id	sid	tid	token	lemma	pos
ejpam-5493	1	1	european	european	PROPN
ejpam-5493	1	2	journal	journal	PROPN
ejpam-5493	1	3	of	of	ADP
ejpam-5493	1	4	pure	pure	ADJ
ejpam-5493	1	5	and	and	CCONJ
ejpam-5493	1	6	applied	applied	ADJ
ejpam-5493	1	7	mathematics	mathematic	NOUN
ejpam-5493	1	8	2025	2025	NUM
ejpam-5493	1	9	,	,	PUNCT
ejpam-5493	1	10	vol	vol	NOUN
ejpam-5493	1	11	.	.	PROPN
ejpam-5493	1	12	18	18	NUM
ejpam-5493	1	13	,	,	PUNCT
ejpam-5493	1	14	issue	issue	NOUN
ejpam-5493	1	15	1	1	NUM
ejpam-5493	1	16	,	,	PUNCT
ejpam-5493	1	17	article	article	NOUN
ejpam-5493	1	18	number	number	NOUN
ejpam-5493	1	19	5493	5493	NUM
ejpam-5493	1	20	issn	issn	VERB
ejpam-5493	1	21	1307	1307	NUM
ejpam-5493	1	22	-	-	SYM
ejpam-5493	1	23	5543	5543	NUM
ejpam-5493	1	24	–	–	PUNCT
ejpam-5493	1	25	ejpam.com	ejpam.com	X
ejpam-5493	1	26	published	publish	VERB
ejpam-5493	1	27	by	by	ADP
ejpam-5493	1	28	new	new	PROPN
ejpam-5493	1	29	york	york	PROPN
ejpam-5493	1	30	business	business	PROPN
ejpam-5493	1	31	global	global	PROPN
ejpam-5493	1	32	jordan	jordan	PROPN
ejpam-5493	1	33	φ	φ	PROPN
ejpam-5493	1	34	-	-	PUNCT
ejpam-5493	1	35	centralizers	centralizer	NOUN
ejpam-5493	1	36	on	on	ADP
ejpam-5493	1	37	semiprime	semiprime	NOUN
ejpam-5493	1	38	and	and	CCONJ
ejpam-5493	1	39	involution	involution	NOUN
ejpam-5493	1	40	rings	ring	NOUN
ejpam-5493	1	41	abu	abu	PROPN
ejpam-5493	1	42	zaid	zaid	PROPN
ejpam-5493	1	43	ansari1	ansari1	PROPN
ejpam-5493	1	44	,	,	PUNCT
ejpam-5493	1	45	faiza	faiza	PROPN
ejpam-5493	1	46	shujat2,∗	shujat2,∗	PROPN
ejpam-5493	1	47	,	,	PUNCT
ejpam-5493	1	48	alwaleed	alwaleed	NOUN
ejpam-5493	1	49	kamel1,3	kamel1,3	PROPN
ejpam-5493	1	50	,	,	PUNCT
ejpam-5493	1	51	ahlam	ahlam	PROPN
ejpam-5493	1	52	fallatah2	fallatah2	PROPN
ejpam-5493	2	1	1	1	NUM
ejpam-5493	2	2	department	department	NOUN
ejpam-5493	2	3	of	of	ADP
ejpam-5493	2	4	mathematics	mathematic	NOUN
ejpam-5493	2	5	,	,	PUNCT
ejpam-5493	2	6	faculty	faculty	NOUN
ejpam-5493	2	7	of	of	ADP
ejpam-5493	2	8	science	science	NOUN
ejpam-5493	2	9	,	,	PUNCT
ejpam-5493	2	10	islamic	islamic	PROPN
ejpam-5493	2	11	university	university	PROPN
ejpam-5493	2	12	of	of	ADP
ejpam-5493	2	13	madinah	madinah	PROPN
ejpam-5493	2	14	,	,	PUNCT
ejpam-5493	2	15	k.s.a	k.s.a	NOUN
ejpam-5493	2	16	.	.	PROPN
ejpam-5493	2	17	2	2	NUM
ejpam-5493	2	18	department	department	NOUN
ejpam-5493	2	19	of	of	ADP
