	98	r	r	NOUN
ejpam-3496	69	99	,	,	PUNCT
ejpam-3496	69	100	then	then	ADV
ejpam-3496	69	101	by	by	ADP
ejpam-3496	69	102	posner	posner	NOUN
ejpam-3496	69	103	’s	’s	PART
ejpam-3496	69	104	result	result	NOUN
ejpam-3496	69	105	[	[	X
ejpam-3496	69	106	18	18	NUM
ejpam-3496	69	107	]	]	X
ejpam-3496	69	108	r	r	NOUN
ejpam-3496	69	109	is	be	AUX
ejpam-3496	69	110	commutative	commutative	ADJ
ejpam-3496	69	111	,	,	PUNCT
ejpam-3496	69	112	a	a	DET
ejpam-3496	69	113	contradiction	contradiction	NOUN
ejpam-3496	69	114	.	.	PUNCT
ejpam-3496	70	1	therefore	therefore	ADV
ejpam-3496	70	2	we	we	PRON
ejpam-3496	70	3	are	be	AUX
ejpam-3496	70	4	left	leave	VERB
ejpam-3496	70	5	with	with	ADP
ejpam-3496	70	6	the	the	DET
ejpam-3496	70	7	case	case	NOUN
ejpam-3496	70	8	d2(h	d2(h	PROPN
ejpam-3496	70	9	)	)	PUNCT
ejpam-3496	70	10	=	=	SYM
ejpam-3496	70	11	0	0	NUM
ejpam-3496	70	12	for	for	ADP
ejpam-3496	70	13	all	all	DET
ejpam-3496	70	14	h	h	NOUN
ejpam-3496	70	15	∈	∈	PROPN
ejpam-3496	70	16	h(r	h(r	NOUN
ejpam-3496	70	17	)	)	PUNCT
ejpam-3496	70	18	∩	∩	NOUN
ejpam-3496	70	19	z(r	z(r	NOUN
ejpam-3496	70	20	)	)	PUNCT
ejpam-3496	70	21	.	.	PUNCT
ejpam-3496	71	1	replacing	replace	VERB
ejpam-3496	71	2	y	y	PRON
ejpam-3496	71	3	by	by	ADP
ejpam-3496	71	4	yx	yx	PROPN
ejpam-3496	71	5	in	in	ADP
ejpam-3496	71	6	(	(	PUNCT
ejpam-3496	71	7	1	1	NUM
ejpam-3496	71	8	)	)	PUNCT
ejpam-3496	71	9	,	,	PUNCT
ejpam-3496	71	10	we	we	PRON
ejpam-3496	71	11	obtain	obtain	VERB
ejpam-3496	71	12	d2(y)[d1(x	d2(y)[d1(x	NOUN
ejpam-3496	71	13	)	)	PUNCT
ejpam-3496	71	14	,	,	PUNCT
ejpam-3496	71	15	x	x	X
ejpam-3496	71	16	]	]	X
ejpam-3496	72	1	+	+	CCONJ
ejpam-3496	72	2	[	[	X
ejpam-3496	72	3	d1(x	d1(x	X
ejpam-3496	72	4	)	)	PUNCT
ejpam-3496	72	5	,	,	PUNCT
ejpam-3496	72	6	d2(y)]x+	d2(y)]x+	ADP
ejpam-3496	72	7	y[d1(x	y[d1(x	NOUN
ejpam-3496	72	8	)	)	PUNCT
ejpam-3496	72	9	,	,	PUNCT
ejpam-3496	72	10	d2(x	d2(x	PROPN
ejpam-3496	72	11	)	)	PUNCT
ejpam-3496	72	12	]	]	PUNCT
ejpam-3496	73	1	+	+	CCONJ
ejpam-3496	73	2	[	[	X
ejpam-3496	73	3	d1(x	d1(x	X
ejpam-3496	73	4	)	)	PUNCT
ejpam-3496	73	5	,	,	PUNCT
ejpam-3496	73	6	y]d2(x	y]d2(x	NOUN
ejpam-3496	73	7	)	)	PUNCT
ejpam-3496	74	1	=	=	PUNCT
ejpam-3496	74	2	xyx+	xyx+	PROPN
ejpam-3496	74	3	yx2	yx2	ADJ
ejpam-3496	74	4	(	(	PUNCT
ejpam-3496	74	5	3	3	NUM
ejpam-3496	74	6	)	)	PUNCT
ejpam-3496	74	7	for	for	ADP
ejpam-3496	74	8	all	all	DET
ejpam-3496	74	9	x	x	NOUN
ejpam-3496	74	10	,	,	PUNCT
ejpam-3496	74	11	y	y	PROPN
ejpam-3496	74	12	∈	∈	PROPN
ejpam-3496	74	13	r.	r.	PROPN
ejpam-3496	74	14	multiplying	multiplying	NOUN
ejpam-3496	74	15	(	(	PUNCT
ejpam-3496	74	16	1	1	NUM
ejpam-3496	74	17	)	)	PUNCT
ejpam-3496	74	18	by	by	ADP
ejpam-3496	74	19	x	x	PUNCT
ejpam-3496	74	20	from	from	ADP
ejpam-3496	74	21	right	right	ADJ
ejpam-3496	74	22	side	side	NOUN
ejpam-3496	74	23	and	and	CCONJ
ejpam-3496	74	24	subtracting	subtract	VERB
ejpam-3496	74	25	it	it	PRON
ejpam-3496	74	26	from	from	ADP
ejpam-3496	74	27	(	(	PUNCT
ejpam-3496	74	28	3	3	NUM
ejpam-3496	74	29	)	)	PUNCT
ejpam-3496	74	30	,	,	PUNCT
ejpam-3496	74	31	we	we	PRON
ejpam-3496	74	32	arrive	arrive	VERB
ejpam-3496	74	33	at	at	ADP
ejpam-3496	74	34	d2(y)[d1(x	d2(y)[d1(x	PROPN
ejpam-3496	74	35	)	)	PUNCT
ejpam-3496	74	36	,	,	PUNCT
ejpam-3496	74	37	x	x	X
ejpam-3496	74	38	]	]	X
ejpam-3496	74	39	+	+	CCONJ
ejpam-3496	74	40	y[d1(x	y[d1(x	NOUN
ejpam-3496	74	41	)	)	PUNCT
ejpam-3496	74	42	,	,	PUNCT
ejpam-3496	74	43	d2(x	d2(x	PROPN
ejpam-3496	74	44	)	)	PUNCT
ejpam-3496	74	45	]	]	PUNCT
ejpam-3496	75	1	+	+	CCONJ
ejpam-3496	75	2	[	[	X
ejpam-3496	75	3	d1(x	d1(x	X
ejpam-3496	75	4	)	)	PUNCT
ejpam-3496	75	5	,	,	PUNCT
ejpam-3496	75	6	y]d2(x	y]d2(x	NOUN
ejpam-3496	75	7	)	)	PUNCT
ejpam-3496	76	1	=	=	SYM
ejpam-3496	76	2	0	0	NUM
ejpam-3496	77	1	for	for	ADP
ejpam-3496	77	2	all	all	DET
ejpam-3496	77	3	x	x	NOUN
ejpam-3496	77	4	,	,	PUNCT
ejpam-3496	77	5	y	y	PROPN
ejpam-3496	77	6	∈	∈	PROPN
ejpam-3496	77	7	r.	r.	PROPN
ejpam-3496	77	8	now	now	ADV
ejpam-3496	77	9	taking	take	VERB
ejpam-3496	77	10	h	h	NOUN
ejpam-3496	77	11	for	for	ADP
ejpam-3496	77	12	y	y	PROPN
ejpam-3496	77	13	where	where	SCONJ
ejpam-3496	77	14	h	h	NOUN
ejpam-3496	77	15	∈	∈	PROPN
ejpam-3496	77	16	h(r	h(r	NOUN
ejpam-3496	77	17	)	)	PUNCT
ejpam-3496	77	18	∩	∩	NOUN
ejpam-3496	77	19	z(r	z(r	NOUN
ejpam-3496	77	20	)	)	PUNCT
ejpam-3496	77	21	,	,	PUNCT
ejpam-3496	77	22	we	we	PRON
ejpam-3496	77	23	get	get	VERB
ejpam-3496	77	24	h[d1(x	h[d1(x	NOUN
ejpam-3496	77	25	)	)	PUNCT
ejpam-3496	77	26	,	,	PUNCT
ejpam-3496	77	27	d2(x	d2(x	PROPN
ejpam-3496	77	28	)	)	PUNCT
ejpam-3496	77	29	]	]	PUNCT
ejpam-3496	78	1	=	=	PUNCT
ejpam-3496	78	2	0	0	PUNCT
ejpam-3496	78	3	for	for	ADP
ejpam-3496	78	4	all	all	DET
ejpam-3496	78	5	x	x	PROPN
ejpam-3496	78	6	∈	∈	PROPN
ejpam-3496	78	7	r.	r.	NOUN
ejpam-3496	78	8	now	now	ADV
ejpam-3496	78	9	using	use	VERB
ejpam-3496	78	10	the	the	DET
ejpam-3496	78	11	primeness	primeness	NOUN
ejpam-3496	78	12	of	of	ADP
ejpam-3496	78	13	r	r	NOUN
ejpam-3496	78	14	and	and	CCONJ
ejpam-3496	78	15	the	the	DET
ejpam-3496	78	16	fact	fact	NOUN
ejpam-3496	78	17	that	that	SCONJ
ejpam-3496	78	18	s(r	s(r	NOUN
ejpam-3496	78	19	)	)	PUNCT
ejpam-3496	78	20	∩	∩	NOUN
ejpam-3496	78	21	z(r	z(r	NOUN
ejpam-3496	78	22	)	)	PUNCT
ejpam-3496	78	23	6=	6=	NUM
ejpam-3496	78	24	(	(	PUNCT
ejpam-3496	78	25	0	0	NUM
ejpam-3496	78	26	)	)	PUNCT
ejpam-3496	78	27	,	,	PUNCT
ejpam-3496	78	28	we	we	PRON
ejpam-3496	78	29	finally	finally	ADV
ejpam-3496	78	30	arrive	arrive	VERB
ejpam-3496	78	31	at	at	ADP
ejpam-3496	78	32	[	[	X
ejpam-3496	78	33	d1(x	d1(x	NOUN
ejpam-3496	78	34	)	)	PUNCT
ejpam-3496	78	35	,	,	PUNCT
ejpam-3496	78	36	d2(x	d2(x	PROPN
ejpam-3496	78	37	)	)	PUNCT
ejpam-3496	78	38	]	]	PUNCT
ejpam-3496	79	1	=	=	PUNCT
ejpam-3496	79	2	0	0	PUNCT
ejpam-3496	79	3	for	for	ADP
ejpam-3496	79	4	all	all	DET
ejpam-3496	79	5	x	x	PROPN
ejpam-3496	79	6	∈	∈	PROPN
ejpam-3496	79	7	r.	r.	NOUN
ejpam-3496	79	8	thus	thus	ADV
ejpam-3496	79	9	in	in	ADP
ejpam-3496	79	10	view	view	NOUN
ejpam-3496	79	11	of	of	ADP
ejpam-3496	79	12	[	[	X
ejpam-3496	79	13	15	15	NUM
ejpam-3496	79	14	,	,	PUNCT
ejpam-3496	79	15	theorem	theorem	VERB
ejpam-3496	79	16	4	4	NUM
ejpam-3496	79	17	]	]	PUNCT
ejpam-3496	79	18	we	we	PRON
ejpam-3496	79	19	get	get	VERB
ejpam-3496	79	20	d1	d1	PROPN
ejpam-3496	79	21	=	=	SYM
ejpam-3496	79	22	λd2	λd2	PROPN
ejpam-3496	79	23	,	,	PUNCT
ejpam-3496	79	24	where	where	SCONJ
ejpam-3496	79	25	λ	λ	PROPN
ejpam-3496	79	26	∈	∈	PROPN
ejpam-3496	79	27	c.	c.	PROPN
ejpam-3496	79	28	(	(	PUNCT
ejpam-3496	79	29	ii	ii	PROPN
ejpam-3496	79	30	)	)	PUNCT
ejpam-3496	79	31	using	use	VERB
ejpam-3496	79	32	a	a	DET
ejpam-3496	79	33	similar	similar	ADJ
ejpam-3496	79	34	approach	approach	NOUN
ejpam-3496	79	35	with	with	ADP
ejpam-3496	79	36	necessary	necessary	ADJ
ejpam-3496	79	37	variations	variation	NOUN
ejpam-3496	79	38	,	,	PUNCT
ejpam-3496	79	39	we	we	PRON
ejpam-3496	79	40	can	can	AUX
ejpam-3496	79	41	prove	prove	VERB
ejpam-3496	79	42	that	that	SCONJ
ejpam-3496	79	43	the	the	DET
ejpam-3496	79	44	same	same	ADJ
ejpam-3496	79	45	conclusion	conclusion	NOUN
ejpam-3496	79	46	holds	hold	VERB
ejpam-3496	79	47	for	for	ADP
ejpam-3496	79	48	the	the	DET
ejpam-3496	79	49	case	case	NOUN
ejpam-3496	79	50	[	[	X
ejpam-3496	79	51	d1(x	d1(x	NOUN
ejpam-3496	79	52	)	)	PUNCT
ejpam-3496	79	53	,	,	PUNCT
ejpam-3496	79	54	d2(y	d2(y	PROPN
ejpam-3496	79	55	)	)	PUNCT
ejpam-3496	79	56	]	]	PUNCT
ejpam-3496	80	1	=	=	PUNCT
ejpam-3496	80	2	−x	−x	PRON
ejpam-3496	80	3	◦	◦	VERB
ejpam-3496	80	4	y	y	NOUN
ejpam-3496	80	5	for	for	ADP
ejpam-3496	80	6	all	all	DET
ejpam-3496	80	7	x	x	NOUN
ejpam-3496	80	8	,	,	PUNCT
ejpam-3496	80	9	y	y	PROPN
ejpam-3496	80	10	∈	∈	PROPN
ejpam-3496	80	11	r.	r.	NOUN
ejpam-3496	80	12	proof	proof	NOUN
ejpam-3496	80	13	of	of	ADP
ejpam-3496	80	14	main	main	ADJ
ejpam-3496	80	15	theorem	theorem	NOUN
ejpam-3496	80	16	.	.	PUNCT
ejpam-3496	81	1	by	by	ADP
ejpam-3496	81	2	the	the	DET
ejpam-3496	81	3	given	give	VERB
ejpam-3496	81	4	assumption	assumption	NOUN
ejpam-3496	81	5	,	,	PUNCT
ejpam-3496	81	6	we	we	PRON
ejpam-3496	81	7	have	have	VERB
ejpam-3496	81	8	[	[	X
ejpam-3496	81	9	d1(x	d1(x	NOUN
ejpam-3496	81	10	)	)	PUNCT
ejpam-3496	81	11	,	,	PUNCT
ejpam-3496	81	12	d2(x	d2(x	NOUN
ejpam-3496	81	13	∗	∗	NOUN
ejpam-3496	81	14	)	)	PUNCT
ejpam-3496	81	15	]	]	PUNCT
ejpam-3496	82	1	=	=	PUNCT
ejpam-3496	82	2	0	0	PUNCT
ejpam-3496	82	3	(	(	PUNCT
ejpam-3496	82	4	4	4	NUM
ejpam-3496	82	5	)	)	PUNCT
ejpam-3496	82	6	for	for	ADP
ejpam-3496	82	7	all	all	DET
ejpam-3496	82	8	x	x	PROPN
ejpam-3496	82	9	∈	∈	PROPN
ejpam-3496	82	10	r.	r.	NOUN
ejpam-3496	82	11	a	a	DET
ejpam-3496	82	12	linearization	linearization	NOUN
ejpam-3496	82	13	of	of	ADP
ejpam-3496	82	14	(	(	PUNCT
ejpam-3496	82	15	4	4	NUM
ejpam-3496	82	16	)	)	PUNCT
ejpam-3496	82	17	yields	yield	NOUN
ejpam-3496	82	18	that	that	PUNCT
ejpam-3496	83	1	[	[	X
ejpam-3496	83	2	d1(x	d1(x	NOUN
ejpam-3496	83	3	)	)	PUNCT
ejpam-3496	83	4	,	,	PUNCT
ejpam-3496	83	5	d2(y	d2(y	PROPN
ejpam-3496	83	6	∗	∗	NOUN
ejpam-3496	83	7	)	)	PUNCT
ejpam-3496	83	8	]	]	PUNCT
ejpam-3496	84	1	+	+	CCONJ
ejpam-3496	85	1	[	[	X
ejpam-3496	85	2	d1(y	d1(y	X
ejpam-3496	85	3	)	)	PUNCT
ejpam-3496	85	4	,	,	PUNCT
ejpam-3496	85	5	d2(x	d2(x	PROPN
ejpam-3496	85	6	∗	∗	NOUN
ejpam-3496	85	7	)	)	PUNCT
ejpam-3496	85	8	]	]	PUNCT
ejpam-3496	86	1	=	=	PUNCT
ejpam-3496	86	2	0	0	PUNCT
ejpam-3496	86	3	(	(	PUNCT
ejpam-3496	86	4	5	5	NUM
ejpam-3496	86	5	)	)	PUNCT
ejpam-3496	86	6	for	for	ADP
ejpam-3496	86	7	all	all	DET
ejpam-3496	86	8	x	x	NOUN
ejpam-3496	86	9	,	,	PUNCT
ejpam-3496	86	10	y	y	PROPN
ejpam-3496	86	11	∈	∈	PROPN
ejpam-3496	86	12	r.	r.	NOUN
ejpam-3496	86	13	replacing	replace	VERB
ejpam-3496	86	14	y	y	PRON
ejpam-3496	86	15	by	by	ADP
ejpam-3496	86	16	hy	hy	NOUN
ejpam-3496	86	17	in	in	ADP
ejpam-3496	86	18	(	(	PUNCT
ejpam-3496	86	19	5	5	NUM
ejpam-3496	86	20	)	)	PUNCT
ejpam-3496	86	21	,	,	PUNCT
ejpam-3496	86	22	where	where	SCONJ
ejpam-3496	86	23	y	y	PROPN
ejpam-3496	86	24	∈	∈	PROPN
ejpam-3496	86	25	r	r	NOUN
ejpam-3496	86	26	and	and	CCONJ
ejpam-3496	86	27	h	h	NOUN
ejpam-3496	86	28	∈	∈	PROPN
ejpam-3496	86	29	h(r	h(r	NOUN
ejpam-3496	86	30	)	)	PUNCT
ejpam-3496	86	31	∩	∩	NOUN
ejpam-3496	86	32	z(r	z(r	NOUN
ejpam-3496	86	33	)	)	PUNCT
ejpam-3496	86	34	,	,	PUNCT
ejpam-3496	86	35	we	we	PRON
ejpam-3496	86	36	get	get	VERB
ejpam-3496	86	37	h([d1(x	h([d1(x	NUM
ejpam-3496	86	38	)	)	PUNCT
ejpam-3496	86	39	,	,	PUNCT
ejpam-3496	86	40	d2(y	d2(y	PROPN
ejpam-3496	86	41	∗	∗	NOUN
ejpam-3496	86	42	)	)	PUNCT
ejpam-3496	86	43	]	]	PUNCT
ejpam-3496	87	1	+	+	CCONJ
ejpam-3496	88	1	[	[	X
ejpam-3496	88	2	d1(y	d1(y	X
ejpam-3496	88	3	)	)	PUNCT
ejpam-3496	88	4	,	,	PUNCT
ejpam-3496	88	5	d2(x	d2(x	PROPN
ejpam-3496	88	6	∗	∗	NOUN
ejpam-3496	88	7	)	)	PUNCT
ejpam-3496	88	8	]	]	PUNCT
ejpam-3496	88	9	)	)	PUNCT
ejpam-3496	89	1	+	+	CCONJ
ejpam-3496	89	2	d2(h)[d1(x	d2(h)[d1(x	NOUN
ejpam-3496	89	3	)	)	PUNCT
ejpam-3496	89	4	,	,	PUNCT
ejpam-3496	89	5	y∗	y∗	PROPN
ejpam-3496	89	6	]	]	PUNCT
ejpam-3496	89	7	+	+	CCONJ
ejpam-3496	89	8	d1(h)[y	d1(h)[y	PROPN
ejpam-3496	89	9	,	,	PUNCT
ejpam-3496	89	10	d2(x	d2(x	NOUN
ejpam-3496	89	11	∗	∗	NOUN
ejpam-3496	89	12	)	)	PUNCT
ejpam-3496	89	13	]	]	PUNCT
ejpam-3496	90	1	=	=	PUNCT
ejpam-3496	90	2	0	0	X
ejpam-3496	90	3	.	.	PUNCT
ejpam-3496	91	1	s.	s.	PROPN
ejpam-3496	91	2	ali	ali	PROPN
ejpam-3496	91	3	et	et	PROPN
ejpam-3496	91	4	al	al	PROPN
ejpam-3496	91	5	.	.	PUNCT
ejpam-3496	91	6	/	/	SYM
ejpam-3496	91	7	eur	eur	PROPN
ejpam-3496	91	8	.	.	PUNCT
ejpam-3496	92	1	j.	j.	PROPN
ejpam-3496	92	2	pure	pure	PROPN
ejpam-3496	92	3	appl	appl	PROPN
ejpam-3496	92	4	.	.	PROPN
ejpam-3496	92	5	math	math	PROPN
ejpam-3496	92	6	,	,	PUNCT
ejpam-3496	92	7	12	12	NUM
ejpam-3496	92	8	(	(	PUNCT
ejpam-3496	92	9	3	3	NUM
ejpam-3496	92	10	)	)	PUNCT
ejpam-3496	92	11	(	(	PUNCT
ejpam-3496	92	12	2019	2019	NUM
ejpam-3496	92	13	)	)	PUNCT
ejpam-3496	92	14	,	,	PUNCT
ejpam-3496	92	15	1138	1138	NUM
ejpam-3496	92	16	-	-	SYM
ejpam-3496	92	17	1148	1148	NUM
ejpam-3496	92	18	1141	1141	NUM
ejpam-3496	92	19	using	use	VERB
ejpam-3496	92	20	(	(	PUNCT
ejpam-3496	92	21	5	5	NUM
ejpam-3496	92	22	)	)	PUNCT
ejpam-3496	92	23	,	,	PUNCT
ejpam-3496	92	24	we	we	PRON
ejpam-3496	92	25	get	get	VERB
ejpam-3496	92	26	d2(h)[d1(x	d2(h)[d1(x	NOUN
ejpam-3496	92	27	)	)	PUNCT
ejpam-3496	92	28	,	,	PUNCT
ejpam-3496	92	29	y∗	y∗	PROPN
ejpam-3496	92	30	]	]	PUNCT
ejpam-3496	93	1	+	+	CCONJ
ejpam-3496	93	2	d1(h)[y	d1(h)[y	PROPN
ejpam-3496	93	3	,	,	PUNCT
ejpam-3496	93	4	d2(x	d2(x	NOUN
ejpam-3496	93	5	∗	∗	NOUN
ejpam-3496	93	6	)	)	PUNCT
ejpam-3496	93	7	]	]	PUNCT
ejpam-3496	94	1	=	=	PUNCT
ejpam-3496	94	2	0	0	PUNCT
ejpam-3496	94	3	(	(	PUNCT
ejpam-3496	94	4	6	6	NUM
ejpam-3496	94	5	)	)	PUNCT
ejpam-3496	94	6	for	for	ADP
ejpam-3496	94	7	all	all	DET
ejpam-3496	94	8	x	x	NOUN
ejpam-3496	94	9	,	,	PUNCT
ejpam-3496	94	10	y	y	PROPN
ejpam-3496	94	11	∈	∈	PROPN
ejpam-3496	94	12	r	r	NOUN
ejpam-3496	94	13	and	and	CCONJ
ejpam-3496	94	14	h	h	NOUN
ejpam-3496	94	15	∈	∈	PROPN
ejpam-3496	94	16	h(r)∩z(r	h(r)∩z(r	NOUN
ejpam-3496	94	17	)	)	PUNCT
ejpam-3496	94	18	.	.	PUNCT
ejpam-3496	95	1	substituting	substitute	VERB
ejpam-3496	95	2	ky	ky	PROPN
ejpam-3496	95	3	for	for	ADP
ejpam-3496	95	4	y	y	PROPN
ejpam-3496	95	5	in	in	ADP
ejpam-3496	95	6	(	(	PUNCT
ejpam-3496	95	7	6	6	NUM
ejpam-3496	95	8	)	)	PUNCT
ejpam-3496	95	9	,	,	PUNCT
ejpam-3496	95	10	where	where	SCONJ
ejpam-3496	95	11	k	k	PROPN
ejpam-3496	95	12	∈	∈	PROPN
ejpam-3496	95	13	s(r)∩z(r	s(r)∩z(r	PUNCT
ejpam-3496	95	14	)	)	PUNCT
ejpam-3496	95	15	,	,	PUNCT
ejpam-3496	95	16	we	we	PRON
ejpam-3496	95	17	have	have	VERB
ejpam-3496	95	18	−d2(h)[d1(x	−d2(h)[d1(x	NUM
ejpam-3496	95	19	)	)	PUNCT
ejpam-3496	95	20	,	,	PUNCT
ejpam-3496	95	21	y∗k	y∗k	AUX
ejpam-3496	95	22	]	]	X
ejpam-3496	95	23	+	+	X
ejpam-3496	95	24	d1(h)[ky	d1(h)[ky	PROPN
ejpam-3496	95	25	,	,	PUNCT
ejpam-3496	95	26	d2(x	d2(x	NOUN
ejpam-3496	95	27	∗	∗	NOUN
ejpam-3496	95	28	)	)	PUNCT
ejpam-3496	95	29	]	]	PUNCT
ejpam-3496	96	1	=	=	PUNCT
ejpam-3496	96	2	0	0	X
ejpam-3496	96	3	.	.	PUNCT
ejpam-3496	97	1	this	this	PRON
ejpam-3496	97	2	further	far	ADV
ejpam-3496	97	3	implies	imply	VERB
ejpam-3496	97	4	that	that	SCONJ
ejpam-3496	97	5	−d2(h)k[d1(x	−d2(h)k[d1(x	NOUN
ejpam-3496	97	6	)	)	PUNCT
ejpam-3496	97	7	,	,	PUNCT
ejpam-3496	97	8	y∗	y∗	PROPN
ejpam-3496	97	9	]	]	PUNCT
ejpam-3496	97	10	+	+	CCONJ
ejpam-3496	97	11	d1(h)k[y	d1(h)k[y	NOUN
ejpam-3496	97	12	,	,	PUNCT
ejpam-3496	97	13	d2(x	d2(x	NOUN
ejpam-3496	97	14	∗	∗	NOUN
ejpam-3496	97	15	)	)	PUNCT
ejpam-3496	97	16	]	]	PUNCT
ejpam-3496	98	1	=	=	PUNCT
ejpam-3496	98	2	0	0	X
ejpam-3496	98	3	.	.	PUNCT
ejpam-3496	99	1	(	(	PUNCT
ejpam-3496	99	2	7	7	X
ejpam-3496	99	3	)	)	PUNCT
ejpam-3496	99	4	multiplying	multiplying	NOUN
ejpam-3496	99	5	(	(	PUNCT
ejpam-3496	99	6	6	6	NUM
ejpam-3496	99	7	)	)	PUNCT
ejpam-3496	99	8	by	by	ADP
ejpam-3496	99	9	k	k	PROPN
ejpam-3496	99	10	and	and	CCONJ
ejpam-3496	99	11	comparing	compare	VERB
ejpam-3496	99	12	with	with	ADP
ejpam-3496	99	13	(	(	PUNCT
ejpam-3496	99	14	7	7	NUM
ejpam-3496	99	15	)	)	PUNCT
ejpam-3496	99	16	,	,	PUNCT
ejpam-3496	99	17	we	we	PRON
ejpam-3496	99	18	obtain	obtain	VERB
ejpam-3496	99	19	2d1(h)k[y	2d1(h)k[y	NOUN
ejpam-3496	99	20	,	,	PUNCT
ejpam-3496	99	21	d2(x	d2(x	NOUN
ejpam-3496	99	22	∗	∗	NOUN
ejpam-3496	99	23	)	)	PUNCT
ejpam-3496	99	24	]	]	PUNCT
ejpam-3496	100	1	=	=	PUNCT
ejpam-3496	100	2	0	0	X
ejpam-3496	100	3	.	.	PUNCT
ejpam-3496	101	1	since	since	SCONJ
ejpam-3496	101	2	char(r	char(r	NOUN
ejpam-3496	101	3	)	)	PUNCT
ejpam-3496	101	4	6=	6=	ADP
ejpam-3496	101	5	2	2	NUM
ejpam-3496	101	6	and	and	CCONJ
ejpam-3496	101	7	s(r	s(r	ADJ
ejpam-3496	101	8	)	)	PUNCT
ejpam-3496	101	9	∩	∩	NOUN
ejpam-3496	101	10	z(r	z(r	NOUN
ejpam-3496	101	11	)	)	PUNCT
ejpam-3496	101	12	6=	6=	NUM
ejpam-3496	101	13	(	(	PUNCT
ejpam-3496	101	14	0	0	NUM
ejpam-3496	101	15	)	)	PUNCT
ejpam-3496	101	16	,	,	PUNCT
ejpam-3496	101	17	the	the	DET
ejpam-3496	101	18	above	above	ADJ
ejpam-3496	101	19	expression	expression	NOUN
ejpam-3496	101	20	gives	give	VERB
ejpam-3496	101	21	d1(h)[y	d1(h)[y	PROPN
ejpam-3496	101	22	,	,	PUNCT
ejpam-3496	101	23	d2(x	d2(x	NOUN
ejpam-3496	101	24	∗	∗	NOUN
ejpam-3496	101	25	)	)	PUNCT
ejpam-3496	101	26	]	]	PUNCT
ejpam-3496	102	1	=	=	PUNCT
ejpam-3496	102	2	0	0	PUNCT
ejpam-3496	102	3	(	(	PUNCT
ejpam-3496	102	4	8)	8)	NUM
ejpam-3496	102	5	for	for	ADP
ejpam-3496	102	6	all	all	DET
ejpam-3496	102	7	x	x	NOUN
ejpam-3496	102	8	,	,	PUNCT
ejpam-3496	102	9	y	y	PROPN
ejpam-3496	102	10	∈	∈	PROPN
ejpam-3496	102	11	r	r	NOUN
ejpam-3496	102	12	and	and	CCONJ
ejpam-3496	102	13	h	h	NOUN
ejpam-3496	102	14	∈	∈	PROPN
ejpam-3496	102	15	h(r	h(r	NOUN
ejpam-3496	102	16	)	)	PUNCT
ejpam-3496	102	17	∩	∩	NOUN
ejpam-3496	102	18	z(r	z(r	NOUN
ejpam-3496	102	19	)	)	PUNCT
ejpam-3496	102	20	.	.	PUNCT
ejpam-3496	103	1	invoking	invoke	VERB
ejpam-3496	103	2	the	the	DET
ejpam-3496	103	3	primeness	primeness	NOUN
ejpam-3496	103	4	of	of	ADP
ejpam-3496	103	5	r	r	NOUN
ejpam-3496	103	6	,	,	PUNCT
ejpam-3496	103	7	we	we	PRON
ejpam-3496	103	8	get	get	VERB
ejpam-3496	103	9	d1(h	d1(h	NOUN
ejpam-3496	103	10	)	)	PUNCT
ejpam-3496	103	11	=	=	SYM
ejpam-3496	103	12	0	0	NUM
ejpam-3496	104	1	for	for	ADP
ejpam-3496	104	2	all	all	DET
ejpam-3496	104	3	h	h	NOUN
ejpam-3496	104	4	∈	∈	PROPN
ejpam-3496	104	5	h(r	h(r	NOUN
ejpam-3496	104	6	)	)	PUNCT
ejpam-3496	104	7	∩	∩	NOUN
ejpam-3496	104	8	z(r	z(r	NOUN
ejpam-3496	104	9	)	)	PUNCT
ejpam-3496	104	10	or	or	CCONJ
ejpam-3496	104	11	[	[	X
ejpam-3496	104	12	y	y	PROPN
ejpam-3496	104	13	,	,	PUNCT
ejpam-3496	104	14	d2(x	d2(x	ADJ
ejpam-3496	104	15	∗	∗	NOUN
ejpam-3496	104	16	)	)	PUNCT
ejpam-3496	104	17	]	]	PUNCT
ejpam-3496	104	18	=	=	PUNCT
ejpam-3496	104	19	0	0	NUM
ejpam-3496	104	20	for	for	ADP
ejpam-3496	104	21	all	all	DET
ejpam-3496	104	22	x	x	NOUN
ejpam-3496	104	23	,	,	PUNCT
ejpam-3496	104	24	y	y	PROPN
ejpam-3496	104	25	∈	∈	PROPN
ejpam-3496	104	26	r.	r.	PROPN
ejpam-3496	104	27	suppose	suppose	VERB
ejpam-3496	105	1	[	[	X
ejpam-3496	105	2	y	y	PROPN
ejpam-3496	105	3	,	,	PUNCT
ejpam-3496	105	4	d2(x	d2(x	ADJ
ejpam-3496	105	5	∗	∗	NOUN
ejpam-3496	105	6	)	)	PUNCT
ejpam-3496	105	7	]	]	PUNCT
ejpam-3496	106	1	=	=	PUNCT
ejpam-3496	106	2	0	0	NUM
ejpam-3496	106	3	for	for	ADP
ejpam-3496	106	4	all	all	DET
ejpam-3496	106	5	x	x	NOUN
ejpam-3496	106	6	,	,	PUNCT
ejpam-3496	106	7	y	y	PROPN
ejpam-3496	106	8	∈	∈	PROPN
ejpam-3496	106	9	r.	r.	NOUN
ejpam-3496	106	10	replacing	replace	VERB
ejpam-3496	106	11	x	x	PUNCT
ejpam-3496	106	12	by	by	ADP
ejpam-3496	106	13	x∗	x∗	PROPN
ejpam-3496	106	14	we	we	PRON
ejpam-3496	106	15	get	get	VERB
ejpam-3496	106	16	[	[	X
ejpam-3496	106	17	y	y	NOUN
ejpam-3496	106	18	,	,	PUNCT