ejpam-5493	2	20	mathematics	mathematic	NOUN
ejpam-5493	2	21	,	,	PUNCT
ejpam-5493	2	22	faculty	faculty	NOUN
ejpam-5493	2	23	of	of	ADP
ejpam-5493	2	24	science	science	NOUN
ejpam-5493	2	25	,	,	PUNCT
ejpam-5493	2	26	taibah	taibah	PROPN
ejpam-5493	2	27	university	university	PROPN
ejpam-5493	2	28	,	,	PUNCT
ejpam-5493	2	29	madinah	madinah	PROPN
ejpam-5493	2	30	,	,	PUNCT
ejpam-5493	2	31	k.s.a	k.s.a	NOUN
ejpam-5493	2	32	.	.	PROPN
ejpam-5493	2	33	3	3	NUM
ejpam-5493	2	34	department	department	NOUN
ejpam-5493	2	35	of	of	ADP
ejpam-5493	2	36	mathematics	mathematic	NOUN
ejpam-5493	2	37	,	,	PUNCT
ejpam-5493	2	38	faculty	faculty	NOUN
ejpam-5493	2	39	of	of	ADP
ejpam-5493	2	40	science	science	NOUN
ejpam-5493	2	41	,	,	PUNCT
ejpam-5493	2	42	sohag	sohag	NOUN
ejpam-5493	2	43	university	university	NOUN
ejpam-5493	2	44	,	,	PUNCT
ejpam-5493	2	45	sohag	sohag	NOUN
ejpam-5493	2	46	82749	82749	NUM
ejpam-5493	2	47	,	,	PUNCT
ejpam-5493	2	48	egypt	egypt	PROPN
ejpam-5493	2	49	abstract	abstract	PROPN
ejpam-5493	2	50	.	.	PUNCT
ejpam-5493	3	1	the	the	DET
ejpam-5493	3	2	intention	intention	NOUN
ejpam-5493	3	3	of	of	ADP
ejpam-5493	3	4	the	the	DET
ejpam-5493	3	5	current	current	ADJ
ejpam-5493	3	6	investigation	investigation	NOUN
ejpam-5493	3	7	is	be	AUX
ejpam-5493	3	8	to	to	PART
ejpam-5493	3	9	demonstrate	demonstrate	VERB
ejpam-5493	3	10	that	that	SCONJ
ejpam-5493	3	11	if	if	SCONJ
ejpam-5493	3	12	an	an	DET
ejpam-5493	3	13	additive	additive	ADJ
ejpam-5493	3	14	mapping	mapping	NOUN
ejpam-5493	3	15	h	h	NOUN
ejpam-5493	3	16	:	:	PUNCT
ejpam-5493	3	17	r	r	NOUN
ejpam-5493	3	18	→	→	SYM
ejpam-5493	3	19	r	r	NOUN
ejpam-5493	3	20	fulfills	fulfill	VERB
ejpam-5493	3	21	certain	certain	ADJ
ejpam-5493	3	22	identities	identity	NOUN
ejpam-5493	3	23	,	,	PUNCT
ejpam-5493	3	24	thenh	thenh	NOUN
ejpam-5493	3	25	is	be	AUX
ejpam-5493	3	26	a	a	DET
ejpam-5493	3	27	φ	φ	NOUN
ejpam-5493	3	28	-	-	PUNCT
ejpam-5493	3	29	centralizer	centralizer	NOUN
ejpam-5493	3	30	on	on	ADP
ejpam-5493	3	31	r	r	NOUN
ejpam-5493	3	32	,	,	PUNCT
ejpam-5493	3	33	where	where	SCONJ
ejpam-5493	3	34	r	r	NOUN
ejpam-5493	3	35	is	be	AUX
ejpam-5493	3	36	any	any	DET
ejpam-5493	3	37	suitable	suitable	ADJ
ejpam-5493	3	38	,	,	PUNCT
ejpam-5493	3	39	torsionfree	torsionfree	ADJ
ejpam-5493	3	40	semiprime	semiprime	NOUN
ejpam-5493	3	41	ring	ring	NOUN
ejpam-5493	3	42	and	and	CCONJ
ejpam-5493	3	43	p	p	NOUN
ejpam-5493	3	44	is	be	AUX
ejpam-5493	3	45	a	a	DET
ejpam-5493	3	46	fixed	fix	VERB
ejpam-5493	3	47	integer	integer	NOUN
ejpam-5493	3	48	greater	great	ADJ
ejpam-5493	3	49	than	than	ADP
ejpam-5493	3	50	or	or	CCONJ
ejpam-5493	3	51	equal	equal	ADJ
ejpam-5493	3	52	to	to	ADP
ejpam-5493	3	53	1	1	NUM
ejpam-5493	3	54	.	.	PUNCT
ejpam-5493	4	1	as	as	ADP
ejpam-5493	4	2	a	a	DET
ejpam-5493	4	3	result	result	NOUN
ejpam-5493	4	4	of	of	ADP
ejpam-5493	4	5	the	the	DET
ejpam-5493	4	6	primary	primary	ADJ
ejpam-5493	4	7	theorems	theorem	NOUN
ejpam-5493	4	8	,	,	PUNCT
ejpam-5493	4	9	involution	involution	NOUN
ejpam-5493	4	10	iv	iv	NUM
ejpam-5493	4	11	related	relate	VERB
ejpam-5493	4	12	observations	observation	NOUN
ejpam-5493	4	13	are	be	AUX
ejpam-5493	4	14	also	also	ADV
ejpam-5493	4	15	provided	provide	VERB
ejpam-5493	4	16	.	.	PUNCT
ejpam-5493	5	1	we	we	PRON
ejpam-5493	5	2	will	will	AUX
ejpam-5493	5	3	also	also	ADV
ejpam-5493	5	4	consider	consider	VERB
ejpam-5493	5	5	criticism	criticism	NOUN
ejpam-5493	5	6	and	and	CCONJ
ejpam-5493	5	7	discussion	discussion	NOUN
ejpam-5493	5	8	alongside	alongside	ADP
ejpam-5493	5	9	the	the	DET
ejpam-5493	5	10	proofs	proof	NOUN
ejpam-5493	5	11	of	of	ADP
ejpam-5493	5	12	theorems	theorem	NOUN
ejpam-5493	5	13	.	.	PUNCT
ejpam-5493	6	1	suitable	suitable	ADJ
ejpam-5493	6	2	examples	example	NOUN
ejpam-5493	6	3	are	be	AUX
ejpam-5493	6	4	given	give	VERB
ejpam-5493	6	5	in	in	ADP
ejpam-5493	6	6	favor	favor	NOUN
ejpam-5493	6	7	of	of	ADP
ejpam-5493	6	8	justification	justification	NOUN
ejpam-5493	6	9	.	.	PUNCT
ejpam-5493	7	1	2020	2020	NUM
ejpam-5493	7	2	mathematics	mathematic	NOUN
ejpam-5493	7	3	subject	subject	NOUN
ejpam-5493	7	4	classifications	classification	NOUN
ejpam-5493	7	5	:	:	PUNCT
ejpam-5493	7	6	ams	am	NOUN
ejpam-5493	7	7	16n60	16n60	NUM
ejpam-5493	7	8	,	,	PUNCT
ejpam-5493	7	9	16w10	16w10	NUM
ejpam-5493	7	10	,	,	PUNCT
ejpam-5493	7	11	16r50	16r50	NUM
ejpam-5493	7	12	,	,	PUNCT
ejpam-5493	7	13	47b47	47b47	VERB
ejpam-5493	7	14	key	key	ADJ
ejpam-5493	7	15	words	word	NOUN
ejpam-5493	7	16	and	and	CCONJ
ejpam-5493	7	17	phrases	phrase	NOUN
ejpam-5493	7	18	:	:	PUNCT
ejpam-5493	7	19	algebraic	algebraic	ADJ
ejpam-5493	7	20	identities	identity	NOUN
ejpam-5493	7	21	,	,	PUNCT
ejpam-5493	7	22	semiprime	semiprime	NOUN