ejpam-3496	106	19	d2(x	d2(x	PROPN
ejpam-3496	106	20	)	)	PUNCT
ejpam-3496	106	21	]	]	PUNCT
ejpam-3496	107	1	=	=	PUNCT
ejpam-3496	107	2	0	0	NUM
ejpam-3496	107	3	for	for	ADP
ejpam-3496	107	4	all	all	DET
ejpam-3496	107	5	x	x	NOUN
ejpam-3496	107	6	,	,	PUNCT
ejpam-3496	107	7	y	y	PROPN
ejpam-3496	107	8	∈	∈	PROPN
ejpam-3496	107	9	r.	r.	PROPN
ejpam-3496	107	10	thus	thus	ADV
ejpam-3496	107	11	in	in	ADP
ejpam-3496	107	12	view	view	NOUN
ejpam-3496	107	13	of	of	ADP
ejpam-3496	107	14	posner	posner	NOUN
ejpam-3496	107	15	’s	’s	PART
ejpam-3496	107	16	result	result	NOUN
ejpam-3496	108	1	[	[	X
ejpam-3496	108	2	18	18	NUM
ejpam-3496	108	3	]	]	PUNCT
ejpam-3496	108	4	,	,	PUNCT
ejpam-3496	108	5	r	r	NOUN
ejpam-3496	108	6	is	be	AUX
ejpam-3496	108	7	commutative	commutative	ADJ
ejpam-3496	108	8	,	,	PUNCT
ejpam-3496	108	9	which	which	PRON
ejpam-3496	108	10	is	be	AUX
ejpam-3496	108	11	a	a	DET
ejpam-3496	108	12	contradiction	contradiction	NOUN
ejpam-3496	108	13	.	.	PUNCT
ejpam-3496	109	1	now	now	ADV
ejpam-3496	109	2	suppose	suppose	VERB
ejpam-3496	109	3	d1(h	d1(h	PRON
ejpam-3496	109	4	)	)	PUNCT
ejpam-3496	109	5	=	=	SYM
ejpam-3496	109	6	0	0	NUM
ejpam-3496	109	7	for	for	ADP
ejpam-3496	109	8	all	all	DET
ejpam-3496	109	9	h	h	NOUN
ejpam-3496	109	10	∈	∈	PROPN
ejpam-3496	109	11	h(r)∩z(r	h(r)∩z(r	NOUN
ejpam-3496	109	12	)	)	PUNCT
ejpam-3496	109	13	.	.	PUNCT
ejpam-3496	110	1	this	this	DET
ejpam-3496	110	2	further	far	ADV
ejpam-3496	110	3	implies	imply	VERB
ejpam-3496	110	4	that	that	SCONJ
ejpam-3496	110	5	0	0	X
ejpam-3496	111	1	=	=	SYM
ejpam-3496	111	2	d1(k	d1(k	DET
ejpam-3496	111	3	2	2	NUM
ejpam-3496	111	4	)	)	PUNCT
ejpam-3496	111	5	=	=	SYM
ejpam-3496	111	6	2d1(k)k	2d1(k)k	NUM
ejpam-3496	111	7	.	.	PUNCT
ejpam-3496	112	1	since	since	SCONJ
ejpam-3496	112	2	char(r	char(r	NOUN
ejpam-3496	112	3	)	)	PUNCT
ejpam-3496	112	4	6=	6=	ADP
ejpam-3496	112	5	2	2	NUM
ejpam-3496	112	6	and	and	CCONJ
ejpam-3496	112	7	s(r)∩z(r	s(r)∩z(r	NUM
ejpam-3496	112	8	)	)	PUNCT
ejpam-3496	112	9	6=	6=	PUNCT
ejpam-3496	112	10	(	(	PUNCT
ejpam-3496	112	11	0	0	NUM
ejpam-3496	112	12	)	)	PUNCT
ejpam-3496	112	13	,	,	PUNCT
ejpam-3496	112	14	we	we	PRON
ejpam-3496	112	15	have	have	VERB
ejpam-3496	112	16	d1(k	d1(k	NUM
ejpam-3496	112	17	)	)	PUNCT
ejpam-3496	112	18	=	=	SYM
ejpam-3496	112	19	0	0	NUM
ejpam-3496	112	20	for	for	ADP
ejpam-3496	112	21	all	all	DET
ejpam-3496	112	22	k	k	PROPN
ejpam-3496	112	23	∈	∈	PROPN
ejpam-3496	112	24	s(r)∩z(r	s(r)∩z(r	PUNCT
ejpam-3496	112	25	)	)	PUNCT
ejpam-3496	112	26	.	.	PUNCT
ejpam-3496	113	1	now	now	ADV
ejpam-3496	113	2	since	since	SCONJ
ejpam-3496	113	3	every	every	DET
ejpam-3496	113	4	z	z	PROPN
ejpam-3496	113	5	∈	∈	PROPN
ejpam-3496	113	6	z(r	z(r	PROPN
ejpam-3496	113	7	)	)	PUNCT
ejpam-3496	113	8	can	can	AUX
ejpam-3496	113	9	be	be	AUX
ejpam-3496	113	10	represented	represent	VERB
ejpam-3496	113	11	as	as	ADP
ejpam-3496	113	12	2z	2z	NUM
ejpam-3496	113	13	=	=	SYM
ejpam-3496	114	1	h	h	NOUN
ejpam-3496	115	1	+	+	CCONJ
ejpam-3496	115	2	k	k	X
ejpam-3496	115	3	where	where	SCONJ
ejpam-3496	115	4	h	h	NOUN
ejpam-3496	115	5	∈	∈	PROPN
ejpam-3496	115	6	h(r	h(r	NOUN
ejpam-3496	115	7	)	)	PUNCT
ejpam-3496	115	8	∩	∩	NOUN
ejpam-3496	115	9	z(r	z(r	NOUN
ejpam-3496	115	10	)	)	PUNCT
ejpam-3496	115	11	and	and	CCONJ
ejpam-3496	115	12	k	k	PROPN
ejpam-3496	115	13	∈	∈	PROPN
ejpam-3496	115	14	s(r	s(r	PROPN
ejpam-3496	115	15	)	)	PUNCT
ejpam-3496	115	16	∩	∩	NOUN
ejpam-3496	115	17	z(r	z(r	NOUN
ejpam-3496	115	18	)	)	PUNCT
ejpam-3496	115	19	,	,	PUNCT
ejpam-3496	115	20	we	we	PRON
ejpam-3496	115	21	get	get	VERB
ejpam-3496	115	22	d1(z(r	d1(z(r	PRON
ejpam-3496	115	23	)	)	PUNCT
ejpam-3496	115	24	)	)	PUNCT
ejpam-3496	116	1	=	=	PUNCT
ejpam-3496	116	2	(	(	PUNCT
ejpam-3496	116	3	0	0	NUM
ejpam-3496	116	4	)	)	PUNCT
ejpam-3496	116	5	.	.	PUNCT
ejpam-3496	117	1	now	now	ADV
ejpam-3496	117	2	in	in	ADP
ejpam-3496	117	3	view	view	NOUN
ejpam-3496	117	4	of	of	ADP
ejpam-3496	117	5	(	(	PUNCT
ejpam-3496	117	6	7	7	NUM
ejpam-3496	117	7	)	)	PUNCT
ejpam-3496	117	8	,	,	PUNCT
ejpam-3496	117	9	we	we	PRON
ejpam-3496	117	10	have	have	VERB
ejpam-3496	117	11	d2(h)k[d1(x	d2(h)k[d1(x	NOUN
ejpam-3496	117	12	)	)	PUNCT
ejpam-3496	117	13	,	,	PUNCT
ejpam-3496	117	14	y∗	y∗	PROPN
ejpam-3496	117	15	]	]	X
ejpam-3496	118	1	=	=	SYM
ejpam-3496	118	2	0	0	PUNCT
ejpam-3496	118	3	for	for	ADP
ejpam-3496	118	4	all	all	DET
ejpam-3496	118	5	x	x	NOUN
ejpam-3496	118	6	,	,	PUNCT
ejpam-3496	118	7	y	y	PROPN
ejpam-3496	118	8	∈	∈	PROPN
ejpam-3496	118	9	r	r	PROPN
ejpam-3496	118	10	,	,	PUNCT
ejpam-3496	118	11	h	h	NOUN
ejpam-3496	118	12	∈	∈	PROPN
ejpam-3496	118	13	h(r	h(r	NOUN
ejpam-3496	118	14	)	)	PUNCT
ejpam-3496	118	15	∩	∩	NOUN
ejpam-3496	118	16	z(r	z(r	NOUN
ejpam-3496	118	17	)	)	PUNCT
ejpam-3496	118	18	and	and	CCONJ
ejpam-3496	118	19	k	k	PROPN
ejpam-3496	118	20	∈	∈	PROPN
ejpam-3496	118	21	s(r	s(r	PROPN
ejpam-3496	118	22	)	)	PUNCT
ejpam-3496	118	23	∩	∩	NOUN
ejpam-3496	118	24	z(r	z(r	NOUN
ejpam-3496	118	25	)	)	PUNCT
ejpam-3496	118	26	.	.	PUNCT
ejpam-3496	119	1	using	use	VERB
ejpam-3496	119	2	primeness	primeness	NOUN
ejpam-3496	119	3	,	,	PUNCT
ejpam-3496	119	4	we	we	PRON
ejpam-3496	119	5	get	get	VERB
ejpam-3496	119	6	either	either	PRON
ejpam-3496	119	7	d2(h	d2(h	PROPN
ejpam-3496	119	8	)	)	PUNCT
ejpam-3496	119	9	=	=	SYM
ejpam-3496	119	10	0	0	NUM
ejpam-3496	119	11	for	for	ADP
ejpam-3496	119	12	all	all	DET
ejpam-3496	119	13	h	h	NOUN
ejpam-3496	119	14	∈	∈	PROPN
ejpam-3496	119	15	h(r)∩z(r	h(r)∩z(r	NOUN
ejpam-3496	119	16	)	)	PUNCT
ejpam-3496	119	17	or	or	CCONJ
ejpam-3496	119	18	[	[	X
ejpam-3496	119	19	d1(x	d1(x	NOUN
ejpam-3496	119	20	)	)	PUNCT
ejpam-3496	119	21	,	,	PUNCT
ejpam-3496	119	22	y∗	y∗	PROPN
ejpam-3496	119	23	]	]	X
ejpam-3496	119	24	=	=	SYM
ejpam-3496	119	25	0	0	PUNCT
ejpam-3496	119	26	for	for	ADP
ejpam-3496	119	27	all	all	DET
ejpam-3496	119	28	x	x	NOUN
ejpam-3496	119	29	,	,	PUNCT
ejpam-3496	119	30	y	y	PROPN
ejpam-3496	119	31	∈	∈	PROPN
ejpam-3496	119	32	r.	r.	NOUN
ejpam-3496	119	33	replacing	replace	VERB
ejpam-3496	119	34	y	y	PRON
ejpam-3496	119	35	by	by	ADP
ejpam-3496	119	36	y∗	y∗	PROPN
ejpam-3496	119	37	,	,	PUNCT
ejpam-3496	119	38	we	we	PRON
ejpam-3496	119	39	get	get	VERB
ejpam-3496	119	40	[	[	X
ejpam-3496	119	41	d1(x	d1(x	NOUN
ejpam-3496	119	42	)	)	PUNCT
ejpam-3496	119	43	,	,	PUNCT
ejpam-3496	119	44	y	y	PROPN
ejpam-3496	119	45	]	]	X
ejpam-3496	119	46	=	=	SYM
ejpam-3496	119	47	0	0	NUM
ejpam-3496	119	48	for	for	ADP
ejpam-3496	119	49	all	all	DET
ejpam-3496	119	50	x	x	NOUN
ejpam-3496	119	51	,	,	PUNCT
ejpam-3496	119	52	y	y	PROPN
ejpam-3496	119	53	∈	∈	PROPN
ejpam-3496	119	54	r.	r.	PROPN
ejpam-3496	119	55	again	again	ADV
ejpam-3496	119	56	using	use	VERB
ejpam-3496	119	57	posner	posner	NOUN
ejpam-3496	119	58	’s	’s	PART
ejpam-3496	119	59	result	result	NOUN
ejpam-3496	119	60	[	[	X
ejpam-3496	119	61	18	18	NUM
ejpam-3496	119	62	]	]	PUNCT
ejpam-3496	119	63	,	,	PUNCT
ejpam-3496	119	64	we	we	PRON
ejpam-3496	119	65	get	get	VERB
ejpam-3496	119	66	a	a	DET
ejpam-3496	119	67	contradiction	contradiction	NOUN
ejpam-3496	119	68	.	.	PUNCT
ejpam-3496	120	1	now	now	ADV
ejpam-3496	120	2	suppose	suppose	VERB
ejpam-3496	120	3	d2(h	d2(h	PROPN
ejpam-3496	120	4	)	)	PUNCT
ejpam-3496	120	5	=	=	SYM
ejpam-3496	120	6	0	0	NUM
ejpam-3496	120	7	for	for	ADP
ejpam-3496	120	8	all	all	DET
ejpam-3496	120	9	h	h	NOUN
ejpam-3496	120	10	∈	∈	PROPN
ejpam-3496	120	11	h(r)∩z(r	h(r)∩z(r	NOUN
ejpam-3496	120	12	)	)	PUNCT
ejpam-3496	120	13	.	.	PUNCT
ejpam-3496	121	1	this	this	DET
ejpam-3496	121	2	intern	intern	NOUN
ejpam-3496	121	3	implies	imply	VERB
ejpam-3496	121	4	that	that	SCONJ
ejpam-3496	121	5	d2(z(r	d2(z(r	NUM
ejpam-3496	121	6	)	)	PUNCT
ejpam-3496	121	7	)	)	PUNCT
ejpam-3496	122	1	=	=	PUNCT
ejpam-3496	122	2	(	(	PUNCT
ejpam-3496	122	3	0	0	NUM
ejpam-3496	122	4	)	)	PUNCT
ejpam-3496	122	5	.	.	PUNCT
ejpam-3496	123	1	replacing	replace	VERB
ejpam-3496	123	2	y	y	PRON
ejpam-3496	123	3	by	by	ADP
ejpam-3496	123	4	−ky	−ky	NOUN
ejpam-3496	123	5	in	in	ADP
ejpam-3496	123	6	(	(	PUNCT
ejpam-3496	123	7	5	5	NUM
ejpam-3496	123	8	)	)	PUNCT
ejpam-3496	123	9	,	,	PUNCT
ejpam-3496	123	10	we	we	PRON
ejpam-3496	123	11	have	have	VERB
ejpam-3496	123	12	k([d1(x	k([d1(x	NOUN
ejpam-3496	123	13	)	)	PUNCT
ejpam-3496	123	14	,	,	PUNCT
ejpam-3496	124	1	d2(y	d2(y	PROPN
ejpam-3496	124	2	∗)]−	∗)]−	PROPN
ejpam-3496	125	1	[	[	X
ejpam-3496	125	2	d1(y	d1(y	X
ejpam-3496	125	3	)	)	PUNCT
ejpam-3496	125	4	,	,	PUNCT
ejpam-3496	125	5	d2(x	d2(x	PROPN
ejpam-3496	125	6	∗	∗	NOUN
ejpam-3496	125	7	)	)	PUNCT
ejpam-3496	125	8	]	]	PUNCT
ejpam-3496	125	9	)	)	PUNCT
ejpam-3496	126	1	=	=	SYM
ejpam-3496	126	2	0	0	X
ejpam-3496	126	3	.	.	PUNCT
ejpam-3496	127	1	this	this	DET
ejpam-3496	127	2	further	far	ADV
ejpam-3496	127	3	implies	imply	VERB
ejpam-3496	127	4	that	that	SCONJ
ejpam-3496	128	1	[	[	X
ejpam-3496	128	2	d1(x	d1(x	NOUN
ejpam-3496	128	3	)	)	PUNCT
ejpam-3496	128	4	,	,	PUNCT
ejpam-3496	128	5	d2(y	d2(y	PROPN
ejpam-3496	128	6	∗)]−	∗)]−	PROPN
ejpam-3496	129	1	[	[	X
ejpam-3496	129	2	d1(y	d1(y	X
ejpam-3496	129	3	)	)	PUNCT
ejpam-3496	129	4	,	,	PUNCT
ejpam-3496	129	5	d2(x	d2(x	PROPN
ejpam-3496	129	6	∗	∗	NOUN
ejpam-3496	129	7	)	)	PUNCT
ejpam-3496	129	8	]	]	PUNCT
ejpam-3496	130	1	=	=	PUNCT
ejpam-3496	130	2	0	0	PUNCT
ejpam-3496	130	3	(	(	PUNCT
ejpam-3496	130	4	9	9	NUM
ejpam-3496	130	5	)	)	PUNCT
ejpam-3496	130	6	for	for	ADP
ejpam-3496	130	7	all	all	DET
ejpam-3496	130	8	x	x	NOUN
ejpam-3496	130	9	,	,	PUNCT
ejpam-3496	130	10	y	y	PROPN
ejpam-3496	130	11	∈	∈	PROPN
ejpam-3496	130	12	r	r	NOUN
ejpam-3496	130	13	,	,	PUNCT
ejpam-3496	130	14	since	since	SCONJ
ejpam-3496	130	15	s(r	s(r	ADJ
ejpam-3496	130	16	)	)	PUNCT
ejpam-3496	130	17	∩	∩	NOUN
ejpam-3496	130	18	z(r	z(r	NOUN
ejpam-3496	130	19	)	)	PUNCT
ejpam-3496	130	20	6=	6=	NUM
ejpam-3496	130	21	(	(	PUNCT
ejpam-3496	130	22	0	0	NUM
ejpam-3496	130	23	)	)	PUNCT
ejpam-3496	130	24	.	.	PUNCT
ejpam-3496	131	1	on	on	ADP
ejpam-3496	131	2	comparing	compare	VERB
ejpam-3496	131	3	(	(	PUNCT
ejpam-3496	131	4	9	9	NUM
ejpam-3496	131	5	)	)	PUNCT
ejpam-3496	131	6	with	with	ADP
ejpam-3496	131	7	(	(	PUNCT
ejpam-3496	131	8	5	5	NUM
ejpam-3496	131	9	)	)	PUNCT
ejpam-3496	131	10	,	,	PUNCT
ejpam-3496	131	11	we	we	PRON
ejpam-3496	131	12	get	get	VERB
ejpam-3496	131	13	2[d1(x	2[d1(x	NUM
ejpam-3496	131	14	)	)	PUNCT
ejpam-3496	131	15	,	,	PUNCT
ejpam-3496	131	16	d2(y	d2(y	PROPN
ejpam-3496	131	17	∗	∗	NOUN
ejpam-3496	131	18	)	)	PUNCT
ejpam-3496	131	19	]	]	PUNCT
ejpam-3496	132	1	=	=	PUNCT
ejpam-3496	132	2	0	0	NUM
ejpam-3496	132	3	for	for	ADP
ejpam-3496	132	4	all	all	DET
ejpam-3496	132	5	x	x	NOUN
ejpam-3496	132	6	,	,	PUNCT
ejpam-3496	132	7	y	y	PROPN
ejpam-3496	132	8	∈	∈	PROPN
ejpam-3496	132	9	r.	r.	PROPN
ejpam-3496	132	10	the	the	DET
ejpam-3496	132	11	last	last	ADJ
ejpam-3496	132	12	relation	relation	NOUN
ejpam-3496	132	13	gives	give	VERB
ejpam-3496	132	14	,	,	PUNCT
ejpam-3496	132	15	[	[	X
ejpam-3496	132	16	d1(x	d1(x	NOUN
ejpam-3496	132	17	)	)	PUNCT
ejpam-3496	132	18	,	,	PUNCT
ejpam-3496	132	19	d2(y	d2(y	PROPN
ejpam-3496	132	20	)	)	PUNCT
ejpam-3496	132	21	]	]	PUNCT
ejpam-3496	133	1	=	=	PUNCT
ejpam-3496	133	2	0	0	NUM
ejpam-3496	133	3	for	for	ADP
ejpam-3496	133	4	all	all	DET
ejpam-3496	133	5	x	x	NOUN
ejpam-3496	133	6	,	,	PUNCT
ejpam-3496	133	7	y	y	PROPN
ejpam-3496	133	8	∈	∈	PROPN
ejpam-3496	133	9	r.	r.	PROPN
ejpam-3496	133	10	this	this	PRON
ejpam-3496	133	11	implies	imply	VERB
ejpam-3496	133	12	that	that	SCONJ
ejpam-3496	133	13	[	[	X
ejpam-3496	133	14	d1(x	d1(x	NOUN
ejpam-3496	133	15	)	)	PUNCT
ejpam-3496	133	16	,	,	PUNCT
ejpam-3496	133	17	d2(x	d2(x	PROPN
ejpam-3496	133	18	)	)	PUNCT
ejpam-3496	133	19	]	]	PUNCT
ejpam-3496	134	1	=	=	PUNCT
ejpam-3496	134	2	0	0	PUNCT
ejpam-3496	134	3	for	for	SCONJ
ejpam-3496	134	4	all	all	DET
ejpam-3496	134	5	x	x	SYM
ejpam-3496	134	6	∈	∈	PROPN
ejpam-3496	134	7	r.	r.	NOUN
ejpam-3496	134	8	hence	hence	ADV
ejpam-3496	134	9	in	in	ADP
ejpam-3496	134	10	view	view	NOUN
ejpam-3496	134	11	of	of	ADP
ejpam-3496	134	12	[	[	X
ejpam-3496	134	13	15	15	NUM
ejpam-3496	134	14	,	,	PUNCT
ejpam-3496	134	15	theorem	theorem	VERB
ejpam-3496	134	16	4	4	NUM
ejpam-3496	134	17	]	]	PUNCT
ejpam-3496	134	18	,	,	PUNCT
ejpam-3496	134	19	we	we	PRON
ejpam-3496	134	20	conclude	conclude	VERB
ejpam-3496	134	21	that	that	SCONJ
ejpam-3496	134	22	d1	d1	PROPN
ejpam-3496	134	23	=	=	SYM
ejpam-3496	134	24	λd2	λd2	PROPN
ejpam-3496	134	25	,	,	PUNCT
ejpam-3496	134	26	where	where	SCONJ
ejpam-3496	134	27	λ	λ	PROPN
ejpam-3496	134	28	∈	∈	PROPN
ejpam-3496	134	29	c.	c.	NOUN
ejpam-3496	134	30	this	this	PRON
ejpam-3496	134	31	completes	complete	VERB
ejpam-3496	134	32	the	the	DET
ejpam-3496	134	33	proof	proof	NOUN
ejpam-3496	134	34	of	of	ADP
ejpam-3496	134	35	the	the	DET
ejpam-3496	134	36	theorem	theorem	PROPN
ejpam-3496	134	37	.	.	PUNCT
ejpam-3496	134	38	�	�	PROPN
ejpam-3496	134	39	s.	s.	PROPN
ejpam-3496	134	40	ali	ali	PROPN
ejpam-3496	134	41	et	et	PROPN
ejpam-3496	134	42	al	al	PROPN
ejpam-3496	134	43	.	.	PUNCT
ejpam-3496	134	44	/	/	SYM
ejpam-3496	134	45	eur	eur	PROPN
ejpam-3496	134	46	.	.	PUNCT
ejpam-3496	135	1	j.	j.	PROPN
ejpam-3496	135	2	pure	pure	PROPN
ejpam-3496	135	3	appl	appl	PROPN
ejpam-3496	135	4	.	.	PROPN
ejpam-3496	135	5	math	math	PROPN
ejpam-3496	135	6	,	,	PUNCT
ejpam-3496	135	7	12	12	NUM
ejpam-3496	135	8	(	(	PUNCT
ejpam-3496	135	9	3	3	NUM
ejpam-3496	135	10	)	)	PUNCT
ejpam-3496	135	11	(	(	PUNCT
ejpam-3496	135	12	2019	2019	NUM
ejpam-3496	135	13	)	)	PUNCT
ejpam-3496	135	14	,	,	PUNCT
ejpam-3496	135	15	1138	1138	NUM
ejpam-3496	135	16	-	-	SYM
ejpam-3496	135	17	1148	1148	NUM
ejpam-3496	135	18	1142	1142	NUM
ejpam-3496	135	19	corollary	corollary	NOUN
ejpam-3496	135	20	1	1	NUM
ejpam-3496	135	21	.	.	PUNCT
ejpam-3496	136	1	let	let	VERB
ejpam-3496	136	2	r	r	PRON
ejpam-3496	136	3	be	be	AUX
ejpam-3496	136	4	a	a	DET
ejpam-3496	136	5	2	2	NUM
ejpam-3496	136	6	-	-	PUNCT
ejpam-3496	136	7	torsion	torsion	NOUN
ejpam-3496	136	8	free	free	ADJ
ejpam-3496	136	9	noncommutative	noncommutative	ADJ
ejpam-3496	136	10	prime	prime	ADJ
ejpam-3496	136	11	ring	ring	NOUN
ejpam-3496	136	12	with	with	ADP
ejpam-3496	136	13	involution	involution	NOUN
ejpam-3496	136	14	∗	∗	NOUN
ejpam-3496	136	15	of	of	ADP
ejpam-3496	136	16	the	the	DET
ejpam-3496	136	17	second	second	ADJ
ejpam-3496	136	18	kind	kind	NOUN
ejpam-3496	136	19	and	and	CCONJ
ejpam-3496	136	20	d1	d1	PROPN
ejpam-3496	136	21	,	,	PUNCT
ejpam-3496	136	22	d2	d2	PROPN
ejpam-3496	136	23	be	be	AUX
ejpam-3496	136	24	two	two	NUM
ejpam-3496	136	25	nonzero	nonzero	ADJ
ejpam-3496	136	26	derivations	derivation	NOUN
ejpam-3496	136	27	on	on	ADP
ejpam-3496	136	28	r	r	NOUN
ejpam-3496	137	1	such	such	ADJ
ejpam-3496	137	2	that	that	SCONJ
ejpam-3496	137	3	[	[	X
ejpam-3496	137	4	d1(x	d1(x	NOUN
ejpam-3496	137	5	)	)	PUNCT
ejpam-3496	137	6	,	,	PUNCT
ejpam-3496	137	7	d2(y	d2(y	PROPN
ejpam-3496	137	8	∗	∗	NOUN
ejpam-3496	137	9	)	)	PUNCT
ejpam-3496	137	10	]	]	PUNCT
ejpam-3496	138	1	=	=	PUNCT
ejpam-3496	138	2	0	0	NUM
ejpam-3496	138	3	for	for	ADP
ejpam-3496	138	4	all	all	DET
ejpam-3496	138	5	x	x	NOUN
ejpam-3496	138	6	,	,	PUNCT
ejpam-3496	138	7	y	y	PROPN
ejpam-3496	138	8	∈	∈	PROPN
ejpam-3496	138	9	r.	r.	PROPN
ejpam-3496	138	10	then	then	ADV
ejpam-3496	138	11	d1	d1	PROPN
ejpam-3496	138	12	=	=	SYM
ejpam-3496	138	13	λd2	λd2	PROPN
ejpam-3496	138	14	,	,	PUNCT
ejpam-3496	138	15	where	where	SCONJ
ejpam-3496	138	16	λ	λ	PROPN
ejpam-3496	138	17	∈	∈	PROPN
ejpam-3496	138	18	c.	c.	PROPN
ejpam-3496	138	19	theorem	theorem	VERB
ejpam-3496	138	20	1	1	X
ejpam-3496	138	21	.	.	PUNCT
ejpam-3496	139	1	let	let	VERB
ejpam-3496	139	2	r	r	PRON
ejpam-3496	139	3	be	be	AUX
ejpam-3496	139	4	a	a	DET
ejpam-3496	139	5	2	2	NUM
ejpam-3496	139	6	-	-	PUNCT
ejpam-3496	139	7	torsion	torsion	NOUN
ejpam-3496	139	8	free	free	ADJ
ejpam-3496	139	9	noncommutative	noncommutative	ADJ
ejpam-3496	139	10	prime	prime	ADJ
ejpam-3496	139	11	ring	ring	NOUN
ejpam-3496	139	12	with	with	ADP
ejpam-3496	139	13	involution	involution	NOUN
ejpam-3496	139	14	∗	∗	NOUN
ejpam-3496	139	15	of	of	ADP
ejpam-3496	139	16	the	the	DET
ejpam-3496	139	17	second	second	ADJ
ejpam-3496	139	18	kind	kind	NOUN
ejpam-3496	139	19	and	and	CCONJ
ejpam-3496	139	20	d1	d1	PROPN
ejpam-3496	139	21	,	,	PUNCT
ejpam-3496	139	22	d2	d2	PROPN
ejpam-3496	139	23	be	be	AUX
ejpam-3496	139	24	two	two	NUM
ejpam-3496	139	25	nonzero	nonzero	ADJ
ejpam-3496	139	26	derivations	derivation	NOUN
ejpam-3496	139	27	on	on	ADP
ejpam-3496	139	28	r.	r.	PROPN
ejpam-3496	139	29	if	if	SCONJ
ejpam-3496	139	30	one	one	NUM
ejpam-3496	139	31	of	of	ADP
ejpam-3496	139	32	the	the	DET
ejpam-3496	139	33	following	follow	VERB
ejpam-3496	139	34	conditions	condition	NOUN
ejpam-3496	139	35	holds	hold	VERB
ejpam-3496	139	36	:	:	PUNCT
ejpam-3496	139	37	(	(	PUNCT
ejpam-3496	139	38	i	i	NOUN
ejpam-3496	139	39	)	)	PUNCT
ejpam-3496	140	1	[	[	X
ejpam-3496	140	2	d1(x	d1(x	NOUN
ejpam-3496	140	3	)	)	PUNCT
ejpam-3496	140	4	,	,	PUNCT
ejpam-3496	140	5	d2(x	d2(x	NOUN
ejpam-3496	140	6	∗	∗	NOUN
ejpam-3496	140	7	)	)	PUNCT
ejpam-3496	140	8	]	]	PUNCT
ejpam-3496	141	1	=	=	PUNCT
ejpam-3496	142	1	[	[	X
ejpam-3496	142	2	x	x	X
ejpam-3496	142	3	,	,	PUNCT
ejpam-3496	142	4	x∗	x∗	PROPN
ejpam-3496	142	5	]	]	PUNCT
ejpam-3496	142	6	for	for	ADP
ejpam-3496	142	7	all	all	DET
ejpam-3496	142	8	x	x	SYM
ejpam-3496	142	9	∈	∈	PROPN
ejpam-3496	142	10	r	r	NOUN
ejpam-3496	142	11	,	,	PUNCT
ejpam-3496	142	12	(	(	PUNCT
ejpam-3496	142	13	ii	ii	NOUN
ejpam-3496	142	14	)	)	PUNCT
ejpam-3496	142	15	[	[	X
ejpam-3496	142	16	d1(x	d1(x	NOUN
ejpam-3496	142	17	)	)	PUNCT
ejpam-3496	142	18	,	,	PUNCT
ejpam-3496	142	19	d2(x	d2(x	NOUN
ejpam-3496	142	20	∗	∗	NOUN
ejpam-3496	142	21	)	)	PUNCT
ejpam-3496	142	22	]	]	PUNCT
ejpam-3496	142	23	=	=	PUNCT
ejpam-3496	142	24	−[x	−[x	PROPN
ejpam-3496	142	25	,	,	PUNCT
ejpam-3496	142	26	x∗	x∗	PROPN
ejpam-3496	142	27	]	]	PUNCT
ejpam-3496	142	28	for	for	ADP
ejpam-3496	142	29	all	all	DET
ejpam-3496	142	30	x	x	SYM
ejpam-3496	142	31	∈	∈	PROPN
ejpam-3496	142	32	r	r	NOUN
ejpam-3496	142	33	,	,	PUNCT
ejpam-3496	142	34	then	then	ADV
ejpam-3496	142	35	d1	d1	PROPN
ejpam-3496	142	36	=	=	SYM
ejpam-3496	142	37	λd2	λd2	PROPN
ejpam-3496	142	38	,	,	PUNCT
ejpam-3496	142	39	where	where	SCONJ
ejpam-3496	142	40	λ	λ	PROPN
ejpam-3496	142	41	∈	∈	PROPN
ejpam-3496	142	42	c.	c.	NOUN
ejpam-3496	142	43	proof	proof	NOUN
ejpam-3496	142	44	.	.	PUNCT
ejpam-3496	143	1	by	by	ADP
ejpam-3496	143	2	the	the	DET
ejpam-3496	143	3	given	give	VERB
ejpam-3496	143	4	assumption	assumption	NOUN
ejpam-3496	143	5	,	,	PUNCT
ejpam-3496	143	6	we	we	PRON
ejpam-3496	143	7	have	have	VERB
ejpam-3496	143	8	[	[	X