ejpam-5493	7	23	ring	ring	NOUN
ejpam-5493	7	24	,	,	PUNCT
ejpam-5493	7	25	(	(	PUNCT
ejpam-5493	7	26	jordan	jordan	PROPN
ejpam-5493	7	27	)	)	PUNCT
ejpam-5493	7	28	φ	φ	PROPN
ejpam-5493	7	29	-	-	PUNCT
ejpam-5493	7	30	centralizer	centralizer	NOUN
ejpam-5493	7	31	1	1	NUM
ejpam-5493	7	32	.	.	PUNCT
ejpam-5493	8	1	introduction	introduction	NOUN
ejpam-5493	8	2	in	in	ADP
ejpam-5493	8	3	order	order	NOUN
ejpam-5493	8	4	to	to	PART
ejpam-5493	8	5	effectively	effectively	ADV
ejpam-5493	8	6	comprehend	comprehend	VERB
ejpam-5493	8	7	our	our	PRON
ejpam-5493	8	8	concept	concept	NOUN
ejpam-5493	8	9	,	,	PUNCT
ejpam-5493	8	10	we	we	PRON
ejpam-5493	8	11	must	must	AUX
ejpam-5493	8	12	first	first	ADV
ejpam-5493	8	13	recall	recall	VERB
ejpam-5493	8	14	a	a	DET
ejpam-5493	8	15	few	few	ADJ
ejpam-5493	8	16	fundamental	fundamental	ADJ
ejpam-5493	8	17	ideas	idea	NOUN
ejpam-5493	8	18	.	.	PUNCT
ejpam-5493	9	1	throughout	throughout	ADV
ejpam-5493	9	2	,	,	PUNCT
ejpam-5493	9	3	r	r	NOUN
ejpam-5493	9	4	shall	shall	AUX
ejpam-5493	9	5	stand	stand	VERB
ejpam-5493	9	6	for	for	ADP
ejpam-5493	9	7	an	an	DET
ejpam-5493	9	8	associative	associative	ADJ
ejpam-5493	9	9	ring	ring	NOUN
ejpam-5493	9	10	with	with	ADP
ejpam-5493	9	11	unity	unity	NOUN
ejpam-5493	9	12	e.	e.	PROPN
ejpam-5493	9	13	a	a	DET
ejpam-5493	9	14	ring	ring	NOUN
ejpam-5493	9	15	r	r	NOUN
ejpam-5493	9	16	is	be	AUX
ejpam-5493	9	17	termed	term	VERB
ejpam-5493	9	18	as	as	ADP
ejpam-5493	9	19	p	p	NOUN
ejpam-5493	9	20	-	-	PUNCT
ejpam-5493	9	21	torsion	torsion	NOUN
ejpam-5493	9	22	free	free	ADJ
ejpam-5493	9	23	,	,	PUNCT
ejpam-5493	9	24	where	where	SCONJ
ejpam-5493	9	25	p	p	X
ejpam-5493	9	26	>	>	X
ejpam-5493	9	27	1	1	NUM
ejpam-5493	9	28	,	,	PUNCT
ejpam-5493	9	29	if	if	SCONJ
ejpam-5493	9	30	pr	pr	VERB
ejpam-5493	9	31	=	=	SYM
ejpam-5493	9	32	0	0	NUM
ejpam-5493	9	33	entails	entail	VERB
ejpam-5493	9	34	r	r	NOUN
ejpam-5493	9	35	=	=	SYM
ejpam-5493	9	36	0	0	NUM
ejpam-5493	9	37	for	for	ADP
ejpam-5493	9	38	every	every	DET
ejpam-5493	9	39	r	r	NOUN
ejpam-5493	9	40	∈	∈	PROPN
ejpam-5493	9	41	r.	r.	NOUN
ejpam-5493	9	42	a	a	DET
ejpam-5493	9	43	ring	ring	NOUN
ejpam-5493	9	44	r	r	NOUN
ejpam-5493	9	45	is	be	AUX
ejpam-5493	9	46	recognised	recognise	VERB
ejpam-5493	9	47	as	as	ADP
ejpam-5493	9	48	a	a	DET
ejpam-5493	9	49	prime	prime	NOUN
ejpam-5493	9	50	if	if	SCONJ
ejpam-5493	9	51	rrt	rrt	VERB
ejpam-5493	9	52	=	=	SYM
ejpam-5493	9	53	{	{	PUNCT
ejpam-5493	9	54	0	0	NUM
ejpam-5493	9	55	}	}	PUNCT
ejpam-5493	9	56	implies	imply	VERB
ejpam-5493	9	57	that	that	SCONJ
ejpam-5493	9	58	either	either	CCONJ
ejpam-5493	9	59	r	r	NOUN
ejpam-5493	9	60	=	=	SYM
ejpam-5493	9	61	0	0	NUM
ejpam-5493	9	62	or	or	CCONJ
ejpam-5493	9	63	t	t	X
ejpam-5493	9	64	=	=	SYM
ejpam-5493	9	65	0	0	NUM
ejpam-5493	9	66	,	,	PUNCT
ejpam-5493	9	67	and	and	CCONJ
ejpam-5493	9	68	is	be	AUX
ejpam-5493	9	69	termed	term	VERB
ejpam-5493	9	70	as	as	ADP
ejpam-5493	9	71	a	a	DET
ejpam-5493	9	72	semiprime	semiprime	NOUN
ejpam-5493	9	73	if	if	SCONJ
ejpam-5493	9	74	rrr	rrr	NOUN
ejpam-5493	9	75	=	=	PUNCT
ejpam-5493	9	76	{	{	PUNCT
ejpam-5493	9	77	0	0	NUM
ejpam-5493	9	78	}	}	PUNCT
ejpam-5493	9	79	yields	yield	NOUN
ejpam-5493	9	80	r	r	NOUN
ejpam-5493	9	81	=	=	SYM
ejpam-5493	9	82	0	0	NUM
ejpam-5493	9	83	.	.	PUNCT
ejpam-5493	10	1	the	the	DET
ejpam-5493	10	2	study	study	NOUN
ejpam-5493	10	3	of	of	ADP
ejpam-5493	10	4	helgosen	helgosen	NOUN
ejpam-5493	10	5	[	[	X
ejpam-5493	10	6	5	5	NUM
ejpam-5493	10	7	]	]	PUNCT
ejpam-5493	10	8	,	,	PUNCT
ejpam-5493	10	9	who	who	PRON
ejpam-5493	10	10	introduced	introduce	VERB
ejpam-5493	10	11	the	the	DET
ejpam-5493	10	12	idea	idea	NOUN
ejpam-5493	10	13	of	of	ADP
ejpam-5493	10	14	centralizers	centralizer	NOUN
ejpam-5493	10	15	on	on	ADP
ejpam-5493	10	16	banach	banach	NOUN
ejpam-5493	10	17	algebras	algebra	NOUN
ejpam-5493	10	18	,	,	PUNCT
ejpam-5493	10	19	which	which	PRON
ejpam-5493	10	20	is	be	AUX
ejpam-5493	10	21	also	also	ADV
ejpam-5493	10	22	known	know	VERB
ejpam-5493	10	23	as	as	ADP
ejpam-5493	10	24	multipliers	multiplier	NOUN
ejpam-5493	10	25	,	,	PUNCT
ejpam-5493	10	26	is	be	AUX
ejpam-5493	10	27	supportive	supportive	ADJ
ejpam-5493	10	28	of	of	ADP
ejpam-5493	10	29	our	our	PRON
ejpam-5493	10	30	current	current	ADJ
ejpam-5493	10	31	understanding	understanding	NOUN
ejpam-5493	10	32	.	.	PUNCT
ejpam-5493	11	1	a	a	DET
ejpam-5493	11	2	possible	possible	ADJ
ejpam-5493	11	3	idea	idea	NOUN
ejpam-5493	11	4	of	of	ADP
ejpam-5493	11	5	centralizers	centralizer	NOUN
ejpam-5493	11	6	on	on	ADP
ejpam-5493	11	7	commutative	commutative	ADJ
ejpam-5493	11	8	banach	banach	NOUN
ejpam-5493	11	9	algebra	algebra	NOUN
ejpam-5493	11	10	put	put	VERB
ejpam-5493	11	11	out	out	ADP
ejpam-5493	11	12	by	by	ADP