ejpam-3496	143	9	d1(x	d1(x	NOUN
ejpam-3496	143	10	)	)	PUNCT
ejpam-3496	143	11	,	,	PUNCT
ejpam-3496	143	12	d2(x	d2(x	NOUN
ejpam-3496	143	13	∗	∗	NOUN
ejpam-3496	143	14	)	)	PUNCT
ejpam-3496	143	15	]	]	PUNCT
ejpam-3496	144	1	=	=	PUNCT
ejpam-3496	145	1	[	[	X
ejpam-3496	145	2	x	x	X
ejpam-3496	145	3	,	,	PUNCT
ejpam-3496	145	4	x∗	x∗	PROPN
ejpam-3496	145	5	]	]	PUNCT
ejpam-3496	145	6	for	for	ADP
ejpam-3496	145	7	all	all	DET
ejpam-3496	145	8	x	x	PROPN
ejpam-3496	145	9	∈	∈	PROPN
ejpam-3496	145	10	r.	r.	NOUN
ejpam-3496	145	11	(	(	PUNCT
ejpam-3496	145	12	10	10	NUM
ejpam-3496	145	13	)	)	PUNCT
ejpam-3496	145	14	a	a	DET
ejpam-3496	145	15	linearization	linearization	NOUN
ejpam-3496	145	16	of	of	ADP
ejpam-3496	145	17	(	(	PUNCT
ejpam-3496	145	18	10	10	NUM
ejpam-3496	145	19	)	)	PUNCT
ejpam-3496	145	20	yields	yield	NOUN
ejpam-3496	145	21	that	that	PUNCT
ejpam-3496	145	22	[	[	X
ejpam-3496	145	23	d1(x	d1(x	NOUN
ejpam-3496	145	24	)	)	PUNCT
ejpam-3496	145	25	,	,	PUNCT
ejpam-3496	145	26	d2(y	d2(y	PROPN
ejpam-3496	145	27	∗	∗	NOUN
ejpam-3496	145	28	)	)	PUNCT
ejpam-3496	145	29	]	]	PUNCT
ejpam-3496	146	1	+	+	CCONJ
ejpam-3496	147	1	[	[	X
ejpam-3496	147	2	d1(y	d1(y	X
ejpam-3496	147	3	)	)	PUNCT
ejpam-3496	147	4	,	,	PUNCT
ejpam-3496	147	5	d2(x	d2(x	PROPN
ejpam-3496	147	6	∗	∗	NOUN
ejpam-3496	147	7	)	)	PUNCT
ejpam-3496	147	8	]	]	PUNCT
ejpam-3496	148	1	=	=	PUNCT
ejpam-3496	149	1	[	[	X
ejpam-3496	149	2	x	x	X
ejpam-3496	149	3	,	,	PUNCT
ejpam-3496	149	4	y∗	y∗	PROPN
ejpam-3496	149	5	]	]	PUNCT
ejpam-3496	150	1	+	+	CCONJ
ejpam-3496	150	2	[	[	X
ejpam-3496	150	3	y	y	NOUN
ejpam-3496	150	4	,	,	PUNCT
ejpam-3496	150	5	x∗	x∗	PROPN
ejpam-3496	150	6	]	]	PUNCT
ejpam-3496	150	7	for	for	ADP
ejpam-3496	150	8	all	all	DET
ejpam-3496	150	9	x	x	NOUN
ejpam-3496	150	10	,	,	PUNCT
ejpam-3496	150	11	y	y	PROPN
ejpam-3496	150	12	∈	∈	PROPN
ejpam-3496	150	13	r.	r.	PROPN
ejpam-3496	150	14	(	(	PUNCT
ejpam-3496	150	15	11	11	NUM
ejpam-3496	150	16	)	)	PUNCT
ejpam-3496	150	17	replace	replace	VERB
ejpam-3496	150	18	y	y	PROPN
ejpam-3496	150	19	by	by	ADP
ejpam-3496	150	20	hy	hy	NOUN
ejpam-3496	150	21	in	in	ADP
ejpam-3496	150	22	(	(	PUNCT
ejpam-3496	150	23	11	11	NUM
ejpam-3496	150	24	)	)	PUNCT
ejpam-3496	150	25	,	,	PUNCT
ejpam-3496	150	26	where	where	SCONJ
ejpam-3496	150	27	h	h	PROPN
ejpam-3496	150	28	∈	∈	PROPN
ejpam-3496	150	29	h(r	h(r	NOUN
ejpam-3496	150	30	)	)	PUNCT
ejpam-3496	150	31	∩	∩	NOUN
ejpam-3496	150	32	z(r	z(r	NOUN
ejpam-3496	150	33	)	)	PUNCT
ejpam-3496	150	34	,	,	PUNCT
ejpam-3496	150	35	we	we	PRON
ejpam-3496	150	36	get	get	VERB
ejpam-3496	150	37	[	[	X
ejpam-3496	150	38	d1(x	d1(x	NOUN
ejpam-3496	150	39	)	)	PUNCT
ejpam-3496	150	40	,	,	PUNCT
ejpam-3496	150	41	d2((hy)∗	d2((hy)∗	PROPN
ejpam-3496	150	42	)	)	PUNCT
ejpam-3496	150	43	]	]	PUNCT
ejpam-3496	151	1	+	+	CCONJ
ejpam-3496	151	2	[	[	X
ejpam-3496	151	3	d1(hy	d1(hy	PROPN
ejpam-3496	151	4	)	)	PUNCT
ejpam-3496	151	5	,	,	PUNCT
ejpam-3496	151	6	d2(x	d2(x	NOUN
ejpam-3496	151	7	∗	∗	NOUN
ejpam-3496	151	8	)	)	PUNCT
ejpam-3496	151	9	]	]	PUNCT
ejpam-3496	152	1	=	=	PUNCT
ejpam-3496	153	1	[	[	X
ejpam-3496	153	2	x	x	X
ejpam-3496	153	3	,	,	PUNCT
ejpam-3496	153	4	(	(	PUNCT
ejpam-3496	153	5	hy)∗	hy)∗	PROPN
ejpam-3496	153	6	]	]	X
ejpam-3496	153	7	+	+	CCONJ
ejpam-3496	153	8	[	[	X
ejpam-3496	153	9	hy	hy	X
ejpam-3496	153	10	,	,	PUNCT
ejpam-3496	153	11	x∗	x∗	PROPN
ejpam-3496	153	12	]	]	PUNCT
ejpam-3496	153	13	(	(	PUNCT
ejpam-3496	153	14	12	12	NUM
ejpam-3496	153	15	)	)	PUNCT
ejpam-3496	153	16	for	for	ADP
ejpam-3496	153	17	all	all	DET
ejpam-3496	153	18	x	x	NOUN
ejpam-3496	153	19	,	,	PUNCT
ejpam-3496	153	20	y	y	PROPN
ejpam-3496	153	21	∈	∈	PROPN
ejpam-3496	153	22	r	r	NOUN
ejpam-3496	153	23	and	and	CCONJ
ejpam-3496	153	24	h	h	NOUN
ejpam-3496	153	25	∈	∈	PROPN
ejpam-3496	153	26	h(r	h(r	NOUN
ejpam-3496	153	27	)	)	PUNCT
ejpam-3496	153	28	∩	∩	NOUN
ejpam-3496	153	29	z(r	z(r	NOUN
ejpam-3496	153	30	)	)	PUNCT
ejpam-3496	153	31	.	.	PUNCT
ejpam-3496	154	1	on	on	ADP
ejpam-3496	154	2	solving	solve	VERB
ejpam-3496	154	3	,	,	PUNCT
ejpam-3496	154	4	we	we	PRON
ejpam-3496	154	5	obtain	obtain	VERB
ejpam-3496	154	6	[	[	X
ejpam-3496	154	7	d1(x	d1(x	NOUN
ejpam-3496	154	8	)	)	PUNCT
ejpam-3496	154	9	,	,	PUNCT
ejpam-3496	154	10	y∗]d2(h	y∗]d2(h	PROPN
ejpam-3496	154	11	)	)	PUNCT
ejpam-3496	155	1	+	+	CCONJ
ejpam-3496	156	1	[	[	X
ejpam-3496	156	2	y	y	X
ejpam-3496	156	3	,	,	PUNCT
ejpam-3496	156	4	d2(x	d2(x	PROPN
ejpam-3496	156	5	∗)]d1(h)+	∗)]d1(h)+	X
ejpam-3496	156	6	(	(	PUNCT
ejpam-3496	156	7	13	13	NUM
ejpam-3496	156	8	)	)	PUNCT
ejpam-3496	156	9	h([d1(x	h([d1(x	PROPN
ejpam-3496	156	10	)	)	PUNCT
ejpam-3496	156	11	,	,	PUNCT
ejpam-3496	156	12	d2(y	d2(y	PROPN
ejpam-3496	156	13	∗	∗	NOUN
ejpam-3496	156	14	)	)	PUNCT
ejpam-3496	156	15	]	]	PUNCT
ejpam-3496	157	1	+	+	CCONJ
ejpam-3496	158	1	[	[	X
ejpam-3496	158	2	d1(y	d1(y	X
ejpam-3496	158	3	)	)	PUNCT
ejpam-3496	158	4	,	,	PUNCT
ejpam-3496	158	5	d2(x	d2(x	PROPN
ejpam-3496	158	6	∗	∗	NOUN
ejpam-3496	158	7	)	)	PUNCT
ejpam-3496	158	8	]	]	PUNCT
ejpam-3496	158	9	)	)	PUNCT
ejpam-3496	159	1	=	=	SYM
ejpam-3496	159	2	(	(	PUNCT
ejpam-3496	159	3	[	[	X
ejpam-3496	159	4	x	x	X
ejpam-3496	159	5	,	,	PUNCT
ejpam-3496	159	6	y∗	y∗	PROPN
ejpam-3496	159	7	]	]	PUNCT
ejpam-3496	160	1	+	+	CCONJ
ejpam-3496	161	1	[	[	X
ejpam-3496	161	2	y	y	X
ejpam-3496	161	3	,	,	PUNCT
ejpam-3496	161	4	x∗])h	x∗])h	VERB
ejpam-3496	161	5	for	for	ADP
ejpam-3496	161	6	all	all	DET
ejpam-3496	161	7	x	x	NOUN
ejpam-3496	161	8	,	,	PUNCT
ejpam-3496	161	9	y	y	PROPN
ejpam-3496	161	10	∈	∈	PROPN
ejpam-3496	161	11	r	r	NOUN
ejpam-3496	161	12	and	and	CCONJ
ejpam-3496	161	13	h	h	NOUN
ejpam-3496	161	14	∈	∈	PROPN
ejpam-3496	161	15	h(r	h(r	NOUN
ejpam-3496	161	16	)	)	PUNCT
ejpam-3496	161	17	∩	∩	NOUN
ejpam-3496	161	18	z(r	z(r	NOUN
ejpam-3496	161	19	)	)	PUNCT
ejpam-3496	161	20	.	.	PUNCT
ejpam-3496	162	1	multiplying	multiply	VERB
ejpam-3496	162	2	(	(	PUNCT
ejpam-3496	162	3	11	11	NUM
ejpam-3496	162	4	)	)	PUNCT
ejpam-3496	162	5	by	by	ADP
ejpam-3496	162	6	h	h	NOUN
ejpam-3496	162	7	and	and	CCONJ
ejpam-3496	162	8	adding	add	VERB
ejpam-3496	162	9	with	with	ADP
ejpam-3496	162	10	(	(	PUNCT
ejpam-3496	162	11	13	13	NUM
ejpam-3496	162	12	)	)	PUNCT
ejpam-3496	162	13	,	,	PUNCT
ejpam-3496	162	14	we	we	PRON
ejpam-3496	162	15	arrive	arrive	VERB
ejpam-3496	162	16	at	at	ADP
ejpam-3496	162	17	[	[	X
ejpam-3496	162	18	d1(x	d1(x	NOUN
ejpam-3496	162	19	)	)	PUNCT
ejpam-3496	162	20	,	,	PUNCT
ejpam-3496	162	21	y∗]d2(h	y∗]d2(h	PROPN
ejpam-3496	162	22	)	)	PUNCT
ejpam-3496	162	23	+	+	CCONJ
ejpam-3496	163	1	[	[	X
ejpam-3496	163	2	y	y	PROPN
ejpam-3496	163	3	,	,	PUNCT
ejpam-3496	163	4	d2(x	d2(x	PROPN
ejpam-3496	163	5	∗)]d1(h	∗)]d1(h	X
ejpam-3496	163	6	)	)	PUNCT
ejpam-3496	163	7	=	=	SYM
ejpam-3496	163	8	0	0	NUM
ejpam-3496	163	9	(	(	PUNCT
ejpam-3496	163	10	14	14	NUM
ejpam-3496	163	11	)	)	PUNCT
ejpam-3496	163	12	for	for	ADP
ejpam-3496	163	13	all	all	DET
ejpam-3496	163	14	x	x	NOUN
ejpam-3496	163	15	,	,	PUNCT
ejpam-3496	163	16	y	y	PROPN
ejpam-3496	163	17	∈	∈	PROPN
ejpam-3496	163	18	r	r	NOUN
ejpam-3496	163	19	and	and	CCONJ
ejpam-3496	163	20	h	h	NOUN
ejpam-3496	163	21	∈	∈	PROPN
ejpam-3496	163	22	h(r)∩z(r	h(r)∩z(r	NOUN
ejpam-3496	163	23	)	)	PUNCT
ejpam-3496	163	24	.	.	PUNCT
ejpam-3496	164	1	replacing	replace	VERB
ejpam-3496	164	2	y	y	PRON
ejpam-3496	164	3	by	by	ADP
ejpam-3496	164	4	ky	ky	PROPN
ejpam-3496	164	5	,	,	PUNCT
ejpam-3496	164	6	where	where	SCONJ
ejpam-3496	164	7	k	k	PROPN
ejpam-3496	164	8	∈	∈	PROPN
ejpam-3496	164	9	s(r)∩z(r	s(r)∩z(r	PUNCT
ejpam-3496	164	10	)	)	PUNCT
ejpam-3496	164	11	,	,	PUNCT
ejpam-3496	164	12	we	we	PRON
ejpam-3496	164	13	get	get	VERB
ejpam-3496	164	14	−[d1(x	−[d1(x	NOUN
ejpam-3496	164	15	)	)	PUNCT
ejpam-3496	164	16	,	,	PUNCT
ejpam-3496	164	17	y∗]kd2(h	y∗]kd2(h	NUM
ejpam-3496	164	18	)	)	PUNCT
ejpam-3496	165	1	+	+	NUM
ejpam-3496	165	2	d1(h)k[y	d1(h)k[y	PROPN
ejpam-3496	165	3	,	,	PUNCT
ejpam-3496	165	4	d2(x	d2(x	NOUN
ejpam-3496	165	5	∗	∗	NOUN
ejpam-3496	165	6	)	)	PUNCT
ejpam-3496	165	7	]	]	PUNCT
ejpam-3496	166	1	=	=	PUNCT
ejpam-3496	166	2	0	0	NUM
ejpam-3496	166	3	for	for	ADP
ejpam-3496	166	4	all	all	DET
ejpam-3496	166	5	x	x	NOUN
ejpam-3496	166	6	,	,	PUNCT
ejpam-3496	166	7	y	y	PROPN
ejpam-3496	166	8	∈	∈	PROPN
ejpam-3496	166	9	r.	r.	PROPN
ejpam-3496	166	10	(	(	PUNCT
ejpam-3496	166	11	15	15	NUM
ejpam-3496	166	12	)	)	PUNCT
ejpam-3496	166	13	multiplying	multiplying	NOUN
ejpam-3496	166	14	(	(	PUNCT
ejpam-3496	166	15	14	14	NUM
ejpam-3496	166	16	)	)	PUNCT
ejpam-3496	166	17	by	by	ADP
ejpam-3496	166	18	k	k	PROPN
ejpam-3496	166	19	and	and	CCONJ
ejpam-3496	166	20	adding	add	VERB
ejpam-3496	166	21	with	with	ADP
ejpam-3496	166	22	(	(	PUNCT
ejpam-3496	166	23	15	15	NUM
ejpam-3496	166	24	)	)	PUNCT
ejpam-3496	166	25	,	,	PUNCT
ejpam-3496	166	26	we	we	PRON
ejpam-3496	166	27	obtain	obtain	VERB
ejpam-3496	166	28	2d1(h)k[y	2d1(h)k[y	NOUN
ejpam-3496	166	29	,	,	PUNCT
ejpam-3496	166	30	d2(x	d2(x	NOUN
ejpam-3496	166	31	∗	∗	NOUN
ejpam-3496	166	32	)	)	PUNCT
ejpam-3496	166	33	]	]	PUNCT
ejpam-3496	167	1	=	=	PUNCT
ejpam-3496	167	2	0	0	NUM
ejpam-3496	167	3	for	for	ADP
ejpam-3496	167	4	all	all	DET
ejpam-3496	167	5	x	x	NOUN
ejpam-3496	167	6	,	,	PUNCT
ejpam-3496	167	7	y	y	PROPN
ejpam-3496	167	8	∈	∈	PROPN
ejpam-3496	167	9	r.	r.	NOUN
ejpam-3496	167	10	this	this	PRON
ejpam-3496	167	11	implies	imply	VERB
ejpam-3496	167	12	that	that	SCONJ
ejpam-3496	167	13	d1(h)k[y	d1(h)k[y	NOUN
ejpam-3496	167	14	,	,	PUNCT
ejpam-3496	167	15	d2(x	d2(x	NOUN
ejpam-3496	167	16	∗	∗	NOUN
ejpam-3496	167	17	)	)	PUNCT
ejpam-3496	167	18	]	]	PUNCT
ejpam-3496	167	19	=	=	PUNCT
ejpam-3496	167	20	0	0	NUM
ejpam-3496	167	21	for	for	ADP
ejpam-3496	167	22	all	all	DET
ejpam-3496	167	23	x	x	NOUN
ejpam-3496	167	24	,	,	PUNCT
ejpam-3496	167	25	y	y	PROPN
ejpam-3496	167	26	∈	∈	PROPN
ejpam-3496	167	27	r.	r.	NOUN
ejpam-3496	167	28	using	use	VERB
ejpam-3496	167	29	the	the	DET
ejpam-3496	167	30	primeness	primeness	NOUN
ejpam-3496	167	31	of	of	ADP
ejpam-3496	167	32	the	the	DET
ejpam-3496	167	33	ring	ring	NOUN
ejpam-3496	167	34	r	r	NOUN
ejpam-3496	167	35	and	and	CCONJ
ejpam-3496	167	36	the	the	DET
ejpam-3496	167	37	fact	fact	NOUN
ejpam-3496	167	38	that	that	SCONJ
ejpam-3496	167	39	s(r	s(r	NOUN
ejpam-3496	167	40	)	)	PUNCT
ejpam-3496	167	41	∩	∩	NOUN
ejpam-3496	167	42	z(r	z(r	NOUN
ejpam-3496	167	43	)	)	PUNCT
ejpam-3496	167	44	6=	6=	NUM
ejpam-3496	167	45	(	(	PUNCT
ejpam-3496	167	46	0	0	NUM
ejpam-3496	167	47	)	)	PUNCT
ejpam-3496	167	48	,	,	PUNCT
ejpam-3496	167	49	we	we	PRON
ejpam-3496	167	50	arrive	arrive	VERB
ejpam-3496	167	51	at	at	ADP
ejpam-3496	167	52	either	either	DET
ejpam-3496	167	53	d1(h	d1(h	PROPN
ejpam-3496	167	54	)	)	PUNCT
ejpam-3496	167	55	=	=	SYM
ejpam-3496	167	56	0	0	NUM
ejpam-3496	167	57	or	or	CCONJ
ejpam-3496	167	58	[	[	X
ejpam-3496	167	59	y	y	PROPN
ejpam-3496	167	60	,	,	PUNCT
ejpam-3496	167	61	d2(x	d2(x	ADJ
ejpam-3496	167	62	∗	∗	NOUN
ejpam-3496	167	63	)	)	PUNCT
ejpam-3496	167	64	]	]	PUNCT
ejpam-3496	168	1	=	=	PUNCT
ejpam-3496	168	2	0	0	NUM
ejpam-3496	168	3	for	for	ADP
ejpam-3496	168	4	all	all	DET
ejpam-3496	168	5	x	x	NOUN
ejpam-3496	168	6	,	,	PUNCT
ejpam-3496	168	7	y	y	PROPN
ejpam-3496	168	8	∈	∈	PROPN
ejpam-3496	168	9	r.	r.	PROPN
ejpam-3496	168	10	(	(	PUNCT
ejpam-3496	168	11	16	16	NUM
ejpam-3496	168	12	)	)	PUNCT
ejpam-3496	168	13	s.	s.	PROPN
ejpam-3496	168	14	ali	ali	PROPN
ejpam-3496	168	15	et	et	PROPN
ejpam-3496	168	16	al	al	PROPN
ejpam-3496	168	17	.	.	PUNCT
ejpam-3496	168	18	/	/	SYM
ejpam-3496	168	19	eur	eur	PROPN
ejpam-3496	168	20	.	.	PUNCT
ejpam-3496	169	1	j.	j.	PROPN
ejpam-3496	169	2	pure	pure	PROPN
ejpam-3496	169	3	appl	appl	PROPN
ejpam-3496	169	4	.	.	PROPN
ejpam-3496	169	5	math	math	PROPN
ejpam-3496	169	6	,	,	PUNCT
ejpam-3496	169	7	12	12	NUM
ejpam-3496	169	8	(	(	PUNCT
ejpam-3496	169	9	3	3	NUM
ejpam-3496	169	10	)	)	PUNCT
ejpam-3496	169	11	(	(	PUNCT
ejpam-3496	169	12	2019	2019	NUM
ejpam-3496	169	13	)	)	PUNCT
ejpam-3496	169	14	,	,	PUNCT
ejpam-3496	169	15	1138	1138	NUM
ejpam-3496	169	16	-	-	SYM
ejpam-3496	169	17	1148	1148	NUM
ejpam-3496	169	18	1143	1143	NUM
ejpam-3496	170	1	[	[	X
ejpam-3496	170	2	y	y	X
ejpam-3496	170	3	,	,	PUNCT
ejpam-3496	170	4	d2(x	d2(x	NOUN
ejpam-3496	170	5	∗	∗	NOUN
ejpam-3496	170	6	)	)	PUNCT
ejpam-3496	170	7	]	]	PUNCT
ejpam-3496	170	8	=	=	PUNCT
ejpam-3496	170	9	0	0	NUM
ejpam-3496	170	10	for	for	ADP
ejpam-3496	170	11	all	all	DET
ejpam-3496	170	12	x	x	NOUN
ejpam-3496	170	13	,	,	PUNCT
ejpam-3496	170	14	y	y	PROPN
ejpam-3496	170	15	∈	∈	PROPN
ejpam-3496	170	16	r	r	NOUN
ejpam-3496	170	17	implies	imply	VERB
ejpam-3496	170	18	that	that	SCONJ
ejpam-3496	170	19	r	r	NOUN
ejpam-3496	170	20	is	be	AUX
ejpam-3496	170	21	commutative	commutative	ADJ
ejpam-3496	170	22	,	,	PUNCT
ejpam-3496	170	23	a	a	DET
ejpam-3496	170	24	contradiction	contradiction	NOUN
ejpam-3496	170	25	.	.	PUNCT
ejpam-3496	171	1	therefore	therefore	ADV
ejpam-3496	171	2	we	we	PRON
ejpam-3496	171	3	are	be	AUX
ejpam-3496	171	4	left	leave	VERB
ejpam-3496	171	5	with	with	ADP
ejpam-3496	171	6	d1(h	d1(h	PROPN
ejpam-3496	171	7	)	)	PUNCT
ejpam-3496	171	8	=	=	SYM
ejpam-3496	171	9	0	0	NUM
ejpam-3496	171	10	for	for	ADP
ejpam-3496	171	11	all	all	DET
ejpam-3496	171	12	h	h	NOUN
ejpam-3496	171	13	∈	∈	PROPN
ejpam-3496	171	14	h(r	h(r	NOUN
ejpam-3496	171	15	)	)	PUNCT
ejpam-3496	171	16	∩	∩	NOUN
ejpam-3496	171	17	z(r	z(r	NOUN
ejpam-3496	171	18	)	)	PUNCT
ejpam-3496	171	19	.	.	PUNCT
ejpam-3496	172	1	using	use	VERB
ejpam-3496	172	2	this	this	PRON
ejpam-3496	172	3	in	in	ADP
ejpam-3496	172	4	(	(	PUNCT
ejpam-3496	172	5	15	15	NUM
ejpam-3496	172	6	)	)	PUNCT
ejpam-3496	172	7	,	,	PUNCT
ejpam-3496	172	8	we	we	PRON
ejpam-3496	172	9	get	get	VERB
ejpam-3496	172	10	−[d2(x	−[d2(x	NOUN
ejpam-3496	172	11	)	)	PUNCT
ejpam-3496	172	12	,	,	PUNCT
ejpam-3496	172	13	y∗]kd2(h	y∗]kd2(h	NUM
ejpam-3496	172	14	)	)	PUNCT
ejpam-3496	172	15	=	=	SYM
ejpam-3496	172	16	0	0	NUM
ejpam-3496	172	17	for	for	ADP
ejpam-3496	172	18	all	all	DET
ejpam-3496	172	19	x	x	NOUN
ejpam-3496	172	20	,	,	PUNCT
ejpam-3496	172	21	y	y	PROPN
ejpam-3496	172	22	∈	∈	PROPN
ejpam-3496	172	23	r.	r.	NOUN
ejpam-3496	172	24	the	the	DET
ejpam-3496	172	25	primeness	primeness	NOUN
ejpam-3496	172	26	of	of	ADP
ejpam-3496	172	27	r	r	NOUN
ejpam-3496	172	28	yields	yield	NOUN
ejpam-3496	172	29	that	that	PRON
ejpam-3496	172	30	d2(h	d2(h	PROPN
ejpam-3496	172	31	)	)	PUNCT
ejpam-3496	172	32	=	=	SYM
ejpam-3496	172	33	0	0	NUM
ejpam-3496	173	1	for	for	ADP
ejpam-3496	173	2	all	all	DET
ejpam-3496	173	3	h	h	NOUN
ejpam-3496	173	4	∈	∈	PROPN
ejpam-3496	173	5	h(r	h(r	NOUN
ejpam-3496	173	6	)	)	PUNCT
ejpam-3496	173	7	∩	∩	NOUN
ejpam-3496	173	8	z(r	z(r	NOUN
ejpam-3496	173	9	)	)	PUNCT
ejpam-3496	173	10	.	.	PUNCT
ejpam-3496	174	1	(	(	PUNCT
ejpam-3496	174	2	17	17	NUM
ejpam-3496	174	3	)	)	PUNCT
ejpam-3496	174	4	or	or	CCONJ
ejpam-3496	174	5	[	[	X
ejpam-3496	174	6	d1(x	d1(x	NOUN
ejpam-3496	174	7	)	)	PUNCT
ejpam-3496	174	8	,	,	PUNCT
ejpam-3496	174	9	y∗	y∗	PROPN
ejpam-3496	174	10	]	]	X
ejpam-3496	175	1	=	=	SYM
ejpam-3496	175	2	0	0	PUNCT
ejpam-3496	175	3	for	for	ADP
ejpam-3496	175	4	all	all	DET
ejpam-3496	175	5	x	x	NOUN
ejpam-3496	175	6	,	,	PUNCT
ejpam-3496	175	7	y	y	PROPN
ejpam-3496	175	8	∈	∈	PROPN
ejpam-3496	175	9	r.	r.	VERB
ejpam-3496	175	10	again	again	ADV
ejpam-3496	175	11	if	if	SCONJ
ejpam-3496	175	12	[	[	X
ejpam-3496	175	13	d1(x	d1(x	NOUN
ejpam-3496	175	14	)	)	PUNCT
ejpam-3496	175	15	,	,	PUNCT
ejpam-3496	175	16	y∗	y∗	PROPN
ejpam-3496	175	17	]	]	X
ejpam-3496	176	1	=	=	SYM
ejpam-3496	176	2	0	0	PUNCT
ejpam-3496	176	3	for	for	ADP
ejpam-3496	176	4	all	all	DET
ejpam-3496	176	5	x	x	NOUN
ejpam-3496	176	6	,	,	PUNCT
ejpam-3496	176	7	y	y	PROPN
ejpam-3496	176	8	∈	∈	PROPN
ejpam-3496	176	9	r	r	NOUN
ejpam-3496	176	10	,	,	PUNCT
ejpam-3496	176	11	we	we	PRON
ejpam-3496	176	12	get	get	VERB
ejpam-3496	176	13	a	a	DET
ejpam-3496	176	14	contradiction	contradiction	NOUN
ejpam-3496	176	15	.	.	PUNCT
ejpam-3496	177	1	therefore	therefore	ADV
ejpam-3496	177	2	we	we	PRON
ejpam-3496	177	3	are	be	AUX
ejpam-3496	177	4	left	leave	VERB
ejpam-3496	177	5	with	with	ADP
ejpam-3496	177	6	d2(h	d2(h	PROPN
ejpam-3496	177	7	)	)	PUNCT
ejpam-3496	177	8	=	=	NOUN
ejpam-3496	178	1	0	0	X
ejpam-3496	178	2	.	.	PUNCT
ejpam-3496	179	1	this	this	PRON
ejpam-3496	179	2	implies	imply	VERB
ejpam-3496	179	3	that	that	SCONJ
ejpam-3496	179	4	d2(k	d2(k	PROPN
ejpam-3496	179	5	)	)	PUNCT
ejpam-3496	179	6	=	=	SYM
ejpam-3496	179	7	0	0	NUM
ejpam-3496	179	8	and	and	CCONJ
ejpam-3496	179	9	hence	hence	ADV
ejpam-3496	179	10	d2(z(r	d2(z(r	NUM
ejpam-3496	179	11	)	)	PUNCT
ejpam-3496	179	12	)	)	PUNCT
ejpam-3496	180	1	=	=	PUNCT
ejpam-3496	180	2	(	(	PUNCT
ejpam-3496	180	3	0	0	NUM
ejpam-3496	180	4	)	)	PUNCT
ejpam-3496	180	5	.	.	PUNCT
ejpam-3496	181	1	similarly	similarly	ADV
ejpam-3496	181	2	in	in	ADP
ejpam-3496	181	3	view	view	NOUN
ejpam-3496	181	4	of	of	ADP
ejpam-3496	181	5	(	(	PUNCT
ejpam-3496	181	6	16	16	NUM
ejpam-3496	181	7	)	)	PUNCT
ejpam-3496	181	8	we	we	PRON
ejpam-3496	181	9	get	get	VERB
ejpam-3496	181	10	d1(z(r	d1(z(r	PRON
ejpam-3496	181	11	)	)	PUNCT
ejpam-3496	181	12	)	)	PUNCT
ejpam-3496	181	13	=	=	PUNCT
ejpam-3496	182	1	(	(	PUNCT
ejpam-3496	182	2	0	0	NUM
ejpam-3496	182	3	)	)	PUNCT
ejpam-3496	182	4	.	.	PUNCT
ejpam-3496	183	1	now	now	ADV
ejpam-3496	183	2	on	on	ADP
ejpam-3496	183	3	replacing	replace	VERB
ejpam-3496	183	4	y	y	PRON
ejpam-3496	183	5	by	by	ADP
ejpam-3496	183	6	ky	ky	PROPN
ejpam-3496	183	7	in	in	ADP
ejpam-3496	183	8	(	(	PUNCT
ejpam-3496	183	9	11	11	NUM
ejpam-3496	183	10	)	)	PUNCT
ejpam-3496	183	11	,	,	PUNCT
ejpam-3496	183	12	where	where	SCONJ
ejpam-3496	183	13	k	k	PROPN
ejpam-3496	183	14	∈	∈	PROPN
ejpam-3496	183	15	s(r	s(r	PROPN
ejpam-3496	183	16	)	)	PUNCT
ejpam-3496	183	17	∩	∩	NOUN
ejpam-3496	183	18	z(r	z(r	NOUN
ejpam-3496	183	19	)	)	PUNCT
ejpam-3496	183	20	,	,	PUNCT
ejpam-3496	183	21	we	we	PRON
ejpam-3496	183	22	get	get	VERB
ejpam-3496	183	23	[	[	X
ejpam-3496	183	24	d1(x	d1(x	NOUN
ejpam-3496	183	25	)	)	PUNCT
ejpam-3496	183	26	,	,	PUNCT
ejpam-3496	183	27	d2((ky)∗	d2((ky)∗	NOUN
ejpam-3496	183	28	)	)	PUNCT
ejpam-3496	183	29	]	]	PUNCT
ejpam-3496	184	1	+	+	CCONJ
ejpam-3496	184	2	[	[	X
ejpam-3496	184	3	d1(ky	d1(ky	PROPN
ejpam-3496	184	4	)	)	PUNCT
ejpam-3496	184	5	,	,	PUNCT
ejpam-3496	184	6	d2(x	d2(x	NOUN
ejpam-3496	184	7	∗	∗	NOUN
ejpam-3496	184	8	)	)	PUNCT
ejpam-3496	184	9	]	]	PUNCT
ejpam-3496	185	1	=	=	PUNCT
ejpam-3496	186	1	[	[	X
ejpam-3496	186	2	x	x	X
ejpam-3496	186	3	,	,	PUNCT
ejpam-3496	186	4	(	(	PUNCT
ejpam-3496	186	5	ky)∗	ky)∗	PROPN
ejpam-3496	186	6	]	]	X
ejpam-3496	186	7	+	+	CCONJ
ejpam-3496	186	8	[	[	X
ejpam-3496	186	9	ky	ky	PROPN
ejpam-3496	186	10	,	,	PUNCT
ejpam-3496	186	11	x∗	x∗	PROPN
ejpam-3496	186	12	]	]	X
ejpam-3496	186	13	(	(	PUNCT
ejpam-3496	186	14	18	18	NUM
ejpam-3496	186	15	)	)	PUNCT
ejpam-3496	186	16	for	for	ADP
ejpam-3496	186	17	all	all	DET
ejpam-3496	186	18	x	x	NOUN
ejpam-3496	186	19	,	,	PUNCT
ejpam-3496	186	20	y	y	PROPN
ejpam-3496	186	21	∈	∈	PROPN
ejpam-3496	186	22	r	r	NOUN
ejpam-3496	186	23	and	and	CCONJ
ejpam-3496	186	24	k	k	PROPN
ejpam-3496	186	25	∈	∈	PROPN
ejpam-3496	186	26	s(r	s(r	PROPN
ejpam-3496	186	27	)	)	PUNCT
ejpam-3496	186	28	∩	∩	NOUN
ejpam-3496	186	29	z(r	z(r	NOUN
ejpam-3496	186	30	)	)	PUNCT
ejpam-3496	186	31	.	.	PUNCT
ejpam-3496	187	1	on	on	ADP
ejpam-3496	187	2	solving	solve	VERB
ejpam-3496	187	3	,	,	PUNCT
ejpam-3496	187	4	we	we	PRON
ejpam-3496	187	5	have	have	VERB
ejpam-3496	187	6	−[d1(x	−[d1(x	NUM
ejpam-3496	187	7	)	)	PUNCT
ejpam-3496	187	8	,	,	PUNCT
ejpam-3496	187	9	d2(y	d2(y	PROPN
ejpam-3496	187	10	∗)]k	∗)]k	PROPN
ejpam-3496	187	11	+	+	CCONJ
ejpam-3496	187	12	k[d1(y	k[d1(y	PROPN
ejpam-3496	187	13	)	)	PUNCT
ejpam-3496	187	14	,	,	PUNCT
ejpam-3496	188	1	d2(x	d2(x	PROPN
ejpam-3496	188	2	∗	∗	NOUN
ejpam-3496	188	3	)	)	PUNCT
ejpam-3496	188	4	]	]	PUNCT
ejpam-3496	189	1	=	=	PUNCT
ejpam-3496	189	2	−[x	−[x	PROPN
ejpam-3496	189	3	,	,	PUNCT
ejpam-3496	189	4	y∗]k	y∗]k	PROPN
ejpam-3496	190	1	+	+	PUNCT
ejpam-3496	190	2	k[y	k[y	PROPN
ejpam-3496	190	3	,	,	PUNCT
ejpam-3496	190	4	x∗	x∗	PROPN
ejpam-3496	190	5	]	]	X
ejpam-3496	190	6	(	(	PUNCT
ejpam-3496	190	7	19	19	NUM
ejpam-3496	190	8	)	)	PUNCT
ejpam-3496	190	9	for	for	ADP
ejpam-3496	190	10	all	all	DET
ejpam-3496	190	11	x	x	NOUN
ejpam-3496	190	12	,	,	PUNCT
ejpam-3496	190	13	y	y	PROPN
ejpam-3496	190	14	∈	∈	PROPN
ejpam-3496	190	15	r	r	NOUN
ejpam-3496	190	16	and	and	CCONJ
ejpam-3496	190	17	k	k	PROPN
ejpam-3496	190	18	∈	∈	PROPN
ejpam-3496	190	19	s(r	s(r	PROPN
ejpam-3496	190	20	)	)	PUNCT
ejpam-3496	190	21	∩	∩	NOUN
ejpam-3496	190	22	z(r	z(r	NOUN
ejpam-3496	190	23	)	)	PUNCT
ejpam-3496	190	24	.	.	PUNCT
ejpam-3496	191	1	multiplying	multiply	VERB
ejpam-3496	191	2	(	(	PUNCT
ejpam-3496	191	3	11	11	NUM
ejpam-3496	191	4	)	)	PUNCT
ejpam-3496	191	5	by	by	ADP
ejpam-3496	191	6	k	k	PROPN
ejpam-3496	191	7	and	and	CCONJ
ejpam-3496	191	8	adding	add	VERB
ejpam-3496	191	9	with	with	ADP
ejpam-3496	191	10	(	(	PUNCT
ejpam-3496	191	11	19	19	NUM
ejpam-3496	191	12	)	)	PUNCT
ejpam-3496	191	13	,	,	PUNCT
ejpam-3496	191	14	we	we	PRON
ejpam-3496	191	15	obtain	obtain	VERB
ejpam-3496	191	16	2k[d1(y	2k[d1(y	NUM
ejpam-3496	191	17	)	)	PUNCT
ejpam-3496	191	18	,	,	PUNCT
ejpam-3496	191	19	d2(x	d2(x	PROPN
ejpam-3496	191	20	∗	∗	NOUN
ejpam-3496	191	21	)	)	PUNCT
ejpam-3496	191	22	]	]	PUNCT
ejpam-3496	192	1	=	=	SYM
ejpam-3496	192	2	2[y	2[y	NUM
ejpam-3496	192	3	,	,	PUNCT
ejpam-3496	192	4	x∗	x∗	PROPN
ejpam-3496	192	5	]	]	PUNCT
ejpam-3496	192	6	.	.	PUNCT
ejpam-3496	193	1	since	since	SCONJ
ejpam-3496	193	2	char(r	char(r	NOUN
ejpam-3496	193	3	)	)	PUNCT
ejpam-3496	193	4	6=	6=	ADP
ejpam-3496	193	5	2	2	NUM
ejpam-3496	193	6	and	and	CCONJ
ejpam-3496	193	7	invoking	invoke	VERB
ejpam-3496	193	8	primeness	primeness	NOUN
ejpam-3496	193	9	of	of	ADP
ejpam-3496	193	10	r	r	NOUN
ejpam-3496	193	11	,	,	PUNCT
ejpam-3496	193	12	we	we	PRON
ejpam-3496	193	13	get	get	VERB
ejpam-3496	193	14	[	[	X
ejpam-3496	193	15	d1(y	d1(y	X
ejpam-3496	193	16	)	)	PUNCT
ejpam-3496	193	17	,	,	PUNCT
ejpam-3496	193	18	d2(x	d2(x	PROPN
ejpam-3496	193	19	∗	∗	NOUN
ejpam-3496	193	20	)	)	PUNCT
ejpam-3496	193	21	]	]	PUNCT
ejpam-3496	194	1	=	=	PUNCT
ejpam-3496	195	1	[	[	X
ejpam-3496	195	2	y	y	NOUN
ejpam-3496	195	3	,	,	PUNCT
ejpam-3496	195	4	x∗	x∗	PROPN
ejpam-3496	195	5	]	]	PUNCT
ejpam-3496	195	6	for	for	ADP
ejpam-3496	195	7	all	all	DET
ejpam-3496	195	8	x	x	NOUN
ejpam-3496	195	9	,	,	PUNCT
ejpam-3496	195	10	y	y	PROPN
ejpam-3496	195	11	∈	∈	PROPN
ejpam-3496	195	12	r.	r.	NOUN
ejpam-3496	195	13	hence	hence	ADV
ejpam-3496	196	1	[	[	X
ejpam-3496	196	2	d1(y	d1(y	X
ejpam-3496	196	3	)	)	PUNCT
ejpam-3496	196	4	,	,	PUNCT
ejpam-3496	196	5	d2(x	d2(x	PROPN
ejpam-3496	196	6	)	)	PUNCT
ejpam-3496	196	7	]	]	PUNCT
ejpam-3496	197	1	=	=	PUNCT
ejpam-3496	198	1	[	[	X
ejpam-3496	198	2	y	y	PROPN
ejpam-3496	198	3	,	,	PUNCT
ejpam-3496	198	4	x	x	X
ejpam-3496	198	5	]	]	X
ejpam-3496	198	6	for	for	ADP
ejpam-3496	198	7	all	all	DET
ejpam-3496	198	8	x	x	NOUN
ejpam-3496	198	9	,	,	PUNCT
ejpam-3496	198	10	y	y	PROPN
ejpam-3496	198	11	∈	∈	PROPN
ejpam-3496	198	12	r.	r.	NOUN
ejpam-3496	198	13	taking	take	VERB
ejpam-3496	198	14	y	y	PRON
ejpam-3496	198	15	for	for	ADP
ejpam-3496	198	16	x	x	SYM
ejpam-3496	198	17	,	,	PUNCT
ejpam-3496	198	18	we	we	PRON
ejpam-3496	198	19	finally	finally	ADV
ejpam-3496	198	20	arrive	arrive	VERB
ejpam-3496	198	21	at	at	ADP
ejpam-3496	198	22	[	[	X
ejpam-3496	198	23	d1(x	d1(x	NOUN
ejpam-3496	198	24	)	)	PUNCT
ejpam-3496	198	25	,	,	PUNCT
ejpam-3496	198	26	d2(x	d2(x	PROPN
ejpam-3496	198	27	)	)	PUNCT
ejpam-3496	198	28	]	]	PUNCT
ejpam-3496	199	1	=	=	PUNCT
ejpam-3496	199	2	0	0	PUNCT
ejpam-3496	199	3	for	for	SCONJ
ejpam-3496	199	4	all	all	DET
ejpam-3496	199	5	x	x	PROPN
ejpam-3496	199	6	∈	∈	PROPN
ejpam-3496	199	7	r.	r.	NOUN
ejpam-3496	199	8	thus	thus	ADV
ejpam-3496	199	9	in	in	ADP
ejpam-3496	199	10	view	view	NOUN
ejpam-3496	199	11	of	of	ADP
ejpam-3496	199	12	[	[	X
ejpam-3496	199	13	15	15	NUM
ejpam-3496	199	14	,	,	PUNCT
ejpam-3496	199	15	theorem	theorem	VERB
ejpam-3496	199	16	4	4	NUM
ejpam-3496	199	17	]	]	PUNCT
ejpam-3496	199	18	,	,	PUNCT
ejpam-3496	199	19	we	we	PRON
ejpam-3496	199	20	get	get	VERB
ejpam-3496	199	21	d1	d1	PROPN
ejpam-3496	199	22	=	=	SYM
ejpam-3496	199	23	λd2	λd2	PROPN
ejpam-3496	199	24	,	,	PUNCT
ejpam-3496	199	25	where	where	SCONJ
ejpam-3496	199	26	λ	λ	PROPN
ejpam-3496	199	27	∈	∈	PROPN
ejpam-3496	199	28	c.	c.	PROPN
ejpam-3496	199	29	(	(	PUNCT
ejpam-3496	199	30	ii	ii	PROPN
ejpam-3496	199	31	)	)	PUNCT
ejpam-3496	199	32	this	this	PRON
ejpam-3496	199	33	can	can	AUX
ejpam-3496	199	34	be	be	AUX
ejpam-3496	199	35	proved	prove	VERB
ejpam-3496	199	36	by	by	ADP
ejpam-3496	199	37	similar	similar	ADJ
ejpam-3496	199	38	manner	manner	NOUN
ejpam-3496	199	39	with	with	ADP
ejpam-3496	199	40	necessary	necessary	ADJ
ejpam-3496	199	41	variations	variation	NOUN
ejpam-3496	199	42	.	.	PUNCT
ejpam-3496	200	1	theorem	theorem	NOUN
ejpam-3496	200	2	2	2	NUM
ejpam-3496	200	3	.	.	PUNCT
ejpam-3496	201	1	let	let	VERB
ejpam-3496	201	2	r	r	PRON
ejpam-3496	201	3	be	be	AUX
ejpam-3496	201	4	a	a	DET
ejpam-3496	201	5	2	2	NUM
ejpam-3496	201	6	-	-	PUNCT
ejpam-3496	201	7	torsion	torsion	NOUN
ejpam-3496	201	8	free	free	ADJ
ejpam-3496	201	9	noncommutative	noncommutative	ADJ
ejpam-3496	201	10	prime	prime	ADJ
ejpam-3496	201	11	ring	ring	NOUN
ejpam-3496	201	12	with	with	ADP
ejpam-3496	201	13	involution	involution	NOUN
ejpam-3496	201	14	∗	∗	NOUN
ejpam-3496	201	15	of	of	ADP
ejpam-3496	201	16	the	the	DET
ejpam-3496	201	17	second	second	ADJ
ejpam-3496	201	18	kind	kind	NOUN
ejpam-3496	201	19	and	and	CCONJ
ejpam-3496	201	20	d1	d1	PROPN
ejpam-3496	201	21	,	,	PUNCT
ejpam-3496	201	22	d2	d2	PROPN
ejpam-3496	201	23	be	be	AUX
ejpam-3496	201	24	two	two	NUM
ejpam-3496	201	25	nonzero	nonzero	ADJ
ejpam-3496	201	26	derivations	derivation	NOUN
ejpam-3496	201	27	on	on	ADP
ejpam-3496	201	28	r	r	NOUN
ejpam-3496	202	1	such	such	ADJ
ejpam-3496	202	2	that	that	SCONJ
ejpam-3496	202	3	[	[	X
ejpam-3496	202	4	d1(x	d1(x	NOUN
ejpam-3496	202	5	)	)	PUNCT
ejpam-3496	202	6	,	,	PUNCT
ejpam-3496	202	7	x∗d2(x	x∗d2(x	NOUN
ejpam-3496	202	8	)	)	PUNCT
ejpam-3496	202	9	]	]	PUNCT
ejpam-3496	202	10	=	=	PUNCT
ejpam-3496	202	11	0	0	NUM
ejpam-3496	202	12	,	,	PUNCT
ejpam-3496	202	13	for	for	ADP
ejpam-3496	202	14	all	all	DET
ejpam-3496	202	15	x	x	SYM
ejpam-3496	202	16	∈	∈	PROPN
ejpam-3496	202	17	r.	r.	NOUN
ejpam-3496	202	18	then	then	ADV
ejpam-3496	202	19	d1	d1	PROPN
ejpam-3496	202	20	=	=	SYM
ejpam-3496	202	21	λd2	λd2	PROPN
ejpam-3496	202	22	,	,	PUNCT
ejpam-3496	202	23	where	where	SCONJ
ejpam-3496	202	24	λ	λ	PROPN
ejpam-3496	202	25	∈	∈	PROPN
ejpam-3496	202	26	c.	c.	NOUN
ejpam-3496	202	27	proof	proof	NOUN
ejpam-3496	202	28	.	.	PUNCT
ejpam-3496	203	1	by	by	ADP
ejpam-3496	203	2	the	the	DET
ejpam-3496	203	3	assumption	assumption	NOUN
ejpam-3496	203	4	,	,	PUNCT
ejpam-3496	203	5	we	we	PRON
ejpam-3496	203	6	have	have	VERB
ejpam-3496	203	7	[	[	X
ejpam-3496	203	8	d1(x	d1(x	NOUN
ejpam-3496	203	9	)	)	PUNCT
ejpam-3496	203	10	,	,	PUNCT
ejpam-3496	203	11	x∗d2(x	x∗d2(x	NOUN
ejpam-3496	203	12	)	)	PUNCT
ejpam-3496	203	13	]	]	PUNCT
ejpam-3496	204	1	=	=	PUNCT
ejpam-3496	204	2	0	0	PUNCT
ejpam-3496	204	3	for	for	ADP
ejpam-3496	204	4	all	all	DET
ejpam-3496	204	5	x	x	PROPN
ejpam-3496	204	6	∈	∈	PROPN
ejpam-3496	204	7	r.	r.	NOUN
ejpam-3496	204	8	(	(	PUNCT
ejpam-3496	204	9	20	20	NUM
ejpam-3496	204	10	)	)	PUNCT
ejpam-3496	204	11	linearization	linearization	NOUN
ejpam-3496	204	12	of	of	ADP
ejpam-3496	204	13	(	(	PUNCT
ejpam-3496	204	14	20	20	NUM
ejpam-3496	204	15	)	)	PUNCT
ejpam-3496	204	16	give	give	VERB
ejpam-3496	204	17	us	we	PRON
ejpam-3496	204	18	[	[	X
ejpam-3496	204	19	d1(x	d1(x	NOUN
ejpam-3496	204	20	)	)	PUNCT
ejpam-3496	204	21	,	,	PUNCT
ejpam-3496	204	22	x∗d2(x	x∗d2(x	NOUN
ejpam-3496	204	23	)	)	PUNCT
ejpam-3496	204	24	]	]	PUNCT
ejpam-3496	205	1	+	+	CCONJ
ejpam-3496	205	2	[	[	X
ejpam-3496	205	3	d1(x	d1(x	X
ejpam-3496	205	4	)	)	PUNCT
ejpam-3496	205	5	,	,	PUNCT
ejpam-3496	205	6	x∗d2(y	x∗d2(y	PROPN
ejpam-3496	205	7	)	)	PUNCT
ejpam-3496	205	8	]	]	PUNCT
ejpam-3496	206	1	+	+	CCONJ
ejpam-3496	206	2	[	[	X
ejpam-3496	206	3	d1(x	d1(x	X
ejpam-3496	206	4	)	)	PUNCT
ejpam-3496	206	5	,	,	PUNCT
ejpam-3496	206	6	y∗d2(x	y∗d2(x	NOUN
ejpam-3496	206	7	)	)	PUNCT
ejpam-3496	206	8	]	]	PUNCT
ejpam-3496	207	1	+	+	CCONJ
ejpam-3496	207	2	[	[	X
ejpam-3496	207	3	d1(x	d1(x	X
ejpam-3496	207	4	)	)	PUNCT
ejpam-3496	207	5	,	,	PUNCT
ejpam-3496	207	6	y∗d2(y	y∗d2(y	NUM
ejpam-3496	207	7	)	)	PUNCT
ejpam-3496	207	8	]	]	PUNCT
ejpam-3496	208	1	+	+	PUNCT
ejpam-3496	208	2	[	[	X
ejpam-3496	208	3	d1(y	d1(y	NUM
ejpam-3496	208	4	)	)	PUNCT
ejpam-3496	208	5	,	,	PUNCT
ejpam-3496	208	6	x∗d2(x	x∗d2(x	NOUN
ejpam-3496	208	7	)	)	PUNCT
ejpam-3496	208	8	]	]	PUNCT
ejpam-3496	209	1	+	+	CCONJ
ejpam-3496	209	2	[	[	X
ejpam-3496	209	3	d1(y	d1(y	X
ejpam-3496	209	4	)	)	PUNCT
ejpam-3496	209	5	,	,	PUNCT
ejpam-3496	209	6	x∗d2(y	x∗d2(y	PROPN
ejpam-3496	209	7	)	)	PUNCT
ejpam-3496	209	8	]	]	PUNCT
ejpam-3496	210	1	+	+	CCONJ
ejpam-3496	210	2	[	[	X
ejpam-3496	210	3	d1(y	d1(y	X
ejpam-3496	210	4	)	)	PUNCT
ejpam-3496	210	5	,	,	PUNCT
ejpam-3496	210	6	y∗d2(x	y∗d2(x	NOUN
ejpam-3496	210	7	)	)	PUNCT
ejpam-3496	210	8	]	]	PUNCT
ejpam-3496	211	1	+	+	CCONJ
ejpam-3496	212	1	[	[	X
ejpam-3496	212	2	d1(y	d1(y	X
ejpam-3496	212	3	)	)	PUNCT
ejpam-3496	212	4	,	,	PUNCT
ejpam-3496	212	5	y∗d2(y	y∗d2(y	NUM
ejpam-3496	212	6	)	)	PUNCT
ejpam-3496	212	7	]	]	PUNCT
ejpam-3496	213	1	=	=	PUNCT
ejpam-3496	213	2	0	0	NUM
ejpam-3496	213	3	for	for	ADP
ejpam-3496	213	4	all	all	DET
ejpam-3496	213	5	x	x	NOUN
ejpam-3496	213	6	,	,	PUNCT
ejpam-3496	213	7	y	y	PROPN
ejpam-3496	213	8	∈	∈	PROPN
ejpam-3496	213	9	r.	r.	NOUN
ejpam-3496	213	10	using	use	VERB
ejpam-3496	213	11	(	(	PUNCT
ejpam-3496	213	12	20	20	NUM
ejpam-3496	213	13	)	)	PUNCT
ejpam-3496	213	14	,	,	PUNCT
ejpam-3496	213	15	we	we	PRON
ejpam-3496	213	16	get	get	VERB
ejpam-3496	213	17	[	[	X
ejpam-3496	213	18	d1(x	d1(x	NOUN
ejpam-3496	213	19	)	)	PUNCT
ejpam-3496	213	20	,	,	PUNCT
ejpam-3496	213	21	x∗d2(y	x∗d2(y	PROPN
ejpam-3496	213	22	)	)	PUNCT
ejpam-3496	213	23	]	]	PUNCT
ejpam-3496	214	1	+	+	CCONJ
ejpam-3496	214	2	[	[	X
ejpam-3496	214	3	d1(x	d1(x	X
ejpam-3496	214	4	)	)	PUNCT
ejpam-3496	214	5	,	,	PUNCT
ejpam-3496	214	6	y∗d2(x	y∗d2(x	NOUN
ejpam-3496	214	7	)	)	PUNCT
ejpam-3496	214	8	]	]	PUNCT
ejpam-3496	215	1	+	+	CCONJ
ejpam-3496	216	1	[	[	X
ejpam-3496	216	2	d1(x	d1(x	X
ejpam-3496	216	3	)	)	PUNCT
ejpam-3496	216	4	,	,	PUNCT
ejpam-3496	216	5	y∗d2(y	y∗d2(y	NUM
ejpam-3496	216	6	)	)	PUNCT
ejpam-3496	216	7	]	]	PUNCT
ejpam-3496	216	8	(	(	PUNCT
ejpam-3496	216	9	21	21	NUM
ejpam-3496	216	10	)	)	PUNCT
ejpam-3496	216	11	s.	s.	PROPN
ejpam-3496	216	12	ali	ali	PROPN
ejpam-3496	216	13	et	et	PROPN
ejpam-3496	216	14	al	al	PROPN
ejpam-3496	216	15	.	.	PUNCT
ejpam-3496	216	16	/	/	SYM
ejpam-3496	216	17	eur	eur	PROPN
ejpam-3496	216	18	.	.	PUNCT
ejpam-3496	217	1	j.	j.	PROPN
ejpam-3496	217	2	pure	pure	PROPN
ejpam-3496	217	3	appl	appl	PROPN
ejpam-3496	217	4	.	.	PROPN
ejpam-3496	217	5	math	math	PROPN
ejpam-3496	217	6	,	,	PUNCT
ejpam-3496	217	7	12	12	NUM
ejpam-3496	217	8	(	(	PUNCT
ejpam-3496	217	9	3	3	NUM
ejpam-3496	217	10	)	)	PUNCT
ejpam-3496	217	11	(	(	PUNCT
ejpam-3496	217	12	2019	2019	NUM
ejpam-3496	217	13	)	)	PUNCT
ejpam-3496	217	14	,	,	PUNCT
ejpam-3496	217	15	1138	1138	NUM
ejpam-3496	217	16	-	-	SYM
ejpam-3496	217	17	1148	1148	NUM
ejpam-3496	217	18	1144	1144	NUM
ejpam-3496	217	19	+	+	PROPN
ejpam-3496	217	20	[	[	X
ejpam-3496	217	21	d1(y	d1(y	NUM
ejpam-3496	217	22	)	)	PUNCT
ejpam-3496	217	23	,	,	PUNCT
ejpam-3496	217	24	x∗d2(x	x∗d2(x	NOUN
ejpam-3496	217	25	)	)	PUNCT
ejpam-3496	217	26	]	]	PUNCT
ejpam-3496	218	1	+	+	CCONJ
ejpam-3496	218	2	[	[	X
ejpam-3496	218	3	d1(y	d1(y	X
ejpam-3496	218	4	)	)	PUNCT
ejpam-3496	218	5	,	,	PUNCT
ejpam-3496	218	6	x∗d2(y	x∗d2(y	PROPN
ejpam-3496	218	7	)	)	PUNCT
ejpam-3496	218	8	]	]	PUNCT
ejpam-3496	219	1	+	+	CCONJ
ejpam-3496	219	2	[	[	X
ejpam-3496	219	3	d1(y	d1(y	X
ejpam-3496	219	4	)	)	PUNCT
ejpam-3496	219	5	,	,	PUNCT
ejpam-3496	219	6	y∗d2(x	y∗d2(x	NOUN
ejpam-3496	219	7	)	)	PUNCT
ejpam-3496	219	8	]	]	PUNCT
ejpam-3496	220	1	=	=	PUNCT
ejpam-3496	220	2	0	0	NUM
ejpam-3496	220	3	for	for	ADP
ejpam-3496	220	4	all	all	DET
ejpam-3496	220	5	x	x	NOUN
ejpam-3496	220	6	,	,	PUNCT
ejpam-3496	220	7	y	y	PROPN
ejpam-3496	220	8	∈	∈	PROPN
ejpam-3496	220	9	r.	r.	NOUN
ejpam-3496	220	10	replacing	replace	VERB
ejpam-3496	220	11	y	y	PRON
ejpam-3496	220	12	by	by	ADP
ejpam-3496	220	13	h	h	NOUN
ejpam-3496	220	14	where	where	SCONJ
ejpam-3496	220	15	h	h	NOUN
ejpam-3496	220	16	∈	∈	PROPN
ejpam-3496	220	17	h(r	h(r	NOUN
ejpam-3496	220	18	)	)	PUNCT
ejpam-3496	220	19	∩	∩	NOUN
ejpam-3496	220	20	z(r	z(r	NOUN
ejpam-3496	220	21	)	)	PUNCT
ejpam-3496	220	22	,	,	PUNCT
ejpam-3496	220	23	we	we	PRON
ejpam-3496	220	24	get	get	VERB
ejpam-3496	220	25	[	[	X
ejpam-3496	220	26	d1(x	d1(x	NOUN
ejpam-3496	220	27	)	)	PUNCT
ejpam-3496	220	28	,	,	PUNCT
ejpam-3496	220	29	x∗]d2(h	x∗]d2(h	PROPN
ejpam-3496	220	30	)	)	PUNCT
ejpam-3496	221	1	+	+	SYM
ejpam-3496	221	2	h[d1(x	h[d1(x	NOUN
ejpam-3496	221	3	)	)	PUNCT
ejpam-3496	221	4	,	,	PUNCT
ejpam-3496	221	5	d2(x	d2(x	PROPN
ejpam-3496	221	6	)	)	PUNCT
ejpam-3496	221	7	]	]	PUNCT
ejpam-3496	222	1	=	=	PUNCT
ejpam-3496	222	2	0	0	PUNCT
ejpam-3496	222	3	for	for	ADP
ejpam-3496	222	4	all	all	DET
ejpam-3496	222	5	x	x	PROPN
ejpam-3496	222	6	∈	∈	PROPN
ejpam-3496	222	7	r.	r.	NOUN
ejpam-3496	222	8	(	(	PUNCT
ejpam-3496	222	9	22	22	NUM
ejpam-3496	222	10	)	)	PUNCT
ejpam-3496	222	11	substituting	substitute	VERB
ejpam-3496	222	12	x+	x+	ADJ
ejpam-3496	222	13	y	y	PROPN
ejpam-3496	222	14	for	for	ADP
ejpam-3496	222	15	x	x	SYM
ejpam-3496	222	16	where	where	SCONJ
ejpam-3496	222	17	x	x	X
ejpam-3496	222	18	,	,	PUNCT
ejpam-3496	222	19	y	y	PROPN
ejpam-3496	222	20	∈	∈	PROPN
ejpam-3496	222	21	r	r	NOUN
ejpam-3496	222	22	and	and	CCONJ
ejpam-3496	222	23	combining	combine	VERB
ejpam-3496	222	24	it	it	PRON
ejpam-3496	222	25	with	with	ADP
ejpam-3496	222	26	(	(	PUNCT
ejpam-3496	222	27	22	22	NUM
ejpam-3496	222	28	)	)	PUNCT
ejpam-3496	222	29	,	,	PUNCT
ejpam-3496	222	30	we	we	PRON
ejpam-3496	222	31	have	have	VERB
ejpam-3496	222	32	(	(	PUNCT
ejpam-3496	222	33	[	[	X
ejpam-3496	222	34	d1(x	d1(x	NOUN
ejpam-3496	222	35	)	)	PUNCT
ejpam-3496	222	36	,	,	PUNCT
ejpam-3496	222	37	y∗	y∗	PROPN
ejpam-3496	222	38	]	]	PUNCT
ejpam-3496	223	1	+	+	CCONJ
ejpam-3496	224	1	[	[	X
ejpam-3496	224	2	d1(y	d1(y	X
ejpam-3496	224	3	)	)	PUNCT
ejpam-3496	224	4	,	,	PUNCT
ejpam-3496	224	5	x∗])d2(h	x∗])d2(h	NUM
ejpam-3496	224	6	)	)	PUNCT
ejpam-3496	224	7	+	+	NUM
ejpam-3496	224	8	h([d1(x	h([d1(x	NUM
ejpam-3496	224	9	)	)	PUNCT
ejpam-3496	224	10	,	,	PUNCT
ejpam-3496	224	11	d2(y	d2(y	PROPN
ejpam-3496	224	12	)	)	PUNCT
ejpam-3496	224	13	]	]	PUNCT
ejpam-3496	225	1	+	+	CCONJ
ejpam-3496	226	1	[	[	X
ejpam-3496	226	2	d1(y	d1(y	NUM
ejpam-3496	226	3	)	)	PUNCT
ejpam-3496	226	4	,	,	PUNCT
ejpam-3496	226	5	d2(x	d2(x	PROPN
ejpam-3496	226	6	)	)	PUNCT
ejpam-3496	226	7	]	]	PUNCT
ejpam-3496	226	8	)	)	PUNCT
ejpam-3496	227	1	=	=	SYM
ejpam-3496	227	2	0	0	PUNCT
ejpam-3496	227	3	(	(	PUNCT
ejpam-3496	227	4	23	23	NUM
ejpam-3496	227	5	)	)	PUNCT
ejpam-3496	227	6	for	for	ADP
ejpam-3496	227	7	all	all	DET
ejpam-3496	227	8	x	x	NOUN
ejpam-3496	227	9	,	,	PUNCT
ejpam-3496	227	10	y	y	PROPN
ejpam-3496	227	11	∈	∈	PROPN
ejpam-3496	227	12	r.	r.	PROPN
ejpam-3496	227	13	now	now	ADV
ejpam-3496	227	14	replacing	replace	VERB
ejpam-3496	227	15	y	y	PRON
ejpam-3496	227	16	by	by	ADP
ejpam-3496	227	17	hy	hy	NOUN
ejpam-3496	227	18	where	where	SCONJ
ejpam-3496	227	19	y	y	PROPN
ejpam-3496	227	20	∈	∈	PROPN
ejpam-3496	227	21	r	r	NOUN
ejpam-3496	227	22	and	and	CCONJ
ejpam-3496	227	23	h	h	NOUN
ejpam-3496	227	24	∈	∈	PROPN
ejpam-3496	227	25	h(r	h(r	NOUN
ejpam-3496	227	26	)	)	PUNCT
ejpam-3496	227	27	∩	∩	NOUN
ejpam-3496	227	28	z(r	z(r	NOUN
ejpam-3496	227	29	)	)	PUNCT
ejpam-3496	227	30	,	,	PUNCT
ejpam-3496	227	31	we	we	PRON
ejpam-3496	227	32	obtain	obtain	VERB
ejpam-3496	227	33	[	[	X
ejpam-3496	227	34	d1(x	d1(x	NOUN
ejpam-3496	227	35	)	)	PUNCT
ejpam-3496	227	36	,	,	PUNCT
ejpam-3496	227	37	y∗]hd2(h	y∗]hd2(h	NUM
ejpam-3496	227	38	)	)	PUNCT
ejpam-3496	227	39	+	+	CCONJ
ejpam-3496	228	1	[	[	X
ejpam-3496	228	2	d1(y	d1(y	X
ejpam-3496	228	3	)	)	PUNCT
ejpam-3496	228	4	,	,	PUNCT
ejpam-3496	228	5	x∗]hd2(h	x∗]hd2(h	PUNCT
ejpam-3496	228	6	)	)	PUNCT
ejpam-3496	229	1	+	+	CCONJ
ejpam-3496	230	1	[	[	X
ejpam-3496	230	2	y	y	PROPN
ejpam-3496	230	3	,	,	PUNCT
ejpam-3496	230	4	x∗]d1(h)d2(h	x∗]d1(h)d2(h	PROPN
ejpam-3496	230	5	)	)	PUNCT
ejpam-3496	231	1	+	+	PUNCT
ejpam-3496	231	2	h2[d1(x	h2[d1(x	X
ejpam-3496	231	3	)	)	PUNCT
ejpam-3496	231	4	,	,	PUNCT
ejpam-3496	231	5	d2(y	d2(y	PROPN
ejpam-3496	231	6	)	)	PUNCT
ejpam-3496	231	7	]	]	PUNCT
ejpam-3496	232	1	(	(	PUNCT
ejpam-3496	232	2	24	24	NUM
ejpam-3496	232	3	)	)	PUNCT
ejpam-3496	232	4	+	+	NOUN
ejpam-3496	232	5	h[d1(x	h[d1(x	NOUN
ejpam-3496	232	6	)	)	PUNCT
ejpam-3496	232	7	,	,	PUNCT
ejpam-3496	232	8	y]d2(h	y]d2(h	PROPN
ejpam-3496	232	9	)	)	PUNCT
ejpam-3496	233	1	+	+	CCONJ
ejpam-3496	233	2	h2[d1(y	h2[d1(y	PROPN
ejpam-3496	233	3	)	)	PUNCT
ejpam-3496	233	4	,	,	PUNCT
ejpam-3496	233	5	d2(x	d2(x	PROPN
ejpam-3496	233	6	)	)	PUNCT