ejpam-5493	11	13	wang	wang	PROPN
ejpam-5493	12	1	[	[	X
ejpam-5493	12	2	14	14	NUM
ejpam-5493	12	3	]	]	PUNCT
ejpam-5493	12	4	.	.	PUNCT
ejpam-5493	13	1	further	further	ADJ
ejpam-5493	13	2	study	study	VERB
ejpam-5493	13	3	on	on	ADP
ejpam-5493	13	4	centralizers	centralizer	NOUN
ejpam-5493	13	5	for	for	ADP
ejpam-5493	13	6	topological	topological	ADJ
ejpam-5493	13	7	algebras	algebra	NOUN
ejpam-5493	13	8	and	and	CCONJ
ejpam-5493	13	9	the	the	DET
ejpam-5493	13	10	continuity	continuity	NOUN
ejpam-5493	13	11	of	of	ADP
ejpam-5493	13	12	centralizers	centralizer	NOUN
ejpam-5493	13	13	on	on	ADP
ejpam-5493	13	14	banach	banach	NOUN
ejpam-5493	13	15	algebras	algebras	PROPN
ejpam-5493	13	16	is	be	AUX
ejpam-5493	13	17	done	do	VERB
ejpam-5493	13	18	by	by	ADP
ejpam-5493	13	19	johnson	johnson	PROPN
ejpam-5493	14	1	[	[	X
ejpam-5493	14	2	9	9	NUM
ejpam-5493	14	3	]	]	PUNCT
ejpam-5493	14	4	.	.	PUNCT
ejpam-5493	15	1	further	far	ADV
ejpam-5493	15	2	,	,	PUNCT
ejpam-5493	15	3	johnson	johnson	PROPN
ejpam-5493	15	4	studiedthe	studiedthe	PROPN
ejpam-5493	15	5	behaviour	behaviour	NOUN
ejpam-5493	15	6	of	of	ADP
ejpam-5493	15	7	centralizers	centralizer	NOUN
ejpam-5493	15	8	on	on	ADP
ejpam-5493	15	9	algebra	algebra	NOUN
ejpam-5493	15	10	of	of	ADP
ejpam-5493	15	11	compact	compact	ADJ
ejpam-5493	15	12	operators	operator	NOUN
ejpam-5493	15	13	on	on	ADP
ejpam-5493	15	14	banach	banach	NOUN
ejpam-5493	15	15	space	space	NOUN
ejpam-5493	15	16	over	over	ADP
ejpam-5493	15	17	itself	itself	PRON
ejpam-5493	15	18	in	in	ADP
ejpam-5493	15	19	[	[	X
ejpam-5493	15	20	7	7	NUM
ejpam-5493	15	21	]	]	PUNCT
ejpam-5493	15	22	.	.	PUNCT
ejpam-5493	16	1	since	since	SCONJ
ejpam-5493	16	2	,	,	PUNCT
ejpam-5493	16	3	every	every	DET
ejpam-5493	16	4	centralizer	centralizer	NOUN
ejpam-5493	16	5	on	on	ADP
ejpam-5493	16	6	a	a	DET
ejpam-5493	16	7	commutative	commutative	ADJ
ejpam-5493	16	8	faithful	faithful	ADJ
ejpam-5493	16	9	banach	banach	NOUN
ejpam-5493	16	10	algebra	algebra	NOUN
ejpam-5493	16	11	is	be	AUX
ejpam-5493	16	12	continuous	continuous	ADJ
ejpam-5493	16	13	.	.	PUNCT
ejpam-5493	17	1	simultaneously	simultaneously	ADV
ejpam-5493	17	2	,	,	PUNCT
ejpam-5493	17	3	he	he	PRON
ejpam-5493	17	4	studied	study	VERB
ejpam-5493	17	5	another	another	DET
ejpam-5493	17	6	class	class	NOUN
ejpam-5493	17	7	of	of	ADP
ejpam-5493	17	8	banach	banach	NOUN