ejpam-3496	233	7	]	]	PUNCT
ejpam-3496	234	1	+	+	CCONJ
ejpam-3496	234	2	hd1(h)[y	hd1(h)[y	X
ejpam-3496	234	3	,	,	PUNCT
ejpam-3496	234	4	d2(x	d2(x	NOUN
ejpam-3496	234	5	)	)	PUNCT
ejpam-3496	234	6	]	]	PUNCT
ejpam-3496	235	1	=	=	PUNCT
ejpam-3496	235	2	0	0	NUM
ejpam-3496	235	3	for	for	ADP
ejpam-3496	235	4	all	all	DET
ejpam-3496	235	5	x	x	NOUN
ejpam-3496	235	6	,	,	PUNCT
ejpam-3496	235	7	y	y	PROPN
ejpam-3496	235	8	∈	∈	PROPN
ejpam-3496	235	9	r.	r.	PROPN
ejpam-3496	235	10	multiplying	multiplying	NOUN
ejpam-3496	235	11	(	(	PUNCT
ejpam-3496	235	12	23	23	NUM
ejpam-3496	235	13	)	)	PUNCT
ejpam-3496	235	14	by	by	ADP
ejpam-3496	235	15	h	h	NOUN
ejpam-3496	235	16	where	where	SCONJ
ejpam-3496	235	17	h	h	NOUN
ejpam-3496	235	18	∈	∈	PROPN
ejpam-3496	235	19	h(r	h(r	NOUN
ejpam-3496	235	20	)	)	PUNCT
ejpam-3496	235	21	∩	∩	NOUN
ejpam-3496	235	22	z(r	z(r	NOUN
ejpam-3496	235	23	)	)	PUNCT
ejpam-3496	235	24	and	and	CCONJ
ejpam-3496	235	25	using	use	VERB
ejpam-3496	235	26	in	in	ADP
ejpam-3496	235	27	(	(	PUNCT
ejpam-3496	235	28	24	24	NUM
ejpam-3496	235	29	)	)	PUNCT
ejpam-3496	235	30	we	we	PRON
ejpam-3496	235	31	get	get	VERB
ejpam-3496	235	32	[	[	X
ejpam-3496	235	33	y	y	PROPN
ejpam-3496	235	34	,	,	PUNCT
ejpam-3496	235	35	x∗]d1(h)d2(h	x∗]d1(h)d2(h	PROPN
ejpam-3496	235	36	)	)	PUNCT
ejpam-3496	236	1	+	+	SYM
ejpam-3496	237	1	h[d1(x	h[d1(x	NOUN
ejpam-3496	237	2	)	)	PUNCT
ejpam-3496	237	3	,	,	PUNCT
ejpam-3496	238	1	y]d2(h	y]d2(h	PROPN
ejpam-3496	238	2	)	)	PUNCT
ejpam-3496	239	1	+	+	CCONJ
ejpam-3496	239	2	hd1(h)[y	hd1(h)[y	ADJ
ejpam-3496	239	3	,	,	PUNCT
ejpam-3496	239	4	d2(x	d2(x	NOUN
ejpam-3496	239	5	)	)	PUNCT
ejpam-3496	239	6	]	]	PUNCT
ejpam-3496	240	1	=	=	SYM
ejpam-3496	240	2	0	0	PUNCT
ejpam-3496	240	3	(	(	PUNCT
ejpam-3496	240	4	25	25	NUM
ejpam-3496	240	5	)	)	PUNCT
ejpam-3496	240	6	for	for	ADP
ejpam-3496	240	7	all	all	DET
ejpam-3496	240	8	x	x	NOUN
ejpam-3496	240	9	,	,	PUNCT
ejpam-3496	240	10	y	y	PROPN
ejpam-3496	240	11	∈	∈	PROPN
ejpam-3496	240	12	r.	r.	NOUN
ejpam-3496	240	13	replacing	replace	VERB
ejpam-3496	240	14	x	x	PUNCT
ejpam-3496	240	15	by	by	ADP
ejpam-3496	240	16	kx	kx	PRON
ejpam-3496	240	17	where	where	SCONJ
ejpam-3496	240	18	x	x	SYM
ejpam-3496	240	19	∈	∈	PROPN
ejpam-3496	240	20	r	r	NOUN
ejpam-3496	240	21	and	and	CCONJ
ejpam-3496	240	22	k	k	PROPN
ejpam-3496	240	23	∈	∈	PROPN
ejpam-3496	240	24	s(r	s(r	PROPN
ejpam-3496	240	25	)	)	PUNCT
ejpam-3496	240	26	∩	∩	NOUN
ejpam-3496	240	27	z(r	z(r	NOUN
ejpam-3496	240	28	)	)	PUNCT
ejpam-3496	240	29	,	,	PUNCT
ejpam-3496	240	30	we	we	PRON
ejpam-3496	240	31	arrive	arrive	VERB
ejpam-3496	240	32	at	at	ADP
ejpam-3496	240	33	−[y	−[y	NOUN
ejpam-3496	240	34	,	,	PUNCT
ejpam-3496	240	35	x∗]kd1(h)d2(h	x∗]kd1(h)d2(h	PUNCT
ejpam-3496	240	36	)	)	PUNCT
ejpam-3496	240	37	+	+	CCONJ
ejpam-3496	240	38	hk[d1(x	hk[d1(x	ADJ
ejpam-3496	240	39	)	)	PUNCT
ejpam-3496	240	40	,	,	PUNCT
ejpam-3496	240	41	y]d2(h	y]d2(h	PROPN
ejpam-3496	240	42	)	)	PUNCT
ejpam-3496	240	43	+	+	SYM
ejpam-3496	240	44	h[x	h[x	ADJ
ejpam-3496	240	45	,	,	PUNCT
ejpam-3496	240	46	y]d1(k)d2(h	y]d1(k)d2(h	NUM
ejpam-3496	240	47	)	)	PUNCT
ejpam-3496	240	48	(	(	PUNCT
ejpam-3496	240	49	26	26	NUM
ejpam-3496	240	50	)	)	PUNCT
ejpam-3496	241	1	+	+	ADV
ejpam-3496	241	2	hd1(h)[y	hd1(h)[y	ADJ
ejpam-3496	241	3	,	,	PUNCT
ejpam-3496	241	4	d2(x)]k	d2(x)]k	PUNCT
ejpam-3496	242	1	+	+	CCONJ
ejpam-3496	242	2	hd1(h)[y	hd1(h)[y	ADJ
ejpam-3496	242	3	,	,	PUNCT
ejpam-3496	242	4	x]d2(k	x]d2(k	PROPN
ejpam-3496	242	5	)	)	PUNCT
ejpam-3496	243	1	=	=	SYM
ejpam-3496	243	2	0	0	NUM
ejpam-3496	243	3	for	for	ADP
ejpam-3496	243	4	all	all	DET
ejpam-3496	243	5	x	x	NOUN
ejpam-3496	243	6	,	,	PUNCT
ejpam-3496	243	7	y	y	PROPN
ejpam-3496	243	8	∈	∈	PROPN
ejpam-3496	243	9	r.	r.	PROPN
ejpam-3496	243	10	multiplying	multiplying	NOUN
ejpam-3496	243	11	(	(	PUNCT
ejpam-3496	243	12	25	25	NUM
ejpam-3496	243	13	)	)	PUNCT
ejpam-3496	243	14	by	by	ADP
ejpam-3496	243	15	k	k	PROPN
ejpam-3496	243	16	where	where	SCONJ
ejpam-3496	243	17	k	k	PROPN
ejpam-3496	243	18	∈	∈	PROPN
ejpam-3496	243	19	s(r	s(r	PROPN
ejpam-3496	243	20	)	)	PUNCT
ejpam-3496	243	21	∩	∩	NOUN
ejpam-3496	243	22	z(r	z(r	NOUN
ejpam-3496	243	23	)	)	PUNCT
ejpam-3496	243	24	and	and	CCONJ
ejpam-3496	243	25	adding	add	VERB
ejpam-3496	243	26	it	it	PRON
ejpam-3496	243	27	with	with	ADP
ejpam-3496	243	28	(	(	PUNCT
ejpam-3496	243	29	26	26	NUM
ejpam-3496	243	30	)	)	PUNCT
ejpam-3496	243	31	,	,	PUNCT
ejpam-3496	243	32	we	we	PRON
ejpam-3496	243	33	get	get	VERB
ejpam-3496	243	34	2hk([d1(x	2hk([d1(x	NUM
ejpam-3496	243	35	)	)	PUNCT
ejpam-3496	243	36	,	,	PUNCT
ejpam-3496	243	37	y]d2(h	y]d2(h	PROPN
ejpam-3496	243	38	)	)	PUNCT
ejpam-3496	244	1	+	+	CCONJ
ejpam-3496	245	1	[	[	X
ejpam-3496	245	2	y	y	PROPN
ejpam-3496	245	3	,	,	PUNCT
ejpam-3496	245	4	d2(x)]d1(h	d2(x)]d1(h	NOUN
ejpam-3496	245	5	)	)	PUNCT
ejpam-3496	245	6	)	)	PUNCT
ejpam-3496	246	1	+	+	CCONJ
ejpam-3496	246	2	h[x	h[x	ADJ
ejpam-3496	246	3	,	,	PUNCT
ejpam-3496	246	4	y]d1(k)d2(h	y]d1(k)d2(h	PROPN
ejpam-3496	246	5	)	)	PUNCT
ejpam-3496	247	1	+	+	X
ejpam-3496	247	2	hd1(h)[y	hd1(h)[y	ADJ
ejpam-3496	247	3	,	,	PUNCT
ejpam-3496	247	4	x]d2(k	x]d2(k	PROPN
ejpam-3496	247	5	)	)	PUNCT
ejpam-3496	248	1	=	=	SYM
ejpam-3496	248	2	0	0	NUM
ejpam-3496	248	3	for	for	ADP
ejpam-3496	248	4	all	all	DET
ejpam-3496	248	5	x	x	NOUN
ejpam-3496	248	6	,	,	PUNCT
ejpam-3496	248	7	y	y	PROPN
ejpam-3496	248	8	∈	∈	PROPN
ejpam-3496	248	9	r.	r.	NOUN
ejpam-3496	248	10	taking	take	VERB
ejpam-3496	248	11	y	y	PROPN
ejpam-3496	248	12	=	=	PUNCT
ejpam-3496	248	13	x	x	NOUN
ejpam-3496	248	14	,	,	PUNCT
ejpam-3496	248	15	we	we	PRON
ejpam-3496	248	16	obtain	obtain	VERB
ejpam-3496	248	17	2hk([d1(x	2hk([d1(x	NUM
ejpam-3496	248	18	)	)	PUNCT
ejpam-3496	248	19	,	,	PUNCT
ejpam-3496	248	20	x]d2(h	x]d2(h	PROPN
ejpam-3496	248	21	)	)	PUNCT
ejpam-3496	249	1	+	+	CCONJ
ejpam-3496	250	1	[	[	X
ejpam-3496	250	2	x	x	X
ejpam-3496	250	3	,	,	PUNCT
ejpam-3496	250	4	d2(x)]d1(h	d2(x)]d1(h	NOUN
ejpam-3496	250	5	)	)	PUNCT
ejpam-3496	250	6	)	)	PUNCT
ejpam-3496	251	1	=	=	SYM
ejpam-3496	251	2	0	0	NUM
ejpam-3496	251	3	for	for	ADP
ejpam-3496	251	4	all	all	DET
ejpam-3496	251	5	x	x	PROPN
ejpam-3496	251	6	∈	∈	PROPN
ejpam-3496	251	7	r.	r.	NOUN
ejpam-3496	251	8	since	since	SCONJ
ejpam-3496	251	9	r	r	NOUN
ejpam-3496	251	10	is	be	AUX
ejpam-3496	251	11	2	2	NUM
ejpam-3496	251	12	-	-	PUNCT
ejpam-3496	251	13	torsion	torsion	NOUN
ejpam-3496	251	14	free	free	ADJ
ejpam-3496	251	15	prime	prime	ADJ
ejpam-3496	251	16	ring	ring	NOUN
ejpam-3496	251	17	and	and	CCONJ
ejpam-3496	251	18	s(r	s(r	ADJ
ejpam-3496	251	19	)	)	PUNCT
ejpam-3496	251	20	∩	∩	NOUN
ejpam-3496	251	21	z(r	z(r	NOUN
ejpam-3496	251	22	)	)	PUNCT
ejpam-3496	251	23	6=	6=	NUM
ejpam-3496	251	24	(	(	PUNCT
ejpam-3496	251	25	0	0	NUM
ejpam-3496	251	26	)	)	PUNCT
ejpam-3496	251	27	,	,	PUNCT
ejpam-3496	251	28	the	the	DET
ejpam-3496	251	29	above	above	ADJ
ejpam-3496	251	30	relation	relation	NOUN
ejpam-3496	251	31	implies	imply	VERB
ejpam-3496	251	32	that	that	SCONJ
ejpam-3496	251	33	[	[	X
ejpam-3496	251	34	d1(x	d1(x	NOUN
ejpam-3496	251	35	)	)	PUNCT
ejpam-3496	251	36	,	,	PUNCT
ejpam-3496	251	37	x]d2(h	x]d2(h	PROPN
ejpam-3496	251	38	)	)	PUNCT
ejpam-3496	251	39	+	+	CCONJ
ejpam-3496	252	1	[	[	X
ejpam-3496	252	2	x	x	X
ejpam-3496	252	3	,	,	PUNCT
ejpam-3496	252	4	d2(x)]d1(h	d2(x)]d1(h	NOUN
ejpam-3496	252	5	)	)	PUNCT
ejpam-3496	252	6	=	=	SYM
ejpam-3496	252	7	0	0	NUM
ejpam-3496	252	8	for	for	ADP
ejpam-3496	252	9	all	all	DET
ejpam-3496	252	10	x	x	PROPN
ejpam-3496	252	11	∈	∈	PROPN
ejpam-3496	252	12	r.	r.	NOUN
ejpam-3496	252	13	(	(	PUNCT
ejpam-3496	252	14	27	27	NUM
ejpam-3496	252	15	)	)	PUNCT
ejpam-3496	252	16	replacing	replace	VERB
ejpam-3496	252	17	y	y	PRON
ejpam-3496	252	18	by	by	ADP
ejpam-3496	252	19	x	x	PUNCT
ejpam-3496	252	20	in	in	ADP
ejpam-3496	252	21	(	(	PUNCT
ejpam-3496	252	22	25	25	NUM
ejpam-3496	252	23	)	)	PUNCT
ejpam-3496	252	24	,	,	PUNCT
ejpam-3496	252	25	we	we	PRON
ejpam-3496	252	26	get	get	VERB
ejpam-3496	252	27	[	[	X
ejpam-3496	252	28	x	x	NOUN
ejpam-3496	252	29	,	,	PUNCT
ejpam-3496	252	30	x∗]d1(h)d2(h	x∗]d1(h)d2(h	PROPN
ejpam-3496	252	31	)	)	PUNCT
ejpam-3496	252	32	+	+	SYM
ejpam-3496	252	33	h[d1(x	h[d1(x	NOUN
ejpam-3496	252	34	)	)	PUNCT
ejpam-3496	252	35	,	,	PUNCT
ejpam-3496	252	36	x]d2(h	x]d2(h	PROPN
ejpam-3496	252	37	)	)	PUNCT
ejpam-3496	253	1	+	+	CCONJ
ejpam-3496	253	2	hd1(h)[x	hd1(h)[x	X
ejpam-3496	253	3	,	,	PUNCT
ejpam-3496	253	4	d2(x	d2(x	NOUN
ejpam-3496	253	5	)	)	PUNCT
ejpam-3496	253	6	]	]	PUNCT
ejpam-3496	254	1	=	=	SYM
ejpam-3496	254	2	0	0	NUM
ejpam-3496	254	3	(	(	PUNCT
ejpam-3496	254	4	28	28	NUM
ejpam-3496	254	5	)	)	PUNCT
ejpam-3496	254	6	for	for	ADP
ejpam-3496	254	7	x	x	SYM
ejpam-3496	254	8	∈	∈	PROPN
ejpam-3496	254	9	r	r	NOUN
ejpam-3496	254	10	and	and	CCONJ
ejpam-3496	254	11	h	h	NOUN
ejpam-3496	254	12	∈	∈	PROPN
ejpam-3496	254	13	h(r	h(r	NOUN
ejpam-3496	254	14	)	)	PUNCT
ejpam-3496	254	15	∩	∩	NOUN
ejpam-3496	254	16	z(r	z(r	NOUN
ejpam-3496	254	17	)	)	PUNCT
ejpam-3496	254	18	.	.	PUNCT
ejpam-3496	255	1	using	use	VERB
ejpam-3496	255	2	(	(	PUNCT
ejpam-3496	255	3	27	27	NUM
ejpam-3496	255	4	)	)	PUNCT
ejpam-3496	255	5	in	in	ADP
ejpam-3496	255	6	(	(	PUNCT
ejpam-3496	255	7	28	28	NUM
ejpam-3496	255	8	)	)	PUNCT
ejpam-3496	255	9	,	,	PUNCT
ejpam-3496	255	10	we	we	PRON
ejpam-3496	255	11	get	get	VERB
ejpam-3496	255	12	[	[	X
ejpam-3496	255	13	x	x	NOUN
ejpam-3496	255	14	,	,	PUNCT
ejpam-3496	255	15	x∗]d1(h)d2(h	x∗]d1(h)d2(h	PROPN
ejpam-3496	255	16	)	)	PUNCT
ejpam-3496	256	1	=	=	SYM
ejpam-3496	256	2	0	0	NUM
ejpam-3496	257	1	for	for	ADP
ejpam-3496	257	2	all	all	PRON
ejpam-3496	257	3	x	x	SYM
ejpam-3496	257	4	∈	∈	NOUN
ejpam-3496	257	5	r	r	NOUN
ejpam-3496	257	6	and	and	CCONJ
ejpam-3496	257	7	h	h	NOUN
ejpam-3496	257	8	∈	∈	PROPN
ejpam-3496	257	9	h(r	h(r	NOUN
ejpam-3496	257	10	)	)	PUNCT
ejpam-3496	257	11	∩	∩	NOUN
ejpam-3496	257	12	z(r	z(r	NOUN
ejpam-3496	257	13	)	)	PUNCT
ejpam-3496	257	14	.	.	PUNCT
ejpam-3496	258	1	now	now	ADV
ejpam-3496	258	2	use	use	VERB
ejpam-3496	258	3	the	the	DET
ejpam-3496	258	4	primeness	primeness	NOUN
ejpam-3496	258	5	condition	condition	NOUN
ejpam-3496	258	6	we	we	PRON
ejpam-3496	258	7	get	get	VERB
ejpam-3496	258	8	either	either	CCONJ
ejpam-3496	258	9	[	[	X
ejpam-3496	258	10	x	x	X
ejpam-3496	258	11	,	,	PUNCT
ejpam-3496	258	12	x∗	x∗	X
ejpam-3496	258	13	]	]	X
ejpam-3496	258	14	=	=	SYM
ejpam-3496	258	15	0	0	NUM
ejpam-3496	258	16	for	for	ADP
ejpam-3496	258	17	all	all	PRON
ejpam-3496	258	18	x	x	SYM
ejpam-3496	258	19	∈	∈	NOUN
ejpam-3496	258	20	r	r	NOUN
ejpam-3496	258	21	or	or	CCONJ
ejpam-3496	258	22	d1(h)d2(h	d1(h)d2(h	PROPN
ejpam-3496	258	23	)	)	PUNCT
ejpam-3496	258	24	=	=	SYM
ejpam-3496	258	25	0	0	NUM
ejpam-3496	258	26	for	for	ADP
ejpam-3496	258	27	all	all	DET
ejpam-3496	258	28	h	h	NOUN
ejpam-3496	258	29	∈	∈	PROPN
ejpam-3496	258	30	h(r	h(r	NOUN
ejpam-3496	258	31	)	)	PUNCT
ejpam-3496	258	32	∩	∩	NOUN
ejpam-3496	258	33	z(r	z(r	NOUN
ejpam-3496	258	34	)	)	PUNCT
ejpam-3496	258	35	.	.	PUNCT
ejpam-3496	259	1	if	if	SCONJ
ejpam-3496	259	2	we	we	PRON
ejpam-3496	259	3	consider	consider	VERB
ejpam-3496	259	4	[	[	X
ejpam-3496	259	5	x	x	NOUN
ejpam-3496	259	6	,	,	PUNCT
ejpam-3496	259	7	x∗	x∗	X
ejpam-3496	259	8	]	]	X
ejpam-3496	259	9	=	=	SYM
ejpam-3496	259	10	0	0	NUM
ejpam-3496	259	11	,	,	PUNCT
ejpam-3496	259	12	then	then	ADV
ejpam-3496	259	13	in	in	ADP
ejpam-3496	259	14	view	view	NOUN
ejpam-3496	259	15	of	of	ADP
ejpam-3496	259	16	[	[	X
ejpam-3496	259	17	16	16	NUM
ejpam-3496	259	18	,	,	PUNCT
ejpam-3496	259	19	lemma	lemma	PROPN
ejpam-3496	259	20	2.1	2.1	NUM
ejpam-3496	259	21	]	]	X
ejpam-3496	260	1	r	r	NOUN
ejpam-3496	260	2	is	be	AUX
ejpam-3496	260	3	commutative	commutative	ADJ
ejpam-3496	260	4	,	,	PUNCT
ejpam-3496	260	5	which	which	PRON
ejpam-3496	260	6	is	be	AUX
ejpam-3496	260	7	a	a	DET
ejpam-3496	260	8	contradiction	contradiction	NOUN
ejpam-3496	260	9	to	to	ADP
ejpam-3496	260	10	our	our	PRON
ejpam-3496	260	11	assumption	assumption	NOUN
ejpam-3496	260	12	,	,	PUNCT
ejpam-3496	260	13	now	now	ADV
ejpam-3496	260	14	we	we	PRON
ejpam-3496	260	15	have	have	AUX
ejpam-3496	260	16	d1(h)d2(h	d1(h)d2(h	VERB
ejpam-3496	260	17	)	)	PUNCT
ejpam-3496	260	18	=	=	SYM
ejpam-3496	260	19	0	0	NUM
ejpam-3496	260	20	for	for	ADP
ejpam-3496	260	21	all	all	DET
ejpam-3496	260	22	h	h	NOUN
ejpam-3496	260	23	∈	∈	PROPN
ejpam-3496	260	24	h(r	h(r	NOUN
ejpam-3496	260	25	)	)	PUNCT
ejpam-3496	260	26	∩	∩	NOUN
ejpam-3496	260	27	z(r	z(r	NOUN
ejpam-3496	260	28	)	)	PUNCT
ejpam-3496	260	29	.	.	PUNCT
ejpam-3496	261	1	using	use	VERB
ejpam-3496	261	2	the	the	DET
ejpam-3496	261	3	primeness	primeness	NOUN
ejpam-3496	261	4	of	of	ADP
ejpam-3496	261	5	the	the	DET
ejpam-3496	261	6	ring	ring	NOUN
ejpam-3496	261	7	r	r	NOUN
ejpam-3496	261	8	we	we	PRON
ejpam-3496	261	9	get	get	VERB
ejpam-3496	261	10	either	either	DET
ejpam-3496	261	11	d1(h	d1(h	NOUN
ejpam-3496	261	12	)	)	PUNCT
ejpam-3496	261	13	=	=	SYM
ejpam-3496	261	14	0	0	NUM
ejpam-3496	261	15	or	or	CCONJ
ejpam-3496	261	16	d2(h	d2(h	PROPN
ejpam-3496	261	17	)	)	PUNCT
ejpam-3496	261	18	=	=	SYM
ejpam-3496	261	19	0	0	NUM
ejpam-3496	261	20	for	for	ADP
ejpam-3496	261	21	all	all	DET
ejpam-3496	261	22	h	h	NOUN
ejpam-3496	261	23	∈	∈	PROPN
ejpam-3496	261	24	h(r	h(r	NOUN
ejpam-3496	261	25	)	)	PUNCT
ejpam-3496	261	26	∩	∩	NOUN
ejpam-3496	261	27	z(r	z(r	NOUN
ejpam-3496	261	28	)	)	PUNCT
ejpam-3496	261	29	.	.	PUNCT
ejpam-3496	262	1	if	if	SCONJ
ejpam-3496	262	2	consider	consider	VERB
ejpam-3496	262	3	d1(h	d1(h	NOUN
ejpam-3496	262	4	)	)	PUNCT
ejpam-3496	262	5	=	=	SYM
ejpam-3496	262	6	0	0	X
ejpam-3496	262	7	.	.	PUNCT
ejpam-3496	263	1	s.	s.	PROPN
ejpam-3496	263	2	ali	ali	PROPN
ejpam-3496	263	3	et	et	PROPN
ejpam-3496	263	4	al	al	PROPN
ejpam-3496	263	5	.	.	PUNCT
ejpam-3496	263	6	/	/	SYM
ejpam-3496	263	7	eur	eur	PROPN
ejpam-3496	263	8	.	.	PUNCT
ejpam-3496	264	1	j.	j.	PROPN
ejpam-3496	264	2	pure	pure	PROPN
ejpam-3496	264	3	appl	appl	PROPN
ejpam-3496	264	4	.	.	PROPN
ejpam-3496	264	5	math	math	PROPN
ejpam-3496	264	6	,	,	PUNCT
ejpam-3496	264	7	12	12	NUM
ejpam-3496	264	8	(	(	PUNCT
ejpam-3496	264	9	3	3	NUM
ejpam-3496	264	10	)	)	PUNCT
ejpam-3496	264	11	(	(	PUNCT
ejpam-3496	264	12	2019	2019	NUM
ejpam-3496	264	13	)	)	PUNCT
ejpam-3496	264	14	,	,	PUNCT
ejpam-3496	264	15	1138	1138	NUM
ejpam-3496	264	16	-	-	SYM
ejpam-3496	264	17	1148	1148	NUM
ejpam-3496	264	18	1145	1145	NUM
ejpam-3496	264	19	then	then	ADV
ejpam-3496	264	20	by	by	ADP
ejpam-3496	264	21	(	(	PUNCT
ejpam-3496	264	22	25	25	NUM
ejpam-3496	264	23	)	)	PUNCT
ejpam-3496	264	24	we	we	PRON
ejpam-3496	264	25	get	get	VERB
ejpam-3496	264	26	h[d1(x	h[d1(x	NOUN
ejpam-3496	264	27	)	)	PUNCT
ejpam-3496	264	28	,	,	PUNCT
ejpam-3496	264	29	y]d2(h	y]d2(h	PROPN
ejpam-3496	264	30	)	)	PUNCT
ejpam-3496	265	1	=	=	SYM
ejpam-3496	265	2	0	0	NUM
ejpam-3496	265	3	for	for	ADP
ejpam-3496	265	4	all	all	DET
ejpam-3496	265	5	x	x	NOUN
ejpam-3496	265	6	,	,	PUNCT
ejpam-3496	265	7	y	y	PROPN
ejpam-3496	265	8	∈	∈	PROPN
ejpam-3496	265	9	r.	r.	PROPN
ejpam-3496	265	10	now	now	ADV
ejpam-3496	265	11	using	use	VERB
ejpam-3496	265	12	the	the	DET
ejpam-3496	265	13	primeness	primeness	NOUN
ejpam-3496	265	14	of	of	ADP
ejpam-3496	265	15	the	the	DET
ejpam-3496	265	16	ring	ring	NOUN
ejpam-3496	265	17	r	r	NOUN
ejpam-3496	265	18	,	,	PUNCT
ejpam-3496	265	19	we	we	PRON
ejpam-3496	265	20	obtain	obtain	VERB
ejpam-3496	265	21	[	[	X
ejpam-3496	265	22	d1(x	d1(x	NOUN
ejpam-3496	265	23	)	)	PUNCT
ejpam-3496	265	24	,	,	PUNCT
ejpam-3496	265	25	y]d2(h	y]d2(h	NOUN
ejpam-3496	265	26	)	)	PUNCT
ejpam-3496	265	27	=	=	SYM
ejpam-3496	265	28	0	0	NUM
ejpam-3496	265	29	for	for	ADP
ejpam-3496	265	30	all	all	DET
ejpam-3496	265	31	x	x	NOUN
ejpam-3496	265	32	,	,	PUNCT
ejpam-3496	265	33	y	y	PROPN
ejpam-3496	265	34	∈	∈	PROPN
ejpam-3496	265	35	r.	r.	PROPN
ejpam-3496	265	36	again	again	ADV
ejpam-3496	265	37	by	by	ADP
ejpam-3496	265	38	the	the	DET
ejpam-3496	265	39	primeness	primeness	NOUN
ejpam-3496	265	40	of	of	ADP
ejpam-3496	265	41	the	the	DET
ejpam-3496	265	42	ring	ring	NOUN
ejpam-3496	265	43	r	r	NOUN
ejpam-3496	265	44	,	,	PUNCT
ejpam-3496	265	45	we	we	PRON
ejpam-3496	265	46	have	have	VERB
ejpam-3496	265	47	either	either	PRON
ejpam-3496	265	48	d2(h	d2(h	PROPN
ejpam-3496	265	49	)	)	PUNCT
ejpam-3496	265	50	=	=	SYM
ejpam-3496	265	51	0	0	NUM
ejpam-3496	265	52	for	for	ADP
ejpam-3496	265	53	all	all	DET
ejpam-3496	265	54	h	h	NOUN
ejpam-3496	265	55	∈	∈	PROPN
ejpam-3496	265	56	h(r	h(r	NOUN
ejpam-3496	265	57	)	)	PUNCT
ejpam-3496	265	58	∩	∩	NOUN
ejpam-3496	265	59	z(r	z(r	NOUN
ejpam-3496	265	60	)	)	PUNCT
ejpam-3496	265	61	or	or	CCONJ
ejpam-3496	265	62	[	[	X
ejpam-3496	265	63	d1(x	d1(x	NOUN
ejpam-3496	265	64	)	)	PUNCT
ejpam-3496	265	65	,	,	PUNCT
ejpam-3496	265	66	y	y	PROPN
ejpam-3496	265	67	]	]	X
ejpam-3496	265	68	=	=	SYM
ejpam-3496	265	69	0	0	NUM
ejpam-3496	265	70	for	for	ADP
ejpam-3496	265	71	all	all	DET
ejpam-3496	265	72	x	x	NOUN
ejpam-3496	265	73	,	,	PUNCT
ejpam-3496	265	74	y	y	PROPN
ejpam-3496	265	75	∈	∈	PROPN
ejpam-3496	265	76	r.	r.	PROPN
ejpam-3496	265	77	if	if	SCONJ
ejpam-3496	265	78	we	we	PRON
ejpam-3496	265	79	consider	consider	VERB
ejpam-3496	265	80	[	[	X
ejpam-3496	265	81	d1(x	d1(x	NOUN
ejpam-3496	265	82	)	)	PUNCT
ejpam-3496	265	83	,	,	PUNCT
ejpam-3496	265	84	y	y	PROPN
ejpam-3496	265	85	]	]	X
ejpam-3496	265	86	=	=	SYM
ejpam-3496	265	87	0	0	NUM
ejpam-3496	265	88	for	for	ADP
ejpam-3496	265	89	all	all	DET
ejpam-3496	265	90	x	x	NOUN
ejpam-3496	265	91	,	,	PUNCT
ejpam-3496	265	92	y	y	PROPN
ejpam-3496	265	93	∈	∈	PROPN
ejpam-3496	265	94	r.	r.	NOUN
ejpam-3496	265	95	this	this	PRON
ejpam-3496	265	96	gives	give	VERB
ejpam-3496	265	97	r	r	NOUN
ejpam-3496	265	98	is	be	AUX
ejpam-3496	265	99	commutative	commutative	ADJ
ejpam-3496	265	100	by	by	ADP
ejpam-3496	265	101	posner	posner	NOUN
ejpam-3496	265	102	’s	’s	PART
ejpam-3496	265	103	result	result	NOUN
ejpam-3496	265	104	[	[	X
ejpam-3496	265	105	18	18	NUM
ejpam-3496	265	106	]	]	X
ejpam-3496	265	107	,	,	PUNCT
ejpam-3496	265	108	a	a	DET
ejpam-3496	265	109	contradiction	contradiction	NOUN
ejpam-3496	265	110	.	.	PUNCT
ejpam-3496	266	1	therefore	therefore	ADV
ejpam-3496	266	2	we	we	PRON
ejpam-3496	266	3	are	be	AUX
ejpam-3496	266	4	left	leave	VERB
ejpam-3496	266	5	with	with	ADP
ejpam-3496	266	6	d2(h	d2(h	PROPN
ejpam-3496	266	7	)	)	PUNCT
ejpam-3496	266	8	=	=	SYM
ejpam-3496	266	9	0	0	NUM
ejpam-3496	266	10	for	for	ADP
ejpam-3496	266	11	all	all	DET
ejpam-3496	266	12	h	h	NOUN
ejpam-3496	266	13	∈	∈	PROPN
ejpam-3496	266	14	h(r)∩z(r	h(r)∩z(r	NOUN
ejpam-3496	266	15	)	)	PUNCT
ejpam-3496	266	16	.	.	PUNCT
ejpam-3496	267	1	similarly	similarly	ADV
ejpam-3496	267	2	in	in	ADP
ejpam-3496	267	3	view	view	NOUN
ejpam-3496	267	4	of	of	ADP
ejpam-3496	267	5	(	(	PUNCT
ejpam-3496	267	6	25	25	NUM
ejpam-3496	267	7	)	)	PUNCT
ejpam-3496	267	8	we	we	PRON
ejpam-3496	267	9	get	get	VERB
ejpam-3496	267	10	d1(h	d1(h	NOUN
ejpam-3496	267	11	)	)	PUNCT
ejpam-3496	267	12	=	=	SYM
ejpam-3496	267	13	0	0	NUM
ejpam-3496	267	14	for	for	ADP
ejpam-3496	267	15	all	all	DET
ejpam-3496	267	16	h	h	NOUN
ejpam-3496	267	17	∈	∈	PROPN
ejpam-3496	267	18	h(r)∩z(r	h(r)∩z(r	NOUN
ejpam-3496	267	19	)	)	PUNCT
ejpam-3496	267	20	.	.	PUNCT
ejpam-3496	268	1	replacing	replace	VERB
ejpam-3496	268	2	y	y	PRON
ejpam-3496	268	3	by	by	ADP
ejpam-3496	268	4	h	h	NOUN
ejpam-3496	268	5	where	where	SCONJ
ejpam-3496	268	6	h	h	NOUN
ejpam-3496	268	7	∈	∈	PROPN
ejpam-3496	268	8	h(r	h(r	NOUN
ejpam-3496	268	9	)	)	PUNCT
ejpam-3496	268	10	∩	∩	NOUN
ejpam-3496	268	11	z(r	z(r	NOUN
ejpam-3496	268	12	)	)	PUNCT
ejpam-3496	268	13	in	in	ADP
ejpam-3496	268	14	(	(	PUNCT
ejpam-3496	268	15	21	21	NUM
ejpam-3496	268	16	)	)	PUNCT
ejpam-3496	268	17	and	and	CCONJ
ejpam-3496	268	18	using	use	VERB
ejpam-3496	268	19	d1(h	d1(h	NOUN
ejpam-3496	268	20	)	)	PUNCT
ejpam-3496	268	21	=	=	SYM
ejpam-3496	268	22	0	0	NUM
ejpam-3496	268	23	and	and	CCONJ
ejpam-3496	268	24	d2(h	d2(h	PROPN
ejpam-3496	268	25	)	)	PUNCT
ejpam-3496	268	26	=	=	SYM
ejpam-3496	268	27	0	0	NUM
ejpam-3496	268	28	,	,	PUNCT
ejpam-3496	268	29	we	we	PRON
ejpam-3496	268	30	get	get	VERB
ejpam-3496	268	31	h[d1(x	h[d1(x	NOUN
ejpam-3496	268	32	)	)	PUNCT
ejpam-3496	268	33	,	,	PUNCT
ejpam-3496	268	34	d2(x	d2(x	PROPN
ejpam-3496	268	35	)	)	PUNCT
ejpam-3496	268	36	]	]	PUNCT
ejpam-3496	269	1	=	=	PUNCT
ejpam-3496	269	2	0	0	PUNCT
ejpam-3496	269	3	for	for	ADP
ejpam-3496	269	4	all	all	DET
ejpam-3496	269	5	x	x	PROPN
ejpam-3496	269	6	∈	∈	PROPN
ejpam-3496	269	7	r.	r.	NOUN
ejpam-3496	269	8	now	now	ADV
ejpam-3496	269	9	using	use	VERB
ejpam-3496	269	10	the	the	DET
ejpam-3496	269	11	primeness	primeness	NOUN
ejpam-3496	269	12	and	and	CCONJ
ejpam-3496	269	13	s(r	s(r	NOUN
ejpam-3496	269	14	)	)	PUNCT
ejpam-3496	269	15	∩	∩	NOUN
ejpam-3496	269	16	z(r	z(r	NOUN
ejpam-3496	269	17	)	)	PUNCT
ejpam-3496	269	18	6=	6=	NUM
ejpam-3496	269	19	(	(	PUNCT
ejpam-3496	269	20	0	0	NUM
ejpam-3496	269	21	)	)	PUNCT
ejpam-3496	269	22	conditions	condition	NOUN
ejpam-3496	269	23	,	,	PUNCT
ejpam-3496	269	24	we	we	PRON
ejpam-3496	269	25	get	get	VERB
ejpam-3496	269	26	[	[	X
ejpam-3496	269	27	d1(x	d1(x	NOUN
ejpam-3496	269	28	)	)	PUNCT
ejpam-3496	269	29	,	,	PUNCT
ejpam-3496	269	30	d2(x	d2(x	PROPN
ejpam-3496	269	31	)	)	PUNCT
ejpam-3496	269	32	]	]	PUNCT
ejpam-3496	270	1	=	=	PUNCT
ejpam-3496	270	2	0	0	PUNCT
ejpam-3496	270	3	for	for	ADP
ejpam-3496	270	4	all	all	DET
ejpam-3496	270	5	x	x	PROPN
ejpam-3496	270	6	∈	∈	PROPN
ejpam-3496	270	7	r.	r.	NOUN
ejpam-3496	270	8	thus	thus	ADV
ejpam-3496	270	9	by	by	ADP
ejpam-3496	270	10	the	the	DET
ejpam-3496	270	11	result	result	NOUN
ejpam-3496	270	12	of	of	ADP
ejpam-3496	270	13	lanski	lanski	NOUN
ejpam-3496	270	14	[	[	X
ejpam-3496	270	15	15	15	NUM
ejpam-3496	270	16	,	,	PUNCT
ejpam-3496	270	17	theorem	theorem	VERB
ejpam-3496	270	18	4	4	NUM
ejpam-3496	270	19	]	]	PUNCT
ejpam-3496	270	20	,	,	PUNCT
ejpam-3496	270	21	we	we	PRON
ejpam-3496	270	22	get	get	VERB
ejpam-3496	270	23	d1	d1	PROPN
ejpam-3496	270	24	=	=	SYM
ejpam-3496	270	25	λd2	λd2	PROPN
ejpam-3496	270	26	,	,	PUNCT
ejpam-3496	270	27	where	where	SCONJ
ejpam-3496	270	28	λ	λ	PROPN
ejpam-3496	270	29	∈	∈	PROPN
ejpam-3496	270	30	c.	c.	PROPN
ejpam-3496	270	31	corollary	corollary	NOUN
ejpam-3496	270	32	2	2	X
ejpam-3496	270	33	.	.	PUNCT
ejpam-3496	271	1	let	let	VERB
ejpam-3496	271	2	r	r	PRON
ejpam-3496	271	3	be	be	AUX
ejpam-3496	271	4	a	a	DET
ejpam-3496	271	5	2	2	NUM
ejpam-3496	271	6	-	-	PUNCT
ejpam-3496	271	7	torsion	torsion	NOUN
ejpam-3496	271	8	free	free	ADJ
ejpam-3496	271	9	noncommutative	noncommutative	ADJ
ejpam-3496	271	10	prime	prime	ADJ
ejpam-3496	271	11	ring	ring	NOUN
ejpam-3496	271	12	with	with	ADP
ejpam-3496	271	13	involution	involution	NOUN
ejpam-3496	271	14	∗	∗	NOUN
ejpam-3496	271	15	of	of	ADP
ejpam-3496	271	16	the	the	DET
ejpam-3496	271	17	second	second	ADJ
ejpam-3496	271	18	kind	kind	NOUN
ejpam-3496	271	19	and	and	CCONJ
ejpam-3496	271	20	d1	d1	PROPN
ejpam-3496	271	21	,	,	PUNCT
ejpam-3496	271	22	d2	d2	PROPN
ejpam-3496	271	23	be	be	AUX
ejpam-3496	271	24	two	two	NUM
ejpam-3496	271	25	nonzero	nonzero	ADJ
ejpam-3496	271	26	derivations	derivation	NOUN
ejpam-3496	271	27	on	on	ADP
ejpam-3496	271	28	r	r	NOUN
ejpam-3496	272	1	such	such	ADJ
ejpam-3496	272	2	that	that	SCONJ
ejpam-3496	272	3	[	[	X
ejpam-3496	272	4	d1(x	d1(x	NOUN
ejpam-3496	272	5	)	)	PUNCT
ejpam-3496	272	6	,	,	PUNCT
ejpam-3496	272	7	y∗d2(y	y∗d2(y	NUM
ejpam-3496	272	8	)	)	PUNCT
ejpam-3496	272	9	]	]	PUNCT
ejpam-3496	273	1	=	=	PUNCT
ejpam-3496	273	2	0	0	NUM
ejpam-3496	273	3	for	for	ADP
ejpam-3496	273	4	all	all	DET
ejpam-3496	273	5	x	x	NOUN
ejpam-3496	273	6	,	,	PUNCT
ejpam-3496	273	7	y	y	PROPN
ejpam-3496	273	8	∈	∈	PROPN
ejpam-3496	273	9	r.	r.	PROPN
ejpam-3496	273	10	then	then	ADV
ejpam-3496	273	11	d1	d1	PROPN
ejpam-3496	273	12	=	=	SYM
ejpam-3496	273	13	λd2	λd2	PROPN
ejpam-3496	273	14	,	,	PUNCT
ejpam-3496	273	15	where	where	SCONJ
ejpam-3496	273	16	λ	λ	PROPN
ejpam-3496	273	17	∈	∈	PROPN
ejpam-3496	273	18	c.	c.	PROPN
ejpam-3496	273	19	theorem	theorem	VERB
ejpam-3496	273	20	3	3	X
ejpam-3496	273	21	.	.	PUNCT
ejpam-3496	274	1	let	let	VERB
ejpam-3496	274	2	r	r	PRON
ejpam-3496	274	3	be	be	AUX
ejpam-3496	274	4	a	a	DET
ejpam-3496	274	5	2	2	NUM
ejpam-3496	274	6	-	-	PUNCT
ejpam-3496	274	7	torsion	torsion	NOUN
ejpam-3496	274	8	free	free	ADJ
ejpam-3496	274	9	noncommutative	noncommutative	ADJ
ejpam-3496	274	10	prime	prime	ADJ
ejpam-3496	274	11	ring	ring	NOUN
ejpam-3496	274	12	with	with	ADP
ejpam-3496	274	13	involution	involution	NOUN
ejpam-3496	274	14	∗	∗	NOUN
ejpam-3496	274	15	of	of	ADP
ejpam-3496	274	16	the	the	DET
ejpam-3496	274	17	second	second	ADJ
ejpam-3496	274	18	kind	kind	NOUN
ejpam-3496	274	19	and	and	CCONJ
ejpam-3496	274	20	d1	d1	PROPN
ejpam-3496	274	21	,	,	PUNCT
ejpam-3496	274	22	d2	d2	PROPN
ejpam-3496	274	23	be	be	AUX
ejpam-3496	274	24	two	two	NUM
ejpam-3496	274	25	nonzero	nonzero	ADJ
ejpam-3496	274	26	derivations	derivation	NOUN
ejpam-3496	274	27	on	on	ADP
ejpam-3496	274	28	r.	r.	PROPN
ejpam-3496	274	29	if	if	SCONJ
ejpam-3496	274	30	one	one	NUM
ejpam-3496	274	31	of	of	ADP
ejpam-3496	274	32	the	the	DET
ejpam-3496	274	33	following	follow	VERB
ejpam-3496	274	34	conditions	condition	NOUN
ejpam-3496	274	35	holds	hold	VERB
ejpam-3496	274	36	:	:	PUNCT
ejpam-3496	274	37	(	(	PUNCT
ejpam-3496	274	38	i	i	NOUN
ejpam-3496	274	39	)	)	PUNCT
ejpam-3496	275	1	[	[	X
ejpam-3496	275	2	d1(x	d1(x	NOUN
ejpam-3496	275	3	)	)	PUNCT
ejpam-3496	275	4	,	,	PUNCT
ejpam-3496	275	5	d2(x	d2(x	NOUN
ejpam-3496	275	6	∗	∗	NOUN
ejpam-3496	275	7	)	)	PUNCT
ejpam-3496	275	8	]	]	PUNCT
ejpam-3496	276	1	=	=	PUNCT
ejpam-3496	276	2	x	x	PUNCT
ejpam-3496	276	3	◦	◦	NOUN
ejpam-3496	276	4	x∗	x∗	PROPN
ejpam-3496	276	5	for	for	ADP
ejpam-3496	276	6	all	all	PRON
ejpam-3496	276	7	x	x	SYM
ejpam-3496	276	8	∈	∈	PROPN
ejpam-3496	276	9	r	r	NOUN
ejpam-3496	276	10	,	,	PUNCT
ejpam-3496	276	11	(	(	PUNCT
ejpam-3496	276	12	ii	ii	NOUN
ejpam-3496	276	13	)	)	PUNCT
ejpam-3496	277	1	[	[	X
ejpam-3496	277	2	d1(x	d1(x	NOUN
ejpam-3496	277	3	)	)	PUNCT
ejpam-3496	277	4	,	,	PUNCT
ejpam-3496	277	5	d2(x	d2(x	NOUN
ejpam-3496	277	6	∗	∗	NOUN
ejpam-3496	277	7	)	)	PUNCT
ejpam-3496	277	8	]	]	PUNCT
ejpam-3496	278	1	=	=	PUNCT
ejpam-3496	278	2	−x	−x	NOUN
ejpam-3496	278	3	◦	◦	NOUN
ejpam-3496	278	4	x∗	x∗	PROPN
ejpam-3496	278	5	for	for	ADP
ejpam-3496	278	6	all	all	DET
ejpam-3496	278	7	x	x	SYM
ejpam-3496	278	8	∈	∈	PROPN
ejpam-3496	278	9	r	r	NOUN
ejpam-3496	278	10	,	,	PUNCT
ejpam-3496	278	11	then	then	ADV
ejpam-3496	278	12	d1	d1	PROPN
ejpam-3496	278	13	=	=	SYM
ejpam-3496	278	14	λd2	λd2	PROPN
ejpam-3496	278	15	,	,	PUNCT
ejpam-3496	278	16	where	where	SCONJ
ejpam-3496	278	17	λ	λ	PROPN
ejpam-3496	278	18	∈	∈	PROPN
ejpam-3496	278	19	c.	c.	NOUN
ejpam-3496	278	20	proof	proof	NOUN
ejpam-3496	278	21	.	.	PUNCT
ejpam-3496	279	1	by	by	ADP
ejpam-3496	279	2	the	the	DET
ejpam-3496	279	3	given	give	VERB
ejpam-3496	279	4	hypothesis	hypothesis	NOUN
ejpam-3496	279	5	,	,	PUNCT
ejpam-3496	279	6	we	we	PRON
ejpam-3496	279	7	have	have	VERB
ejpam-3496	279	8	[	[	X
ejpam-3496	279	9	d1(x	d1(x	NOUN
ejpam-3496	279	10	)	)	PUNCT
ejpam-3496	279	11	,	,	PUNCT
ejpam-3496	279	12	d2(x	d2(x	NOUN
ejpam-3496	279	13	∗	∗	NOUN
ejpam-3496	279	14	)	)	PUNCT
ejpam-3496	279	15	]	]	PUNCT
ejpam-3496	280	1	=	=	PUNCT
ejpam-3496	280	2	x	x	PUNCT
ejpam-3496	280	3	◦	◦	NOUN
ejpam-3496	280	4	x∗	x∗	PROPN
ejpam-3496	280	5	for	for	ADP
ejpam-3496	280	6	all	all	DET
ejpam-3496	280	7	x	x	PROPN
ejpam-3496	280	8	∈	∈	PROPN
ejpam-3496	280	9	r.	r.	NOUN
ejpam-3496	280	10	(	(	PUNCT
ejpam-3496	280	11	29	29	NUM
ejpam-3496	280	12	)	)	PUNCT
ejpam-3496	280	13	replacing	replace	VERB
ejpam-3496	280	14	x	x	PUNCT
ejpam-3496	280	15	by	by	ADP
ejpam-3496	280	16	x+	x+	PROPN
ejpam-3496	280	17	y	y	PROPN
ejpam-3496	280	18	in	in	ADP
ejpam-3496	280	19	(	(	PUNCT
ejpam-3496	280	20	29	29	NUM
ejpam-3496	280	21	)	)	PUNCT
ejpam-3496	280	22	,	,	PUNCT
ejpam-3496	280	23	we	we	PRON
ejpam-3496	280	24	get	get	VERB
ejpam-3496	280	25	[	[	X
ejpam-3496	280	26	d1(x	d1(x	NOUN
ejpam-3496	280	27	)	)	PUNCT
ejpam-3496	280	28	,	,	PUNCT
ejpam-3496	280	29	d2(x	d2(x	NOUN
ejpam-3496	280	30	∗	∗	NOUN
ejpam-3496	280	31	)	)	PUNCT
ejpam-3496	280	32	]	]	PUNCT
ejpam-3496	281	1	+	+	CCONJ
ejpam-3496	282	1	[	[	X
ejpam-3496	282	2	d1(y	d1(y	X
ejpam-3496	282	3	)	)	PUNCT
ejpam-3496	282	4	,	,	PUNCT
ejpam-3496	282	5	d2(y	d2(y	PROPN
ejpam-3496	282	6	∗	∗	NOUN
ejpam-3496	282	7	)	)	PUNCT
ejpam-3496	282	8	]	]	PUNCT
ejpam-3496	283	1	+	+	CCONJ
ejpam-3496	283	2	[	[	X
ejpam-3496	283	3	d1(x	d1(x	X
ejpam-3496	283	4	)	)	PUNCT
ejpam-3496	283	5	,	,	PUNCT
ejpam-3496	283	6	d2(y	d2(y	PROPN
ejpam-3496	283	7	∗	∗	NOUN
ejpam-3496	283	8	)	)	PUNCT
ejpam-3496	283	9	]	]	PUNCT
ejpam-3496	284	1	+	+	CCONJ
ejpam-3496	285	1	[	[	X
ejpam-3496	285	2	d1(y	d1(y	X
ejpam-3496	285	3	)	)	PUNCT
ejpam-3496	285	4	,	,	PUNCT
ejpam-3496	285	5	d2(x	d2(x	PROPN
ejpam-3496	285	6	∗	∗	NOUN
ejpam-3496	285	7	)	)	PUNCT
ejpam-3496	285	8	]	]	PUNCT
ejpam-3496	286	1	=	=	PUNCT
ejpam-3496	286	2	x	x	PUNCT
ejpam-3496	286	3	◦	◦	NOUN
ejpam-3496	286	4	x∗	x∗	NOUN
ejpam-3496	287	1	+	+	CCONJ
ejpam-3496	287	2	y	y	PROPN
ejpam-3496	287	3	◦	◦	NOUN
ejpam-3496	287	4	y∗	y∗	PROPN
ejpam-3496	288	1	+	+	NUM
ejpam-3496	288	2	xy∗	xy∗	NOUN
ejpam-3496	289	1	+	+	CCONJ
ejpam-3496	289	2	yx∗	yx∗	NOUN
ejpam-3496	289	3	+	+	CCONJ
ejpam-3496	289	4	x∗y	x∗y	PUNCT
ejpam-3496	290	1	+	+	CCONJ
ejpam-3496	290	2	y∗x	y∗x	ADV
ejpam-3496	290	3	for	for	ADP
ejpam-3496	290	4	all	all	DET
ejpam-3496	290	5	x	x	NOUN
ejpam-3496	290	6	,	,	PUNCT
ejpam-3496	290	7	y	y	PROPN
ejpam-3496	290	8	∈	∈	PROPN
ejpam-3496	290	9	r.	r.	NOUN
ejpam-3496	290	10	using	use	VERB
ejpam-3496	290	11	(	(	PUNCT
ejpam-3496	290	12	29	29	NUM
ejpam-3496	290	13	)	)	PUNCT
ejpam-3496	290	14	,	,	PUNCT
ejpam-3496	290	15	we	we	PRON
ejpam-3496	290	16	get	get	VERB
ejpam-3496	290	17	[	[	X
ejpam-3496	290	18	d1(x	d1(x	NOUN
ejpam-3496	290	19	)	)	PUNCT
ejpam-3496	290	20	,	,	PUNCT
ejpam-3496	290	21	d2(y	d2(y	PROPN
ejpam-3496	290	22	∗	∗	NOUN
ejpam-3496	290	23	)	)	PUNCT
ejpam-3496	290	24	]	]	PUNCT
ejpam-3496	291	1	+	+	CCONJ
ejpam-3496	292	1	[	[	X
ejpam-3496	292	2	d1(y	d1(y	X
ejpam-3496	292	3	)	)	PUNCT
ejpam-3496	292	4	,	,	PUNCT
ejpam-3496	292	5	d2(x	d2(x	PROPN
ejpam-3496	292	6	∗	∗	NOUN
ejpam-3496	292	7	)	)	PUNCT
ejpam-3496	292	8	]	]	PUNCT
ejpam-3496	293	1	=	=	PUNCT
ejpam-3496	293	2	xy∗	xy∗	NOUN
ejpam-3496	294	1	+	+	NUM
ejpam-3496	294	2	yx∗	yx∗	NOUN
ejpam-3496	294	3	+	+	CCONJ
ejpam-3496	294	4	x∗y	x∗y	PUNCT
ejpam-3496	295	1	+	+	CCONJ
ejpam-3496	295	2	y∗x	y∗x	PRON
ejpam-3496	295	3	(	(	PUNCT
ejpam-3496	295	4	30	30	NUM
ejpam-3496	295	5	)	)	PUNCT
ejpam-3496	295	6	for	for	ADP
ejpam-3496	295	7	all	all	DET
ejpam-3496	295	8	x	x	NOUN
ejpam-3496	295	9	,	,	PUNCT
ejpam-3496	295	10	y	y	PROPN
ejpam-3496	295	11	∈	∈	PROPN
ejpam-3496	295	12	r.	r.	PROPN
ejpam-3496	295	13	substituting	substitute	VERB
ejpam-3496	295	14	hy	hy	PROPN
ejpam-3496	295	15	for	for	ADP
ejpam-3496	295	16	y	y	PROPN
ejpam-3496	295	17	in	in	ADP
ejpam-3496	295	18	(	(	PUNCT
ejpam-3496	295	19	30	30	NUM
ejpam-3496	295	20	)	)	PUNCT
ejpam-3496	295	21	where	where	SCONJ
ejpam-3496	295	22	h	h	NOUN
ejpam-3496	295	23	∈	∈	PROPN
ejpam-3496	295	24	h(r	h(r	NOUN
ejpam-3496	295	25	)	)	PUNCT
ejpam-3496	295	26	∩	∩	NOUN
ejpam-3496	295	27	z(r	z(r	NOUN
ejpam-3496	295	28	)	)	PUNCT
ejpam-3496	295	29	,	,	PUNCT
ejpam-3496	295	30	we	we	PRON
ejpam-3496	295	31	have	have	VERB
ejpam-3496	295	32	h([d1(x	h([d1(x	NUM
ejpam-3496	295	33	)	)	PUNCT
ejpam-3496	295	34	,	,	PUNCT
ejpam-3496	295	35	d2(y	d2(y	PROPN
ejpam-3496	295	36	∗	∗	NOUN
ejpam-3496	295	37	)	)	PUNCT
ejpam-3496	295	38	]	]	PUNCT
ejpam-3496	296	1	+	+	CCONJ
ejpam-3496	297	1	[	[	X
ejpam-3496	297	2	d1(y	d1(y	X
ejpam-3496	297	3	)	)	PUNCT
ejpam-3496	297	4	,	,	PUNCT
ejpam-3496	297	5	d2(x	d2(x	PROPN
ejpam-3496	297	6	∗	∗	NOUN
ejpam-3496	297	7	)	)	PUNCT
ejpam-3496	297	8	]	]	PUNCT
ejpam-3496	297	9	)	)	PUNCT
ejpam-3496	298	1	+	+	CCONJ
ejpam-3496	299	1	[	[	X
ejpam-3496	299	2	d1(x	d1(x	X
ejpam-3496	299	3	)	)	PUNCT
ejpam-3496	299	4	,	,	PUNCT
ejpam-3496	299	5	y∗]d2(h	y∗]d2(h	PROPN
ejpam-3496	299	6	)	)	PUNCT
ejpam-3496	299	7	+	+	CCONJ
ejpam-3496	299	8	d1(h)[y	d1(h)[y	PROPN
ejpam-3496	299	9	,	,	PUNCT
ejpam-3496	299	10	d2(x	d2(x	NOUN
ejpam-3496	299	11	∗	∗	NOUN
ejpam-3496	299	12	)	)	PUNCT
ejpam-3496	299	13	]	]	PUNCT
ejpam-3496	299	14	(	(	PUNCT
ejpam-3496	299	15	31	31	NUM
ejpam-3496	299	16	)	)	PUNCT
ejpam-3496	299	17	=	=	SYM
ejpam-3496	299	18	h(xy∗	h(xy∗	PROPN
ejpam-3496	299	19	+	+	X
ejpam-3496	299	20	yx∗	yx∗	NOUN
ejpam-3496	299	21	+	+	CCONJ
ejpam-3496	299	22	x∗y	x∗y	PUNCT
ejpam-3496	299	23	+	+	CCONJ
ejpam-3496	299	24	y∗x	y∗x	X
ejpam-3496	299	25	)	)	PUNCT
ejpam-3496	299	26	for	for	ADP
ejpam-3496	299	27	all	all	DET
ejpam-3496	299	28	x	x	NOUN
ejpam-3496	299	29	,	,	PUNCT
ejpam-3496	299	30	y	y	PROPN
ejpam-3496	299	31	∈	∈	PROPN
ejpam-3496	299	32	r.	r.	NOUN
ejpam-3496	299	33	using	use	VERB
ejpam-3496	299	34	(	(	PUNCT
ejpam-3496	299	35	30	30	NUM
ejpam-3496	299	36	)	)	PUNCT
ejpam-3496	299	37	,	,	PUNCT
ejpam-3496	299	38	(	(	PUNCT
ejpam-3496	299	39	31	31	NUM
ejpam-3496	299	40	)	)	PUNCT
ejpam-3496	299	41	reduces	reduce	VERB
ejpam-3496	299	42	to	to	ADP
ejpam-3496	299	43	[	[	X
ejpam-3496	299	44	d1(x	d1(x	NOUN
ejpam-3496	299	45	)	)	PUNCT
ejpam-3496	299	46	,	,	PUNCT
ejpam-3496	299	47	y∗]d2(h	y∗]d2(h	PROPN
ejpam-3496	299	48	)	)	PUNCT
ejpam-3496	300	1	+	+	CCONJ
ejpam-3496	300	2	d1(h)[y	d1(h)[y	PROPN
ejpam-3496	300	3	,	,	PUNCT
ejpam-3496	300	4	d2(x	d2(x	NOUN
ejpam-3496	300	5	∗	∗	NOUN
ejpam-3496	300	6	)	)	PUNCT
ejpam-3496	300	7	]	]	PUNCT
ejpam-3496	301	1	=	=	PUNCT
ejpam-3496	301	2	0	0	NUM
ejpam-3496	301	3	for	for	ADP
ejpam-3496	301	4	all	all	DET
ejpam-3496	301	5	x	x	NOUN
ejpam-3496	301	6	,	,	PUNCT
ejpam-3496	301	7	y	y	PROPN
ejpam-3496	301	8	∈	∈	PROPN
ejpam-3496	301	9	r.	r.	PROPN
ejpam-3496	301	10	(	(	PUNCT
ejpam-3496	301	11	32	32	NUM
ejpam-3496	301	12	)	)	PUNCT
ejpam-3496	301	13	s.	s.	PROPN
ejpam-3496	301	14	ali	ali	PROPN
ejpam-3496	301	15	et	et	PROPN
ejpam-3496	301	16	al	al	PROPN
ejpam-3496	301	17	.	.	PUNCT
ejpam-3496	301	18	/	/	SYM
ejpam-3496	301	19	eur	eur	PROPN
ejpam-3496	301	20	.	.	PUNCT
ejpam-3496	302	1	j.	j.	PROPN
ejpam-3496	302	2	pure	pure	PROPN
ejpam-3496	302	3	appl	appl	PROPN
ejpam-3496	302	4	.	.	PROPN
ejpam-3496	302	5	math	math	PROPN
ejpam-3496	302	6	,	,	PUNCT
ejpam-3496	302	7	12	12	NUM
ejpam-3496	302	8	(	(	PUNCT
ejpam-3496	302	9	3	3	NUM
ejpam-3496	302	10	)	)	PUNCT
ejpam-3496	302	11	(	(	PUNCT
ejpam-3496	302	12	2019	2019	NUM
ejpam-3496	302	13	)	)	PUNCT
ejpam-3496	302	14	,	,	PUNCT
ejpam-3496	302	15	1138	1138	NUM
ejpam-3496	302	16	-	-	SYM
ejpam-3496	302	17	1148	1148	NUM
ejpam-3496	302	18	1146	1146	NUM
ejpam-3496	302	19	now	now	ADV
ejpam-3496	302	20	(	(	PUNCT
ejpam-3496	302	21	32	32	NUM
ejpam-3496	302	22	)	)	PUNCT
ejpam-3496	302	23	is	be	AUX
ejpam-3496	302	24	same	same	ADJ
ejpam-3496	302	25	as	as	ADP
ejpam-3496	302	26	(	(	PUNCT
ejpam-3496	302	27	14	14	NUM
ejpam-3496	302	28	)	)	PUNCT
ejpam-3496	302	29	and	and	CCONJ
ejpam-3496	302	30	thus	thus	ADV
ejpam-3496	302	31	following	follow	VERB
ejpam-3496	302	32	the	the	DET
ejpam-3496	302	33	same	same	ADJ
ejpam-3496	302	34	techniques	technique	NOUN
ejpam-3496	302	35	we	we	PRON
ejpam-3496	302	36	get	get	VERB
ejpam-3496	302	37	d1(z(r	d1(z(r	PRON
ejpam-3496	302	38	)	)	PUNCT
ejpam-3496	302	39	)	)	PUNCT
ejpam-3496	303	1	=	=	PUNCT
ejpam-3496	303	2	(	(	PUNCT
ejpam-3496	303	3	0	0	NUM
ejpam-3496	303	4	)	)	PUNCT
ejpam-3496	303	5	and	and	CCONJ
ejpam-3496	303	6	d2(z(r	d2(z(r	NOUN
ejpam-3496	303	7	)	)	PUNCT
ejpam-3496	303	8	)	)	PUNCT
ejpam-3496	304	1	=	=	PUNCT
ejpam-3496	304	2	(	(	PUNCT
ejpam-3496	304	3	0	0	NUM
ejpam-3496	304	4	)	)	PUNCT
ejpam-3496	304	5	.	.	PUNCT
ejpam-3496	305	1	now	now	ADV
ejpam-3496	305	2	replace	replace	VERB
ejpam-3496	305	3	y	y	PROPN
ejpam-3496	305	4	by	by	ADP
ejpam-3496	305	5	ky	ky	PROPN
ejpam-3496	305	6	in	in	ADP
ejpam-3496	305	7	(	(	PUNCT
ejpam-3496	305	8	30	30	NUM
ejpam-3496	305	9	)	)	PUNCT
ejpam-3496	305	10	where	where	SCONJ
ejpam-3496	305	11	k	k	PROPN
ejpam-3496	305	12	∈	∈	PROPN
ejpam-3496	305	13	s(r	s(r	PROPN
ejpam-3496	305	14	)	)	PUNCT
ejpam-3496	305	15	∩	∩	NOUN
ejpam-3496	305	16	z(r	z(r	NOUN
ejpam-3496	305	17	)	)	PUNCT
ejpam-3496	305	18	,	,	PUNCT
ejpam-3496	305	19	we	we	PRON
ejpam-3496	305	20	get	get	VERB
ejpam-3496	305	21	−[d1(x	−[d1(x	NOUN
ejpam-3496	305	22	)	)	PUNCT
ejpam-3496	305	23	,	,	PUNCT
ejpam-3496	305	24	d2(y	d2(y	PROPN
ejpam-3496	305	25	∗)]k	∗)]k	PROPN
ejpam-3496	306	1	−	−	PROPN
ejpam-3496	307	1	[	[	X
ejpam-3496	307	2	d1(x	d1(x	NOUN
ejpam-3496	307	3	)	)	PUNCT
ejpam-3496	307	4	,	,	PUNCT
ejpam-3496	307	5	y∗]d2(k	y∗]d2(k	PROPN
ejpam-3496	307	6	)	)	PUNCT
ejpam-3496	307	7	+	+	CCONJ
ejpam-3496	307	8	d1(k)[y	d1(k)[y	ADJ
ejpam-3496	307	9	,	,	PUNCT
ejpam-3496	307	10	d2(x	d2(x	NOUN
ejpam-3496	307	11	∗	∗	NOUN
ejpam-3496	307	12	)	)	PUNCT
ejpam-3496	307	13	]	]	PUNCT
ejpam-3496	308	1	+	+	CCONJ
ejpam-3496	308	2	k[d1(y	k[d1(y	PROPN
ejpam-3496	308	3	)	)	PUNCT
ejpam-3496	308	4	,	,	PUNCT
ejpam-3496	308	5	d2(x	d2(x	PROPN
ejpam-3496	308	6	∗	∗	NOUN
ejpam-3496	308	7	)	)	PUNCT
ejpam-3496	308	8	]	]	PUNCT
ejpam-3496	308	9	(	(	PUNCT
ejpam-3496	308	10	33	33	NUM
ejpam-3496	308	11	)	)	PUNCT
ejpam-3496	308	12	=	=	SYM