ejpam-5493	17	9	algebras	algebra	NOUN
ejpam-5493	17	10	that	that	PRON
ejpam-5493	17	11	includes	include	VERB
ejpam-5493	17	12	the	the	DET
ejpam-5493	17	13	group	group	NOUN
ejpam-5493	17	14	of	of	ADP
ejpam-5493	17	15	algebras	algebra	NOUN
ejpam-5493	17	16	of	of	ADP
ejpam-5493	17	17	locally	locally	ADV
ejpam-5493	17	18	∗corresponding	∗corresponde	VERB
ejpam-5493	17	19	author	author	NOUN
ejpam-5493	17	20	.	.	PUNCT
ejpam-5493	18	1	doi	doi	NOUN
ejpam-5493	18	2	:	:	PUNCT
ejpam-5493	18	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5493	https://doi.org/10.29020/nybg.ejpam.v18i1.5493	PROPN
ejpam-5493	18	4	email	email	NOUN
ejpam-5493	18	5	addresses	address	NOUN
ejpam-5493	18	6	:	:	PUNCT
ejpam-5493	18	7	ansari.abuzaid@gmail.com	ansari.abuzaid@gmail.com	X
ejpam-5493	18	8	(	(	PUNCT
ejpam-5493	18	9	a.	a.	PROPN
ejpam-5493	18	10	z.	z.	PROPN
ejpam-5493	18	11	ansari	ansari	PROPN
ejpam-5493	18	12	)	)	PUNCT
ejpam-5493	18	13	,	,	PUNCT
ejpam-5493	18	14	faiza.shujat@gmail.com	faiza.shujat@gmail.com	X
ejpam-5493	18	15	(	(	PUNCT
ejpam-5493	18	16	f.	f.	PROPN
ejpam-5493	18	17	shujat	shujat	PROPN
ejpam-5493	18	18	)	)	PUNCT
ejpam-5493	18	19	,	,	PUNCT
ejpam-5493	18	20	wld	wld	PROPN
ejpam-5493	18	21	kamel22@yahoo.com	kamel22@yahoo.com	PROPN
ejpam-5493	18	22	(	(	PUNCT
ejpam-5493	18	23	a.	a.	PROPN
ejpam-5493	18	24	kamel	kamel	PROPN
ejpam-5493	18	25	)	)	PUNCT
ejpam-5493	18	26	,	,	PUNCT
ejpam-5493	18	27	afallatah@taibahu.edu.sa	afallatah@taibahu.edu.sa	PROPN
ejpam-5493	18	28	(	(	PUNCT
ejpam-5493	18	29	a.	a.	NOUN
ejpam-5493	18	30	fallatah	fallatah	PROPN
ejpam-5493	18	31	)	)	PUNCT
ejpam-5493	18	32	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5493	19	1	1	1	NUM
ejpam-5493	19	2	copyright	copyright	NOUN
ejpam-5493	19	3	:	:	PUNCT
ejpam-5493	19	4	©	©	PROPN
ejpam-5493	19	5	2025	2025	NUM
ejpam-5493	19	6	the	the	DET
ejpam-5493	19	7	author(s	author(s	NOUN
ejpam-5493	19	8	)	)	PUNCT
ejpam-5493	19	9	.	.	PUNCT
ejpam-5493	20	1	(	(	PUNCT
ejpam-5493	20	2	cc	cc	NOUN
ejpam-5493	20	3	by	by	ADP
ejpam-5493	20	4	-	-	PUNCT
ejpam-5493	20	5	nc	nc	PROPN
ejpam-5493	20	6	4.0	4.0	NUM
ejpam-5493	20	7	)	)	PUNCT
ejpam-5493	20	8	a.	a.	NOUN
ejpam-5493	20	9	z.	z.	PROPN
ejpam-5493	20	10	ansari	ansari	PROPN
ejpam-5493	20	11	et	et	PROPN
ejpam-5493	20	12	al	al	PROPN
ejpam-5493	20	13	.	.	PUNCT
ejpam-5493	20	14	/	/	SYM