ejpam-3496	309	1	−xy∗k	−xy∗k	PROPN
ejpam-3496	310	1	+	+	CCONJ
ejpam-3496	310	2	kyx∗	kyx∗	PROPN
ejpam-3496	311	1	+	+	CCONJ
ejpam-3496	311	2	x∗ky	x∗ky	PROPN
ejpam-3496	311	3	−	−	PROPN
ejpam-3496	311	4	ky∗x	ky∗x	PROPN
ejpam-3496	311	5	for	for	ADP
ejpam-3496	311	6	all	all	DET
ejpam-3496	311	7	x	x	NOUN
ejpam-3496	311	8	,	,	PUNCT
ejpam-3496	311	9	y	y	PROPN
ejpam-3496	311	10	∈	∈	PROPN
ejpam-3496	311	11	r.	r.	PROPN
ejpam-3496	311	12	now	now	ADV
ejpam-3496	311	13	multiplying	multiply	VERB
ejpam-3496	311	14	(	(	PUNCT
ejpam-3496	311	15	30	30	NUM
ejpam-3496	311	16	)	)	PUNCT
ejpam-3496	311	17	by	by	ADP
ejpam-3496	311	18	k	k	PROPN
ejpam-3496	311	19	∈	∈	PROPN
ejpam-3496	311	20	s(r	s(r	PROPN
ejpam-3496	311	21	)	)	PUNCT
ejpam-3496	311	22	∩	∩	NOUN
ejpam-3496	311	23	z(r	z(r	NOUN
ejpam-3496	311	24	)	)	PUNCT
ejpam-3496	311	25	and	and	CCONJ
ejpam-3496	311	26	adding	add	VERB
ejpam-3496	311	27	with	with	ADP
ejpam-3496	311	28	(	(	PUNCT
ejpam-3496	311	29	33	33	NUM
ejpam-3496	311	30	)	)	PUNCT
ejpam-3496	311	31	,	,	PUNCT
ejpam-3496	311	32	we	we	PRON
ejpam-3496	311	33	get	get	VERB
ejpam-3496	311	34	2[d1(y	2[d1(y	NUM
ejpam-3496	311	35	)	)	PUNCT
ejpam-3496	311	36	,	,	PUNCT
ejpam-3496	311	37	d2(x	d2(x	NOUN
ejpam-3496	311	38	∗)]k	∗)]k	NUM
ejpam-3496	311	39	=	=	SYM
ejpam-3496	311	40	2k(yx∗	2k(yx∗	NOUN
ejpam-3496	312	1	+	+	CCONJ
ejpam-3496	312	2	x∗y	x∗y	X
ejpam-3496	312	3	)	)	PUNCT
ejpam-3496	312	4	for	for	ADP
ejpam-3496	312	5	all	all	DET
ejpam-3496	312	6	x	x	NOUN
ejpam-3496	312	7	,	,	PUNCT
ejpam-3496	312	8	y	y	PROPN
ejpam-3496	312	9	∈	∈	PROPN
ejpam-3496	312	10	r.	r.	PROPN
ejpam-3496	312	11	this	this	PRON
ejpam-3496	312	12	implies	imply	VERB
ejpam-3496	312	13	that	that	PRON
ejpam-3496	312	14	k([d1(y	k([d1(y	PROPN
ejpam-3496	312	15	)	)	PUNCT
ejpam-3496	312	16	,	,	PUNCT
ejpam-3496	312	17	d2(x	d2(x	PROPN
ejpam-3496	312	18	∗)]−	∗)]−	PROPN
ejpam-3496	312	19	(	(	PUNCT
ejpam-3496	312	20	y	y	PROPN
ejpam-3496	312	21	◦	◦	NOUN
ejpam-3496	312	22	x∗	x∗	NOUN
ejpam-3496	312	23	)	)	PUNCT
ejpam-3496	312	24	)	)	PUNCT
ejpam-3496	313	1	=	=	SYM
ejpam-3496	313	2	0	0	NUM
ejpam-3496	313	3	for	for	ADP
ejpam-3496	313	4	all	all	DET
ejpam-3496	313	5	x	x	NOUN
ejpam-3496	313	6	,	,	PUNCT
ejpam-3496	313	7	y	y	PROPN
ejpam-3496	313	8	∈	∈	PROPN
ejpam-3496	313	9	r.	r.	NOUN
ejpam-3496	313	10	invoking	invoke	VERB
ejpam-3496	313	11	the	the	DET
ejpam-3496	313	12	primeness	primeness	NOUN
ejpam-3496	313	13	of	of	ADP
ejpam-3496	313	14	r	r	NOUN
ejpam-3496	313	15	,	,	PUNCT
ejpam-3496	313	16	we	we	PRON
ejpam-3496	313	17	get	get	VERB
ejpam-3496	313	18	[	[	X
ejpam-3496	313	19	d1(y	d1(y	X
ejpam-3496	313	20	)	)	PUNCT
ejpam-3496	313	21	,	,	PUNCT
ejpam-3496	313	22	d2(x	d2(x	PROPN
ejpam-3496	313	23	∗)]−	∗)]−	PROPN
ejpam-3496	313	24	(	(	PUNCT
ejpam-3496	313	25	y	y	PROPN
ejpam-3496	313	26	◦	◦	NOUN
ejpam-3496	313	27	x∗	x∗	X
ejpam-3496	313	28	)	)	PUNCT
ejpam-3496	314	1	=	=	SYM
ejpam-3496	314	2	0	0	NUM
ejpam-3496	314	3	for	for	ADP
ejpam-3496	314	4	all	all	DET
ejpam-3496	314	5	x	x	NOUN
ejpam-3496	314	6	,	,	PUNCT
ejpam-3496	314	7	y	y	PROPN
ejpam-3496	314	8	∈	∈	PROPN
ejpam-3496	314	9	r.	r.	PROPN
ejpam-3496	314	10	now	now	ADV
ejpam-3496	314	11	replace	replace	VERB
ejpam-3496	314	12	x	x	VERB
ejpam-3496	314	13	by	by	ADP
ejpam-3496	314	14	x∗	x∗	PROPN
ejpam-3496	314	15	,	,	PUNCT
ejpam-3496	314	16	we	we	PRON
ejpam-3496	314	17	obtain	obtain	VERB
ejpam-3496	314	18	[	[	X
ejpam-3496	314	19	d1(y	d1(y	X
ejpam-3496	314	20	)	)	PUNCT
ejpam-3496	314	21	,	,	PUNCT
ejpam-3496	314	22	d2(x)]−	d2(x)]−	X
ejpam-3496	314	23	(	(	PUNCT
ejpam-3496	314	24	y	y	PROPN
ejpam-3496	314	25	◦	◦	NOUN
ejpam-3496	314	26	x	x	X
ejpam-3496	314	27	)	)	PUNCT
ejpam-3496	314	28	=	=	SYM
ejpam-3496	314	29	0	0	NUM
ejpam-3496	314	30	for	for	ADP
ejpam-3496	314	31	all	all	DET
ejpam-3496	314	32	x	x	NOUN
ejpam-3496	314	33	,	,	PUNCT
ejpam-3496	314	34	y	y	PROPN
ejpam-3496	314	35	∈	∈	PROPN
ejpam-3496	314	36	r.	r.	PROPN
ejpam-3496	314	37	hence	hence	ADV
ejpam-3496	314	38	application	application	NOUN
ejpam-3496	314	39	of	of	ADP
ejpam-3496	314	40	lemma	lemma	PROPN
ejpam-3496	314	41	1	1	NUM
ejpam-3496	314	42	gives	give	VERB
ejpam-3496	314	43	that	that	DET
ejpam-3496	314	44	d1	d1	PROPN
ejpam-3496	314	45	=	=	SYM
ejpam-3496	314	46	λd2	λd2	PROPN
ejpam-3496	314	47	,	,	PUNCT
ejpam-3496	314	48	where	where	SCONJ
ejpam-3496	314	49	λ	λ	PROPN
ejpam-3496	314	50	∈	∈	PROPN
ejpam-3496	314	51	c.	c.	PROPN
ejpam-3496	314	52	(	(	PUNCT
ejpam-3496	314	53	ii	ii	NOUN
ejpam-3496	314	54	)	)	PUNCT
ejpam-3496	314	55	similarly	similarly	ADV
ejpam-3496	314	56	we	we	PRON
ejpam-3496	314	57	can	can	AUX
ejpam-3496	314	58	prove	prove	VERB
ejpam-3496	314	59	the	the	DET
ejpam-3496	314	60	second	second	ADJ
ejpam-3496	314	61	part	part	NOUN
ejpam-3496	314	62	.	.	PUNCT
ejpam-3496	315	1	the	the	DET
ejpam-3496	315	2	following	follow	VERB
ejpam-3496	315	3	example	example	NOUN
ejpam-3496	315	4	shows	show	VERB
ejpam-3496	315	5	that	that	SCONJ
ejpam-3496	315	6	the	the	DET
ejpam-3496	315	7	primeness	primeness	NOUN
ejpam-3496	315	8	hypothesis	hypothesis	NOUN
ejpam-3496	315	9	in	in	ADP
ejpam-3496	315	10	main	main	ADJ
ejpam-3496	315	11	theorem	theorem	NOUN
ejpam-3496	315	12	and	and	CCONJ
ejpam-3496	315	13	theorem	theorem	VERB
ejpam-3496	315	14	2	2	NUM
ejpam-3496	315	15	is	be	AUX
ejpam-3496	315	16	not	not	PART
ejpam-3496	315	17	superfluous	superfluous	ADJ
ejpam-3496	315	18	.	.	PUNCT
ejpam-3496	315	19	example	example	NOUN
ejpam-3496	316	1	1	1	NUM
ejpam-3496	316	2	.	.	PUNCT
ejpam-3496	317	1	let	let	VERB
ejpam-3496	317	2	r	r	NOUN
ejpam-3496	317	3	=	=	PRON
ejpam-3496	317	4	{	{	PUNCT
ejpam-3496	317	5	(	(	PUNCT
ejpam-3496	317	6	a1	a1	NOUN
ejpam-3496	317	7	+	+	CCONJ
ejpam-3496	317	8	ib1	ib1	NOUN
ejpam-3496	317	9	a2	a2	PROPN
ejpam-3496	317	10	+	+	CCONJ
ejpam-3496	317	11	ib2	ib2	NOUN
ejpam-3496	317	12	a3	a3	NOUN
ejpam-3496	317	13	+	+	CCONJ
ejpam-3496	317	14	ib3	ib3	ADJ
ejpam-3496	317	15	a4	a4	NOUN
ejpam-3496	317	16	+	+	CCONJ
ejpam-3496	317	17	ib4	ib4	NOUN
ejpam-3496	317	18	)	)	PUNCT
ejpam-3496	317	19	∣∣∣	∣∣∣	NOUN
ejpam-3496	317	20	a1	a1	PROPN
ejpam-3496	317	21	,	,	PUNCT
ejpam-3496	317	22	a2	a2	PROPN
ejpam-3496	317	23	,	,	PUNCT
ejpam-3496	317	24	a3	a3	NOUN
ejpam-3496	317	25	,	,	PUNCT
ejpam-3496	317	26	a4	a4	PROPN
ejpam-3496	317	27	,	,	PUNCT
ejpam-3496	317	28	b1	b1	NOUN
ejpam-3496	317	29	,	,	PUNCT
ejpam-3496	317	30	b2	b2	NOUN
ejpam-3496	317	31	,	,	PUNCT
ejpam-3496	317	32	b3	b3	NOUN
ejpam-3496	317	33	,	,	PUNCT
ejpam-3496	317	34	b4	b4	NOUN
ejpam-3496	317	35	∈	∈	PROPN
ejpam-3496	317	36	r	r	NOUN
ejpam-3496	317	37	}	}	PUNCT
ejpam-3496	317	38	,	,	PUNCT
ejpam-3496	317	39	where	where	SCONJ
ejpam-3496	317	40	r	r	NOUN
ejpam-3496	317	41	is	be	AUX
ejpam-3496	317	42	a	a	DET
ejpam-3496	317	43	ring	ring	NOUN
ejpam-3496	317	44	of	of	ADP
ejpam-3496	317	45	real	real	ADJ
ejpam-3496	317	46	numbers	number	NOUN
ejpam-3496	317	47	.	.	PUNCT
ejpam-3496	318	1	of	of	ADP
ejpam-3496	318	2	course	course	NOUN
ejpam-3496	318	3	,	,	PUNCT
ejpam-3496	318	4	r	r	NOUN
ejpam-3496	318	5	with	with	ADP
ejpam-3496	318	6	matrix	matrix	NOUN
ejpam-3496	318	7	addition	addition	NOUN
ejpam-3496	318	8	and	and	CCONJ
ejpam-3496	318	9	matrix	matrix	NOUN
ejpam-3496	318	10	multiplication	multiplication	NOUN
ejpam-3496	318	11	is	be	AUX
ejpam-3496	318	12	a	a	DET
ejpam-3496	318	13	noncommutative	noncommutative	ADJ
ejpam-3496	318	14	prime	prime	ADJ
ejpam-3496	318	15	ring	ring	NOUN
ejpam-3496	318	16	.	.	PUNCT
ejpam-3496	319	1	define	define	VERB
ejpam-3496	319	2	mappings	mapping	NOUN
ejpam-3496	319	3	∗	∗	NOUN
ejpam-3496	319	4	,	,	PUNCT
ejpam-3496	319	5	d1	d1	PROPN
ejpam-3496	319	6	:	:	PUNCT
ejpam-3496	319	7	r	r	NOUN
ejpam-3496	319	8	−→	−→	NOUN
ejpam-3496	319	9	r	r	NOUN
ejpam-3496	319	10	such	such	ADJ
ejpam-3496	319	11	that	that	SCONJ
ejpam-3496	319	12	(	(	PUNCT
ejpam-3496	319	13	a1	a1	NOUN
ejpam-3496	319	14	+	+	CCONJ
ejpam-3496	319	15	ib1	ib1	NOUN
ejpam-3496	319	16	a2	a2	PROPN
ejpam-3496	319	17	+	+	CCONJ
ejpam-3496	319	18	ib2	ib2	NOUN
ejpam-3496	319	19	a3	a3	NOUN
ejpam-3496	319	20	+	+	CCONJ
ejpam-3496	319	21	ib3	ib3	ADJ
ejpam-3496	319	22	a4	a4	NOUN
ejpam-3496	319	23	+	+	CCONJ
ejpam-3496	319	24	ib4	ib4	NOUN
ejpam-3496	319	25	)	)	PUNCT
ejpam-3496	319	26	∗	∗	NOUN
ejpam-3496	319	27	=	=	PUNCT
ejpam-3496	319	28	(	(	PUNCT
ejpam-3496	319	29	a1	a1	NOUN
ejpam-3496	319	30	−	−	PROPN
ejpam-3496	319	31	ib1	ib1	NOUN
ejpam-3496	319	32	a3	a3	NOUN
ejpam-3496	319	33	−	−	PROPN
ejpam-3496	319	34	ib3	ib3	PROPN
ejpam-3496	319	35	a2	a2	PROPN
ejpam-3496	319	36	−	−	NOUN
ejpam-3496	319	37	ib2	ib2	NOUN
ejpam-3496	319	38	a4	a4	NOUN
ejpam-3496	319	39	−	−	NOUN
ejpam-3496	319	40	ib4	ib4	NOUN
ejpam-3496	319	41	)	)	PUNCT
ejpam-3496	319	42	and	and	CCONJ
ejpam-3496	319	43	,	,	PUNCT
ejpam-3496	319	44	d1	d1	PROPN
ejpam-3496	319	45	(	(	PUNCT
ejpam-3496	319	46	a1	a1	NOUN
ejpam-3496	319	47	+	+	CCONJ
ejpam-3496	319	48	ib1	ib1	NOUN
ejpam-3496	319	49	a2	a2	PROPN
ejpam-3496	319	50	+	+	CCONJ
ejpam-3496	319	51	ib2	ib2	NOUN
ejpam-3496	319	52	a3	a3	NOUN
ejpam-3496	319	53	+	+	CCONJ
ejpam-3496	319	54	ib3	ib3	ADJ
ejpam-3496	319	55	a4	a4	NOUN
ejpam-3496	319	56	+	+	CCONJ
ejpam-3496	319	57	ib4	ib4	NOUN
ejpam-3496	319	58	)	)	PUNCT
ejpam-3496	320	1	=	=	PUNCT
ejpam-3496	320	2	(	(	PUNCT
ejpam-3496	320	3	0	0	NUM
ejpam-3496	320	4	−(a2	−(a2	PRON
ejpam-3496	320	5	+	+	NUM
ejpam-3496	320	6	ib2	ib2	NOUN
ejpam-3496	320	7	)	)	PUNCT
ejpam-3496	320	8	(	(	PUNCT
ejpam-3496	320	9	a3	a3	VERB
ejpam-3496	320	10	+	+	CCONJ
ejpam-3496	320	11	ib3	ib3	NOUN
ejpam-3496	320	12	)	)	PUNCT
ejpam-3496	320	13	0	0	NUM
ejpam-3496	320	14	)	)	PUNCT
ejpam-3496	320	15	.	.	PUNCT
ejpam-3496	321	1	it	it	PRON
ejpam-3496	321	2	can	can	AUX
ejpam-3496	321	3	be	be	AUX
ejpam-3496	321	4	easily	easily	ADV
ejpam-3496	321	5	checked	check	VERB
ejpam-3496	321	6	that	that	SCONJ
ejpam-3496	321	7	∗	∗	NOUN
ejpam-3496	321	8	and	and	CCONJ
ejpam-3496	321	9	d1	d1	PROPN
ejpam-3496	321	10	are	be	AUX
ejpam-3496	321	11	respectively	respectively	ADV
ejpam-3496	321	12	involution	involution	NOUN
ejpam-3496	321	13	and	and	CCONJ
ejpam-3496	321	14	derivation	derivation	NOUN
ejpam-3496	321	15	on	on	ADP
ejpam-3496	321	16	r.	r.	PROPN
ejpam-3496	321	17	let	let	VERB
ejpam-3496	321	18	h	h	NOUN
ejpam-3496	321	19	be	be	AUX
ejpam-3496	321	20	a	a	DET
ejpam-3496	321	21	ring	ring	NOUN
ejpam-3496	321	22	of	of	ADP
ejpam-3496	321	23	real	real	ADJ
ejpam-3496	321	24	quaternions	quaternion	NOUN
ejpam-3496	321	25	.	.	PUNCT
ejpam-3496	322	1	define	define	VERB
ejpam-3496	322	2	involution	involution	NOUN
ejpam-3496	322	3	−	−	PROPN
ejpam-3496	322	4	and	and	CCONJ
ejpam-3496	322	5	derivation	derivation	NOUN
ejpam-3496	322	6	d2	d2	PROPN
ejpam-3496	322	7	=	=	SYM
ejpam-3496	322	8	di	di	PROPN
ejpam-3496	322	9	(	(	PUNCT
ejpam-3496	322	10	where	where	SCONJ
ejpam-3496	322	11	di	di	NOUN
ejpam-3496	322	12	is	be	AUX
ejpam-3496	322	13	an	an	DET
ejpam-3496	322	14	inner	inner	ADJ
ejpam-3496	322	15	derivation	derivation	NOUN
ejpam-3496	322	16	on	on	ADP
ejpam-3496	322	17	h	h	PROPN
ejpam-3496	322	18	determined	determine	VERB
ejpam-3496	322	19	by	by	ADP
ejpam-3496	322	20	i	i	PROPN
ejpam-3496	322	21	∈	∈	PROPN
ejpam-3496	322	22	h	h	NOUN
ejpam-3496	322	23	)	)	PUNCT
ejpam-3496	322	24	as	as	SCONJ
ejpam-3496	322	25	follows	follow	VERB
ejpam-3496	322	26	q	q	PROPN
ejpam-3496	322	27	=	=	PUNCT
ejpam-3496	322	28	α	α	NOUN
ejpam-3496	322	29	−	−	NOUN
ejpam-3496	322	30	iβ	iβ	ADP
ejpam-3496	322	31	−	−	PROPN
ejpam-3496	322	32	jγ	jγ	NOUN
ejpam-3496	322	33	−	−	PROPN
ejpam-3496	322	34	kδ	kδ	NOUN
ejpam-3496	322	35	and	and	CCONJ
ejpam-3496	322	36	di(q	di(q	NUM
ejpam-3496	322	37	)	)	PUNCT
ejpam-3496	323	1	=	=	PUNCT
ejpam-3496	324	1	[	[	X
ejpam-3496	324	2	i	i	X
ejpam-3496	324	3	,	,	PUNCT
ejpam-3496	324	4	q	q	X
ejpam-3496	324	5	]	]	X
ejpam-3496	324	6	for	for	ADP
ejpam-3496	324	7	all	all	DET
ejpam-3496	324	8	q	q	PROPN
ejpam-3496	324	9	∈	∈	PROPN
ejpam-3496	324	10	h.	h.	NOUN
ejpam-3496	324	11	let	let	VERB
ejpam-3496	324	12	s	s	NOUN
ejpam-3496	324	13	=	=	SYM
ejpam-3496	324	14	r×h	r×h	PROPN
ejpam-3496	324	15	,	,	PUNCT
ejpam-3496	324	16	where	where	SCONJ
ejpam-3496	324	17	r	r	NOUN
ejpam-3496	324	18	is	be	AUX
ejpam-3496	324	19	same	same	ADJ
ejpam-3496	324	20	as	as	ADP
ejpam-3496	324	21	defined	define	VERB
ejpam-3496	324	22	above	above	ADP
ejpam-3496	324	23	with	with	ADP
ejpam-3496	324	24	involution	involution	NOUN
ejpam-3496	324	25	∗	∗	NOUN
ejpam-3496	324	26	and	and	CCONJ
ejpam-3496	324	27	derivation	derivation	NOUN
ejpam-3496	324	28	d1	d1	PROPN
ejpam-3496	324	29	and	and	CCONJ
ejpam-3496	324	30	h	h	NOUN
ejpam-3496	324	31	is	be	AUX
ejpam-3496	324	32	the	the	DET
ejpam-3496	324	33	ring	ring	NOUN
ejpam-3496	324	34	of	of	ADP
ejpam-3496	324	35	real	real	ADJ
ejpam-3496	324	36	quaternions	quaternion	NOUN
ejpam-3496	324	37	with	with	ADP
ejpam-3496	324	38	involution	involution	NOUN
ejpam-3496	324	39	−	−	PROPN
ejpam-3496	324	40	and	and	CCONJ
ejpam-3496	324	41	derivation	derivation	NOUN
ejpam-3496	324	42	d2	d2	PROPN
ejpam-3496	324	43	as	as	ADP
ejpam-3496	324	44	above	above	ADV
ejpam-3496	324	45	.	.	PUNCT
ejpam-3496	325	1	clearly	clearly	ADV
ejpam-3496	325	2	,	,	PUNCT
ejpam-3496	325	3	s	s	VERB
ejpam-3496	325	4	is	be	AUX
ejpam-3496	325	5	a	a	DET
ejpam-3496	325	6	2	2	NUM
ejpam-3496	325	7	-	-	PUNCT
ejpam-3496	325	8	torsion	torsion	NOUN
ejpam-3496	325	9	free	free	ADJ
ejpam-3496	325	10	noncommutative	noncommutative	ADJ
ejpam-3496	325	11	semiprime	semiprime	NOUN
ejpam-3496	325	12	ring	ring	NOUN
ejpam-3496	325	13	.	.	PUNCT
ejpam-3496	326	1	now	now	ADV
ejpam-3496	326	2	define	define	VERB
ejpam-3496	326	3	an	an	DET
ejpam-3496	326	4	involution	involution	NOUN
ejpam-3496	326	5	α	α	NOUN
ejpam-3496	326	6	on	on	ADP
ejpam-3496	326	7	s	s	PROPN
ejpam-3496	326	8	,	,	PUNCT
ejpam-3496	326	9	references	reference	NOUN
ejpam-3496	326	10	1147	1147	NUM
ejpam-3496	326	11	as	as	ADP
ejpam-3496	326	12	(	(	PUNCT
ejpam-3496	326	13	x	x	NOUN
ejpam-3496	326	14	,	,	PUNCT
ejpam-3496	326	15	y)α	y)α	X
ejpam-3496	327	1	=	=	PUNCT
ejpam-3496	327	2	(	(	PUNCT
ejpam-3496	327	3	x∗	x∗	PROPN
ejpam-3496	327	4	,	,	PUNCT
ejpam-3496	327	5	y	y	NOUN
ejpam-3496	327	6	)	)	PUNCT
ejpam-3496	327	7	.	.	PUNCT
ejpam-3496	328	1	clearly	clearly	ADV
ejpam-3496	328	2	,	,	PUNCT
ejpam-3496	328	3	α	α	PROPN
ejpam-3496	328	4	is	be	AUX
ejpam-3496	328	5	an	an	DET
ejpam-3496	328	6	involution	involution	NOUN
ejpam-3496	328	7	of	of	ADP
ejpam-3496	328	8	the	the	DET
ejpam-3496	328	9	second	second	ADJ
ejpam-3496	328	10	kind	kind	NOUN
ejpam-3496	328	11	.	.	PUNCT
ejpam-3496	329	1	further	far	ADV
ejpam-3496	329	2	,	,	PUNCT
ejpam-3496	329	3	we	we	PRON
ejpam-3496	329	4	define	define	VERB
ejpam-3496	329	5	the	the	DET
ejpam-3496	329	6	mappings	mapping	NOUN
ejpam-3496	329	7	d1	d1	PROPN
ejpam-3496	329	8	and	and	CCONJ
ejpam-3496	329	9	d2	d2	PROPN
ejpam-3496	329	10	from	from	ADP
ejpam-3496	329	11	s	s	PRON
ejpam-3496	329	12	to	to	ADP
ejpam-3496	329	13	s	s	PRON
ejpam-3496	329	14	such	such	ADJ
ejpam-3496	329	15	that	that	DET
ejpam-3496	329	16	d1(x	d1(x	NOUN
ejpam-3496	329	17	,	,	PUNCT
ejpam-3496	329	18	y	y	NOUN
ejpam-3496	329	19	)	)	PUNCT
ejpam-3496	329	20	=	=	SYM
ejpam-3496	329	21	(	(	PUNCT
ejpam-3496	329	22	d1(x	d1(x	NOUN
ejpam-3496	329	23	)	)	PUNCT
ejpam-3496	329	24	,	,	PUNCT
ejpam-3496	329	25	0	0	NUM
ejpam-3496	329	26	)	)	PUNCT
ejpam-3496	329	27	and	and	CCONJ
ejpam-3496	329	28	d2(x	d2(x	PROPN
ejpam-3496	329	29	,	,	PUNCT
ejpam-3496	329	30	y	y	NOUN
ejpam-3496	329	31	)	)	PUNCT
ejpam-3496	329	32	=	=	SYM
ejpam-3496	329	33	(	(	PUNCT
ejpam-3496	329	34	0	0	NUM
ejpam-3496	329	35	,	,	PUNCT
ejpam-3496	329	36	d2(x	d2(x	NOUN
ejpam-3496	329	37	)	)	PUNCT
ejpam-3496	329	38	)	)	PUNCT
ejpam-3496	329	39	for	for	ADP
ejpam-3496	329	40	all	all	DET
ejpam-3496	329	41	(	(	PUNCT
ejpam-3496	329	42	x	x	NOUN
ejpam-3496	329	43	,	,	PUNCT
ejpam-3496	329	44	y	y	PROPN
ejpam-3496	329	45	)	)	PUNCT
ejpam-3496	329	46	∈	∈	PROPN
ejpam-3496	329	47	s.	s.	PROPN
ejpam-3496	329	48	it	it	PRON
ejpam-3496	329	49	can	can	AUX
ejpam-3496	329	50	be	be	AUX
ejpam-3496	329	51	easily	easily	ADV
ejpam-3496	329	52	checked	check	VERB
ejpam-3496	329	53	that	that	SCONJ
ejpam-3496	329	54	d1	d1	PROPN
ejpam-3496	329	55	,	,	PUNCT
ejpam-3496	329	56	d2	d2	PROPN
ejpam-3496	329	57	are	be	AUX
ejpam-3496	329	58	derivations	derivation	NOUN
ejpam-3496	329	59	on	on	ADP
ejpam-3496	329	60	s	s	PRON
ejpam-3496	329	61	and	and	CCONJ
ejpam-3496	329	62	satisfying	satisfy	VERB
ejpam-3496	329	63	[	[	X
ejpam-3496	329	64	d1(x	d1(x	NOUN
ejpam-3496	329	65	)	)	PUNCT
ejpam-3496	329	66	,	,	PUNCT
ejpam-3496	329	67	d2(x	d2(x	PROPN
ejpam-3496	329	68	α	α	X
ejpam-3496	329	69	)	)	PUNCT
ejpam-3496	329	70	]	]	PUNCT
ejpam-3496	330	1	=	=	SYM
ejpam-3496	330	2	0	0	PUNCT
ejpam-3496	331	1	and	and	CCONJ
ejpam-3496	332	1	[	[	X
ejpam-3496	332	2	d1(x	d1(x	NOUN
ejpam-3496	332	3	)	)	PUNCT
ejpam-3496	332	4	,	,	PUNCT
ejpam-3496	332	5	xαd2(x	xαd2(x	NOUN
ejpam-3496	332	6	)	)	PUNCT
ejpam-3496	332	7	]	]	PUNCT
ejpam-3496	333	1	=	=	PUNCT
ejpam-3496	333	2	0	0	PUNCT
ejpam-3496	333	3	for	for	ADP
ejpam-3496	333	4	all	all	DET
ejpam-3496	333	5	x	x	SYM
ejpam-3496	333	6	∈	∈	PROPN
ejpam-3496	333	7	s	s	NOUN
ejpam-3496	333	8	,	,	PUNCT
ejpam-3496	333	9	but	but	CCONJ
ejpam-3496	333	10	d1	d1	PROPN
ejpam-3496	333	11	and	and	CCONJ
ejpam-3496	333	12	d2	d2	PROPN
ejpam-3496	333	13	are	be	AUX
ejpam-3496	333	14	linearly	linearly	ADV
ejpam-3496	333	15	independent	independent	ADJ
ejpam-3496	333	16	derivations	derivation	NOUN
ejpam-3496	333	17	.	.	PUNCT
ejpam-3496	334	1	hence	hence	ADV
ejpam-3496	334	2	,	,	PUNCT
ejpam-3496	334	3	in	in	ADP
ejpam-3496	334	4	main	main	ADJ
ejpam-3496	334	5	theorem	theorem	NOUN
ejpam-3496	334	6	and	and	CCONJ
ejpam-3496	334	7	theorem	theorem	VERB
ejpam-3496	334	8	2	2	NUM
ejpam-3496	334	9	,	,	PUNCT
ejpam-3496	334	10	the	the	DET
ejpam-3496	334	11	hypothesis	hypothesis	NOUN
ejpam-3496	334	12	of	of	ADP
ejpam-3496	334	13	primeness	primeness	NOUN
ejpam-3496	334	14	is	be	AUX
ejpam-3496	334	15	essential	essential	ADJ
ejpam-3496	334	16	.	.	PUNCT
ejpam-3496	335	1	acknowledgements	acknowledgement	NOUN
ejpam-3496	335	2	the	the	DET
ejpam-3496	335	3	authors	author	NOUN
ejpam-3496	335	4	would	would	AUX
ejpam-3496	335	5	like	like	VERB
ejpam-3496	335	6	to	to	PART
ejpam-3496	335	7	thank	thank	VERB
ejpam-3496	335	8	the	the	DET
ejpam-3496	335	9	referee(s	referee(s	NOUN
ejpam-3496	335	10	)	)	PUNCT
ejpam-3496	335	11	for	for	ADP
ejpam-3496	335	12	his	his	PRON
ejpam-3496	335	13	/	/	SYM
ejpam-3496	335	14	her	her	PRON
ejpam-3496	335	15	careful	careful	ADJ
ejpam-3496	335	16	reading	reading	NOUN
ejpam-3496	335	17	of	of	ADP
ejpam-3496	335	18	the	the	DET
ejpam-3496	335	19	manuscript	manuscript	NOUN
ejpam-3496	335	20	.	.	PUNCT
ejpam-3496	336	1	references	reference	NOUN
ejpam-3496	336	2	[	[	X
ejpam-3496	336	3	1	1	X
ejpam-3496	336	4	]	]	PUNCT
ejpam-3496	336	5	s.	s.	PROPN
ejpam-3496	336	6	ali	ali	PROPN
ejpam-3496	336	7	and	and	CCONJ
ejpam-3496	336	8	n.	n.	PROPN
ejpam-3496	336	9	a.	a.	PROPN
ejpam-3496	336	10	dar	dar	PROPN
ejpam-3496	336	11	.	.	PUNCT
ejpam-3496	337	1	on	on	ADP
ejpam-3496	337	2	∗-centralizing	∗-centralize	VERB
ejpam-3496	337	3	mappings	mapping	NOUN
ejpam-3496	337	4	in	in	ADP
ejpam-3496	337	5	rings	ring	NOUN
ejpam-3496	337	6	with	with	ADP
ejpam-3496	337	7	involution	involution	NOUN
ejpam-3496	337	8	,	,	PUNCT
ejpam-3496	337	9	georgian	georgian	ADJ
ejpam-3496	337	10	math	math	NOUN
ejpam-3496	337	11	.	.	PUNCT
ejpam-3496	338	1	j.	j.	PROPN
ejpam-3496	338	2	,	,	PUNCT
ejpam-3496	338	3	21:25–28	21:25–28	PROPN
ejpam-3496	338	4	,	,	PUNCT
ejpam-3496	338	5	2014	2014	NUM
ejpam-3496	338	6	.	.	PUNCT
ejpam-3496	339	1	[	[	X
ejpam-3496	339	2	2	2	X
ejpam-3496	339	3	]	]	PUNCT
ejpam-3496	339	4	s.	s.	PROPN
ejpam-3496	339	5	ali	ali	PROPN
ejpam-3496	339	6	,	,	PUNCT
ejpam-3496	339	7	m.	m.	PROPN
ejpam-3496	339	8	s.	s.	PROPN
ejpam-3496	339	9	khan	khan	PROPN
ejpam-3496	339	10	and	and	CCONJ
ejpam-3496	339	11	m.	m.	PROPN
ejpam-3496	339	12	m.	m.	PROPN
ejpam-3496	339	13	al	al	PROPN
ejpam-3496	339	14	-	-	PUNCT
ejpam-3496	339	15	shomrani	shomrani	PROPN
ejpam-3496	339	16	.	.	PUNCT
ejpam-3496	340	1	generalization	generalization	NOUN
ejpam-3496	340	2	of	of	ADP
ejpam-3496	340	3	herstein	herstein	PROPN
ejpam-3496	340	4	theorem	theorem	NOUN
ejpam-3496	340	5	and	and	CCONJ
ejpam-3496	340	6	its	its	PRON
ejpam-3496	340	7	applications	application	NOUN
ejpam-3496	340	8	to	to	PART
ejpam-3496	340	9	range	range	VERB
ejpam-3496	340	10	inclusion	inclusion	NOUN
ejpam-3496	340	11	problems	problem	NOUN
ejpam-3496	340	12	,	,	PUNCT
ejpam-3496	340	13	j.	j.	PROPN
ejpam-3496	340	14	egyptian	egyptian	PROPN
ejpam-3496	340	15	math	math	PROPN
ejpam-3496	340	16	.	.	PUNCT
ejpam-3496	341	1	soc	soc	PROPN
ejpam-3496	341	2	.	.	PUNCT
ejpam-3496	342	1	,	,	PUNCT
ejpam-3496	342	2	22(3):322–326	22(3):322–326	NOUN
ejpam-3496	342	3	,	,	PUNCT
ejpam-3496	342	4	2014	2014	NUM
ejpam-3496	342	5	.	.	PUNCT
ejpam-3496	343	1	[	[	X
ejpam-3496	343	2	3	3	X
ejpam-3496	343	3	]	]	PUNCT
ejpam-3496	343	4	m.	m.	NOUN
ejpam-3496	343	5	ashraf	ashraf	NOUN
ejpam-3496	343	6	and	and	CCONJ
ejpam-3496	343	7	n.	n.	PROPN
ejpam-3496	343	8	rehman	rehman	PROPN
ejpam-3496	343	9	.	.	PUNCT
ejpam-3496	344	1	on	on	ADP
ejpam-3496	344	2	commutativity	commutativity	NOUN
ejpam-3496	344	3	of	of	ADP
ejpam-3496	344	4	rings	ring	NOUN
ejpam-3496	344	5	with	with	ADP
ejpam-3496	344	6	derivations	derivation	NOUN
ejpam-3496	344	7	,	,	PUNCT
ejpam-3496	344	8	results	result	VERB
ejpam-3496	344	9	math	math	NOUN
ejpam-3496	344	10	.	.	PUNCT
ejpam-3496	344	11	,	,	PUNCT
ejpam-3496	344	12	42:3–8	42:3–8	NOUN
ejpam-3496	344	13	,	,	PUNCT
ejpam-3496	344	14	2002	2002	NUM
ejpam-3496	344	15	.	.	PUNCT
ejpam-3496	345	1	[	[	X
ejpam-3496	345	2	4	4	X
ejpam-3496	345	3	]	]	PUNCT
ejpam-3496	345	4	k.	k.	PROPN
ejpam-3496	345	5	i.	i.	PROPN
ejpam-3496	345	6	beider	beider	PROPN
ejpam-3496	345	7	,	,	PUNCT
ejpam-3496	345	8	w.	w.	PROPN
ejpam-3496	345	9	s.	s.	PROPN
ejpam-3496	345	10	martindale	martindale	PROPN
ejpam-3496	345	11	iii	iii	PROPN
ejpam-3496	345	12	and	and	CCONJ
ejpam-3496	345	13	a.	a.	NOUN
ejpam-3496	345	14	v.	v.	ADP
ejpam-3496	345	15	mikhalev	mikhalev	PROPN
ejpam-3496	345	16	.	.	PUNCT
ejpam-3496	346	1	rings	ring	NOUN
ejpam-3496	346	2	with	with	ADP
ejpam-3496	346	3	generalized	generalized	ADJ
ejpam-3496	346	4	identities	identity	NOUN
ejpam-3496	346	5	,	,	PUNCT
ejpam-3496	346	6	monogr	monogr	NOUN
ejpam-3496	346	7	.	.	PUNCT
ejpam-3496	347	1	pure	pure	ADJ
ejpam-3496	347	2	appl	appl	PROPN
ejpam-3496	347	3	.	.	PUNCT
ejpam-3496	347	4	math	math	NOUN
ejpam-3496	347	5	.	.	PUNCT
ejpam-3496	348	1	196	196	NUM
ejpam-3496	348	2	,	,	PUNCT
ejpam-3496	348	3	marcel	marcel	PROPN
ejpam-3496	348	4	dekker	dekker	PROPN
ejpam-3496	348	5	,	,	PUNCT
ejpam-3496	348	6	new	new	PROPN
ejpam-3496	348	7	york	york	PROPN
ejpam-3496	348	8	,	,	PUNCT
ejpam-3496	348	9	11	11	NUM
ejpam-3496	348	10	1996	1996	NUM
ejpam-3496	348	11	.	.	PUNCT
ejpam-3496	349	1	[	[	X
ejpam-3496	349	2	5	5	X
ejpam-3496	349	3	]	]	PUNCT
ejpam-3496	349	4	h.	h.	PROPN
ejpam-3496	349	5	e.	e.	PROPN
ejpam-3496	349	6	bell	bell	PROPN
ejpam-3496	349	7	and	and	CCONJ
ejpam-3496	349	8	m.	m.	NOUN
ejpam-3496	349	9	n.	n.	PROPN
ejpam-3496	349	10	daif	daif	PROPN
ejpam-3496	349	11	.	.	PUNCT
ejpam-3496	350	1	on	on	ADP
ejpam-3496	350	2	derivations	derivation	NOUN
ejpam-3496	350	3	and	and	CCONJ
ejpam-3496	350	4	commutativity	commutativity	NOUN
ejpam-3496	350	5	in	in	ADP
ejpam-3496	350	6	prime	prime	ADJ
ejpam-3496	350	7	rings	ring	NOUN
ejpam-3496	350	8	,	,	PUNCT
ejpam-3496	350	9	acta	acta	PROPN
ejpam-3496	350	10	math	math	PROPN
ejpam-3496	350	11	.	.	PUNCT
ejpam-3496	351	1	hungar	hungar	PROPN
ejpam-3496	351	2	.	.	PUNCT
ejpam-3496	351	3	,	,	PUNCT
ejpam-3496	352	1	66:337–343	66:337–343	PROPN
ejpam-3496	352	2	,	,	PUNCT
ejpam-3496	352	3	1995	1995	NUM
ejpam-3496	352	4	.	.	PUNCT
ejpam-3496	353	1	[	[	X
ejpam-3496	353	2	6	6	NUM
ejpam-3496	353	3	]	]	PUNCT
ejpam-3496	353	4	h.	h.	PROPN
ejpam-3496	353	5	e.	e.	PROPN
ejpam-3496	353	6	bell	bell	PROPN
ejpam-3496	353	7	and	and	CCONJ
ejpam-3496	353	8	m.	m.	NOUN
ejpam-3496	353	9	n.	n.	PROPN
ejpam-3496	353	10	daif	daif	PROPN
ejpam-3496	353	11	.	.	PUNCT
ejpam-3496	354	1	on	on	ADP
ejpam-3496	354	2	commutativity	commutativity	NOUN
ejpam-3496	354	3	and	and	CCONJ
ejpam-3496	354	4	strong	strong	ADJ
ejpam-3496	354	5	commutativity	commutativity	NOUN
ejpam-3496	354	6	preserving	preserve	VERB
ejpam-3496	354	7	maps	map	NOUN
ejpam-3496	354	8	,	,	PUNCT
ejpam-3496	354	9	canad	canad	PROPN
ejpam-3496	354	10	.	.	PUNCT
ejpam-3496	355	1	math	math	NOUN
ejpam-3496	355	2	.	.	PUNCT
ejpam-3496	356	1	bull	bull	PROPN
ejpam-3496	356	2	.	.	PUNCT
ejpam-3496	356	3	,	,	PUNCT
ejpam-3496	357	1	37:443–447	37:443–447	NUM
ejpam-3496	357	2	,	,	PUNCT
ejpam-3496	357	3	1994	1994	NUM
ejpam-3496	357	4	.	.	PUNCT
ejpam-3496	358	1	[	[	X
ejpam-3496	358	2	7	7	X
ejpam-3496	358	3	]	]	X
ejpam-3496	358	4	h.	h.	PROPN
ejpam-3496	358	5	e.	e.	PROPN
ejpam-3496	358	6	bell	bell	PROPN
ejpam-3496	358	7	and	and	CCONJ
ejpam-3496	358	8	w.	w.	PROPN
ejpam-3496	358	9	s.	s.	PROPN
ejpam-3496	358	10	martindale	martindale	PROPN
ejpam-3496	358	11	iii	iii	PROPN
ejpam-3496	358	12	.	.	PUNCT
ejpam-3496	359	1	centralizing	centralize	VERB
ejpam-3496	359	2	mappings	mapping	NOUN
ejpam-3496	359	3	on	on	ADP
ejpam-3496	359	4	semiprime	semiprime	NOUN
ejpam-3496	359	5	rings	ring	NOUN
ejpam-3496	359	6	,	,	PUNCT
ejpam-3496	359	7	canad	canad	PROPN
ejpam-3496	359	8	.	.	PUNCT
ejpam-3496	360	1	math	math	NOUN
ejpam-3496	360	2	.	.	PUNCT
ejpam-3496	361	1	bull	bull	PROPN
ejpam-3496	361	2	.	.	PUNCT
ejpam-3496	361	3	,	,	PUNCT
ejpam-3496	362	1	30:92–101	30:92–101	NUM
ejpam-3496	362	2	,	,	PUNCT
ejpam-3496	362	3	1987	1987	NUM
ejpam-3496	362	4	.	.	PUNCT
ejpam-3496	363	1	[	[	X
ejpam-3496	363	2	8	8	X
ejpam-3496	363	3	]	]	X
ejpam-3496	363	4	h.	h.	PROPN
ejpam-3496	363	5	e.	e.	PROPN
ejpam-3496	363	6	bell	bell	PROPN
ejpam-3496	363	7	and	and	CCONJ
ejpam-3496	363	8	n.	n.	PROPN
ejpam-3496	363	9	rehman	rehman	PROPN
ejpam-3496	363	10	.	.	PUNCT
ejpam-3496	364	1	generalized	generalized	ADJ
ejpam-3496	364	2	derivations	derivation	NOUN
ejpam-3496	364	3	with	with	ADP
ejpam-3496	364	4	commutativity	commutativity	NOUN
ejpam-3496	364	5	and	and	CCONJ
ejpam-3496	364	6	anticommutativity	anticommutativity	NOUN
ejpam-3496	364	7	conditions	condition	NOUN
ejpam-3496	364	8	,	,	PUNCT
ejpam-3496	364	9	math	math	NOUN
ejpam-3496	364	10	.	.	PUNCT
ejpam-3496	365	1	j.	j.	PROPN
ejpam-3496	365	2	okayama	okayama	PROPN
ejpam-3496	365	3	univ	univ	PROPN
ejpam-3496	365	4	.	.	PROPN
ejpam-3496	365	5	,	,	PUNCT
ejpam-3496	366	1	49:139–147	49:139–147	PROPN
ejpam-3496	366	2	,	,	PUNCT
ejpam-3496	366	3	2007	2007	NUM
ejpam-3496	366	4	.	.	PUNCT
ejpam-3496	367	1	[	[	X
ejpam-3496	367	2	9	9	NUM
ejpam-3496	367	3	]	]	PUNCT
ejpam-3496	367	4	m.	m.	NOUN
ejpam-3496	367	5	brešar	brešar	NOUN
ejpam-3496	367	6	and	and	CCONJ
ejpam-3496	367	7	c.	c.	PROPN
ejpam-3496	367	8	r.	r.	PROPN
ejpam-3496	367	9	miers	miers	PROPN
ejpam-3496	367	10	.	.	PUNCT
ejpam-3496	368	1	strong	strong	ADJ
ejpam-3496	368	2	commutativity	commutativity	NOUN
ejpam-3496	368	3	preserving	preserve	VERB
ejpam-3496	368	4	mappings	mapping	NOUN
ejpam-3496	368	5	of	of	ADP
ejpam-3496	368	6	semiprime	semiprime	NOUN
ejpam-3496	368	7	rings	ring	NOUN
ejpam-3496	368	8	,	,	PUNCT
ejpam-3496	368	9	canad	canad	PROPN
ejpam-3496	368	10	.	.	PUNCT
ejpam-3496	369	1	math	math	NOUN
ejpam-3496	369	2	.	.	PUNCT
ejpam-3496	370	1	bull	bull	PROPN
ejpam-3496	370	2	.	.	PUNCT
ejpam-3496	370	3	,	,	PUNCT
ejpam-3496	370	4	37:457–460	37:457–460	NUM
ejpam-3496	370	5	,	,	PUNCT
ejpam-3496	370	6	1994	1994	NUM
ejpam-3496	370	7	.	.	PUNCT
ejpam-3496	371	1	[	[	X
ejpam-3496	371	2	10	10	NUM
ejpam-3496	371	3	]	]	PUNCT
ejpam-3496	371	4	m.	m.	NOUN
ejpam-3496	371	5	n.	n.	PROPN
ejpam-3496	371	6	daif	daif	PROPN
ejpam-3496	371	7	.	.	PUNCT
ejpam-3496	372	1	commutativity	commutativity	NOUN
ejpam-3496	372	2	results	result	VERB
ejpam-3496	372	3	for	for	ADP
ejpam-3496	372	4	semiprime	semiprime	NOUN
ejpam-3496	372	5	rings	ring	NOUN
ejpam-3496	372	6	with	with	ADP
ejpam-3496	372	7	derivations	derivation	NOUN
ejpam-3496	372	8	,	,	PUNCT
ejpam-3496	372	9	internat	internat	PROPN
ejpam-3496	372	10	.	.	PUNCT
ejpam-3496	373	1	j.	j.	PROPN
ejpam-3496	373	2	math	math	PROPN
ejpam-3496	373	3	.	.	PUNCT
ejpam-3496	374	1	math	math	NOUN
ejpam-3496	374	2	.	.	PUNCT
ejpam-3496	375	1	sci	sci	PROPN
ejpam-3496	375	2	.	.	PROPN
ejpam-3496	375	3	,	,	PUNCT
ejpam-3496	375	4	21(3):471–474	21(3):471–474	PROPN
ejpam-3496	375	5	,	,	PUNCT
ejpam-3496	375	6	1998	1998	NUM
ejpam-3496	375	7	.	.	PUNCT
ejpam-3496	376	1	[	[	X
ejpam-3496	376	2	11	11	NUM
ejpam-3496	376	3	]	]	X
ejpam-3496	376	4	n.	n.	PROPN
ejpam-3496	376	5	a.	a.	PROPN
ejpam-3496	376	6	dar	dar	PROPN
ejpam-3496	376	7	and	and	CCONJ
ejpam-3496	376	8	s.	s.	PROPN
ejpam-3496	376	9	ali	ali	PROPN
ejpam-3496	376	10	.	.	PUNCT
ejpam-3496	377	1	on	on	ADP
ejpam-3496	377	2	∗-commuting	∗-commute	VERB
ejpam-3496	377	3	mappings	mapping	NOUN
ejpam-3496	377	4	and	and	CCONJ
ejpam-3496	377	5	derivations	derivation	NOUN
ejpam-3496	377	6	in	in	ADP
ejpam-3496	377	7	rings	ring	NOUN
ejpam-3496	377	8	with	with	ADP
ejpam-3496	377	9	involution	involution	NOUN
ejpam-3496	377	10	,	,	PUNCT
ejpam-3496	377	11	turkish	turkish	ADJ
ejpam-3496	377	12	j.	j.	PROPN
ejpam-3496	377	13	math	math	PROPN
ejpam-3496	377	14	.	.	PROPN
ejpam-3496	377	15	,	,	PUNCT
ejpam-3496	377	16	40:884–894	40:884–894	PROPN
ejpam-3496	377	17	,	,	PUNCT
ejpam-3496	377	18	2016	2016	NUM
ejpam-3496	377	19	.	.	PUNCT
ejpam-3496	378	1	references	reference	NOUN
ejpam-3496	378	2	1148	1148	NUM
ejpam-3496	378	3	[	[	X
ejpam-3496	378	4	12	12	NUM
ejpam-3496	378	5	]	]	PUNCT
ejpam-3496	378	6	n.	n.	NOUN
ejpam-3496	378	7	divinsky	divinsky	NOUN
ejpam-3496	378	8	.	.	PUNCT
ejpam-3496	379	1	on	on	ADP
ejpam-3496	379	2	commuting	commute	VERB
ejpam-3496	379	3	automorphisms	automorphism	NOUN
ejpam-3496	379	4	of	of	ADP
ejpam-3496	379	5	rings	ring	NOUN
ejpam-3496	379	6	trans	trans	PROPN
ejpam-3496	379	7	.	.	PUNCT
ejpam-3496	380	1	roy	roy	PROPN
ejpam-3496	380	2	.	.	PROPN
ejpam-3496	380	3	soc	soc	PROPN
ejpam-3496	380	4	.	.	PUNCT
ejpam-3496	381	1	canada	canada	PROPN
ejpam-3496	381	2	.	.	PUNCT
ejpam-3496	382	1	sect	sect	PROPN
ejpam-3496	382	2	.	.	PUNCT
ejpam-3496	383	1	iii	iii	PROPN
ejpam-3496	383	2	,	,	PUNCT
ejpam-3496	383	3	(	(	PUNCT
ejpam-3496	383	4	3)49:19–22	3)49:19–22	NUM
ejpam-3496	383	5	,	,	PUNCT
ejpam-3496	383	6	1955	1955	NUM
ejpam-3496	383	7	.	.	PUNCT
ejpam-3496	384	1	[	[	X
ejpam-3496	384	2	13	13	NUM
ejpam-3496	384	3	]	]	SYM
ejpam-3496	384	4	i.	i.	PROPN
ejpam-3496	384	5	n.	n.	PROPN
ejpam-3496	384	6	herstein	herstein	PROPN
ejpam-3496	384	7	.	.	PUNCT
ejpam-3496	385	1	a	a	DET
ejpam-3496	385	2	note	note	NOUN
ejpam-3496	385	3	on	on	ADP
ejpam-3496	385	4	derivations	derivation	NOUN
ejpam-3496	385	5	,	,	PUNCT
ejpam-3496	385	6	canad	canad	PROPN
ejpam-3496	385	7	.	.	PUNCT
ejpam-3496	386	1	math	math	NOUN
ejpam-3496	386	2	.	.	PUNCT
ejpam-3496	387	1	bull	bull	PROPN
ejpam-3496	387	2	.	.	PUNCT
ejpam-3496	387	3	,	,	PUNCT
ejpam-3496	387	4	21(3):369–370	21(3):369–370	PROPN
ejpam-3496	387	5	,	,	PUNCT
ejpam-3496	387	6	1978	1978	NUM
ejpam-3496	387	7	.	.	PUNCT
ejpam-3496	388	1	[	[	X
ejpam-3496	388	2	14	14	NUM
ejpam-3496	388	3	]	]	PUNCT
ejpam-3496	388	4	i.	i.	PROPN
ejpam-3496	388	5	n.	n.	PROPN
ejpam-3496	388	6	herstein	herstein	PROPN
ejpam-3496	388	7	.	.	PUNCT
ejpam-3496	389	1	rings	ring	NOUN
ejpam-3496	389	2	with	with	ADP
ejpam-3496	389	3	involution	involution	NOUN
ejpam-3496	389	4	,	,	PUNCT
ejpam-3496	389	5	the	the	DET
ejpam-3496	389	6	university	university	NOUN
ejpam-3496	389	7	of	of	ADP
ejpam-3496	389	8	chicago	chicago	PROPN
ejpam-3496	389	9	press	press	PROPN
ejpam-3496	389	10	,	,	PUNCT
ejpam-3496	389	11	chicago	chicago	PROPN
ejpam-3496	389	12	,	,	PUNCT
ejpam-3496	389	13	1976	1976	NUM
ejpam-3496	389	14	.	.	PUNCT
ejpam-3496	390	1	[	[	X
ejpam-3496	390	2	15	15	NUM
ejpam-3496	390	3	]	]	X
ejpam-3496	390	4	c.	c.	NOUN
ejpam-3496	390	5	lanski	lanski	PROPN
ejpam-3496	390	6	.	.	PUNCT
ejpam-3496	391	1	differential	differential	ADJ
ejpam-3496	391	2	identities	identity	NOUN
ejpam-3496	391	3	of	of	ADP
ejpam-3496	391	4	prime	prime	ADJ
ejpam-3496	391	5	rings	ring	NOUN
ejpam-3496	391	6	,	,	PUNCT
ejpam-3496	391	7	kharchenko	kharchenko	PROPN
ejpam-3496	391	8	’s	’s	PART
ejpam-3496	391	9	theorem	theorem	NOUN
ejpam-3496	391	10	and	and	CCONJ
ejpam-3496	391	11	application	application	NOUN
ejpam-3496	391	12	,	,	PUNCT
ejpam-3496	391	13	azumaya	azumaya	NOUN
ejpam-3496	391	14	algebras	algebra	NOUN
ejpam-3496	391	15	,	,	PUNCT
ejpam-3496	391	16	actions	action	NOUN
ejpam-3496	391	17	,	,	PUNCT
ejpam-3496	391	18	and	and	CCONJ
ejpam-3496	391	19	modules	module	NOUN
ejpam-3496	391	20	(	(	PUNCT
ejpam-3496	391	21	bloomington	bloomington	PROPN
ejpam-3496	391	22	,	,	PUNCT
ejpam-3496	391	23	in	in	ADP
ejpam-3496	391	24	,	,	PUNCT
ejpam-3496	391	25	1990	1990	NUM
ejpam-3496	391	26	)	)	PUNCT
ejpam-3496	391	27	,	,	PUNCT
ejpam-3496	391	28	111128	111128	NUM
ejpam-3496	391	29	,	,	PUNCT
ejpam-3496	391	30	contemp	contemp	NOUN
ejpam-3496	391	31	.	.	PUNCT
ejpam-3496	392	1	math	math	NOUN
ejpam-3496	392	2	.	.	PUNCT
ejpam-3496	393	1	,	,	PUNCT
ejpam-3496	393	2	124	124	NUM
ejpam-3496	393	3	,	,	PUNCT
ejpam-3496	393	4	amer	amer	PROPN
ejpam-3496	393	5	.	.	PROPN
ejpam-3496	393	6	math	math	PROPN
ejpam-3496	393	7	.	.	PUNCT
ejpam-3496	394	1	soc	soc	PROPN
ejpam-3496	394	2	.	.	PUNCT
ejpam-3496	394	3	,	,	PUNCT
ejpam-3496	394	4	providence	providence	NOUN
ejpam-3496	394	5	,	,	PUNCT
ejpam-3496	394	6	ri	ri	NOUN
ejpam-3496	394	7	,	,	PUNCT
ejpam-3496	394	8	1992	1992	NUM
ejpam-3496	394	9	.	.	PUNCT
ejpam-3496	395	1	[	[	X
ejpam-3496	395	2	16	16	NUM
ejpam-3496	395	3	]	]	X
ejpam-3496	395	4	b.	b.	PROPN
ejpam-3496	395	5	nejjar	nejjar	PROPN
ejpam-3496	395	6	,	,	PUNCT
ejpam-3496	395	7	a.	a.	PROPN
ejpam-3496	395	8	kacha	kacha	PROPN
ejpam-3496	395	9	,	,	PUNCT
ejpam-3496	395	10	a.	a.	NOUN
ejpam-3496	395	11	mamouni	mamouni	PROPN
ejpam-3496	395	12	and	and	CCONJ
ejpam-3496	395	13	l.	l.	PROPN
ejpam-3496	395	14	oukhtite	oukhtite	PROPN
ejpam-3496	395	15	.	.	PUNCT
ejpam-3496	396	1	commutativity	commutativity	NOUN
ejpam-3496	396	2	theorems	theorem	VERB
ejpam-3496	396	3	in	in	ADP
ejpam-3496	396	4	rings	ring	NOUN
ejpam-3496	396	5	with	with	ADP
ejpam-3496	396	6	involution	involution	NOUN
ejpam-3496	396	7	,	,	PUNCT
ejpam-3496	396	8	comm	comm	NOUN
ejpam-3496	396	9	.	.	PUNCT
ejpam-3496	397	1	algebra	algebra	PROPN
ejpam-3496	397	2	,	,	PUNCT
ejpam-3496	397	3	45(2):698–708	45(2):698–708	PROPN
ejpam-3496	397	4	,	,	PUNCT
ejpam-3496	397	5	2017	2017	NUM
ejpam-3496	397	6	.	.	PUNCT
ejpam-3496	398	1	[	[	X
ejpam-3496	398	2	17	17	NUM
ejpam-3496	398	3	]	]	X
ejpam-3496	398	4	f.	f.	PROPN
ejpam-3496	398	5	w.	w.	PROPN
ejpam-3496	398	6	niu	niu	PROPN
ejpam-3496	398	7	.	.	PUNCT
ejpam-3496	399	1	on	on	ADP
ejpam-3496	399	2	a	a	DET
ejpam-3496	399	3	pair	pair	NOUN
ejpam-3496	399	4	of	of	ADP
ejpam-3496	399	5	derivations	derivation	NOUN
ejpam-3496	399	6	on	on	ADP
ejpam-3496	399	7	associative	associative	ADJ
ejpam-3496	399	8	rings	ring	NOUN
ejpam-3496	399	9	,	,	PUNCT
ejpam-3496	399	10	j.	j.	PROPN
ejpam-3496	399	11	math	math	PROPN
ejpam-3496	399	12	.	.	PUNCT
ejpam-3496	400	1	(	(	PUNCT
ejpam-3496	400	2	wuhan	wuhan	PROPN
ejpam-3496	400	3	)	)	PUNCT
ejpam-3496	400	4	,	,	PUNCT
ejpam-3496	400	5	10(4):385	10(4):385	NUM
ejpam-3496	400	6	–	–	PUNCT
ejpam-3496	400	7	390	390	NUM
ejpam-3496	400	8	,	,	PUNCT
ejpam-3496	400	9	1990	1990	NUM
ejpam-3496	400	10	.	.	PUNCT
ejpam-3496	401	1	[	[	X
ejpam-3496	401	2	18	18	NUM
ejpam-3496	401	3	]	]	X
ejpam-3496	401	4	e.	e.	PROPN
ejpam-3496	401	5	c.	c.	PROPN
ejpam-3496	401	6	posner	posner	PROPN
ejpam-3496	401	7	.	.	PUNCT
ejpam-3496	402	1	derivations	derivation	NOUN
ejpam-3496	402	2	in	in	ADP
ejpam-3496	402	3	prime	prime	ADJ
ejpam-3496	402	4	rings	ring	NOUN
ejpam-3496	402	5	,	,	PUNCT
ejpam-3496	402	6	proc	proc	NOUN
ejpam-3496	402	7	.	.	PUNCT
ejpam-3496	403	1	amer	amer	PROPN
ejpam-3496	403	2	.	.	PUNCT
ejpam-3496	403	3	math	math	PROPN
ejpam-3496	403	4	.	.	PUNCT
ejpam-3496	404	1	soc	soc	PROPN
ejpam-3496	404	2	.	.	PROPN
ejpam-3496	404	3	,	,	PUNCT
ejpam-3496	404	4	8:1093	8:1093	NUM
ejpam-3496	404	5	-	-	SYM
ejpam-3496	404	6	1100	1100	NUM
ejpam-3496	404	7	,	,	PUNCT
ejpam-3496	404	8	1957	1957	NUM
ejpam-3496	404	9	.	.	PUNCT
ejpam-3496	405	1	[	[	X
ejpam-3496	405	2	19	19	NUM
ejpam-3496	405	3	]	]	X
ejpam-3496	405	4	h.	h.	PROPN
ejpam-3496	405	5	shuliang	shuliang	PROPN
ejpam-3496	405	6	.	.	PUNCT
ejpam-3496	406	1	a	a	DET
ejpam-3496	406	2	note	note	NOUN
ejpam-3496	406	3	on	on	ADP
ejpam-3496	406	4	lie	lie	NOUN
ejpam-3496	406	5	ideals	ideal	NOUN
ejpam-3496	406	6	of	of	ADP
ejpam-3496	406	7	prime	prime	ADJ
ejpam-3496	406	8	rings	ring	NOUN
ejpam-3496	406	9	,	,	PUNCT
ejpam-3496	406	10	commun	commun	PROPN
ejpam-3496	406	11	.	.	PUNCT
ejpam-3496	407	1	korean	korean	ADJ
ejpam-3496	407	2	math	math	PROPN
ejpam-3496	407	3	.	.	PUNCT
ejpam-3496	408	1	soc	soc	PROPN
ejpam-3496	408	2	.	.	PUNCT
ejpam-3496	408	3	,	,	PUNCT
ejpam-3496	408	4	25(3):327–333	25(3):327–333	NUM
ejpam-3496	408	5	,	,	PUNCT
ejpam-3496	408	6	2010	2010	NUM
ejpam-3496	408	7	.	.	PUNCT