ejpam-5493	20	15	eur	eur	PROPN
ejpam-5493	20	16	.	.	PUNCT
ejpam-5493	21	1	j.	j.	PROPN
ejpam-5493	21	2	pure	pure	PROPN
ejpam-5493	21	3	appl	appl	PROPN
ejpam-5493	21	4	.	.	PROPN
ejpam-5493	21	5	math	math	PROPN
ejpam-5493	21	6	,	,	PUNCT
ejpam-5493	21	7	18	18	NUM
ejpam-5493	21	8	(	(	PUNCT
ejpam-5493	21	9	1	1	NUM
ejpam-5493	21	10	)	)	PUNCT
ejpam-5493	21	11	(	(	PUNCT
ejpam-5493	21	12	2025	2025	NUM
ejpam-5493	21	13	)	)	PUNCT
ejpam-5493	21	14	,	,	PUNCT
ejpam-5493	21	15	5493	5493	NUM
ejpam-5493	21	16	2	2	NUM
ejpam-5493	21	17	of	of	ADP
ejpam-5493	21	18	10	10	NUM
ejpam-5493	21	19	compact	compact	ADJ
ejpam-5493	21	20	topological	topological	ADJ
ejpam-5493	21	21	groups	group	NOUN
ejpam-5493	21	22	in	in	ADP
ejpam-5493	21	23	[	[	X
ejpam-5493	21	24	8	8	NUM
ejpam-5493	21	25	]	]	PUNCT
ejpam-5493	21	26	.	.	PUNCT
ejpam-5493	22	1	additionally	additionally	ADV
ejpam-5493	22	2	,	,	PUNCT
ejpam-5493	22	3	husain	husain	PROPN
ejpam-5493	22	4	[	[	X
ejpam-5493	22	5	6	6	NUM
ejpam-5493	22	6	]	]	PUNCT
ejpam-5493	22	7	has	have	AUX
ejpam-5493	22	8	studied	study	VERB
ejpam-5493	22	9	centralizers	centralizer	NOUN
ejpam-5493	22	10	on	on	ADP
ejpam-5493	22	11	topological	topological	ADJ
ejpam-5493	22	12	algebras	algebra	NOUN
ejpam-5493	22	13	,	,	PUNCT
ejpam-5493	22	14	specifically	specifically	ADV
ejpam-5493	22	15	focusing	focus	VERB
ejpam-5493	22	16	on	on	ADP
ejpam-5493	22	17	topological	topological	ADJ
ejpam-5493	22	18	algebras	algebra	NOUN
ejpam-5493	22	19	with	with	ADP
ejpam-5493	22	20	orthogonal	orthogonal	ADJ
ejpam-5493	22	21	bases	basis	NOUN
ejpam-5493	22	22	and	and	CCONJ
ejpam-5493	22	23	full	full	ADJ
ejpam-5493	22	24	metrizable	metrizable	ADJ
ejpam-5493	22	25	locally	locally	ADV
ejpam-5493	22	26	convex	convex	PROPN
ejpam-5493	22	27	algebras	algebra	NOUN
ejpam-5493	22	28	.	.	PUNCT
ejpam-5493	23	1	authors	author	NOUN
ejpam-5493	23	2	have	have	AUX
ejpam-5493	23	3	since	since	SCONJ
ejpam-5493	23	4	examined	examine	VERB
ejpam-5493	23	5	centralizers	centralizer	NOUN
ejpam-5493	23	6	and	and	CCONJ
ejpam-5493	23	7	double	double	ADJ
ejpam-5493	23	8	centralizers	centralizer	NOUN
ejpam-5493	23	9	on	on	ADP
ejpam-5493	23	10	certain	certain	ADJ
ejpam-5493	23	11	topological	topological	ADJ
ejpam-5493	23	12	algebras	algebra	NOUN
ejpam-5493	23	13	in	in	ADP
ejpam-5493	23	14	[	[	X
ejpam-5493	23	15	10	10	NUM
ejpam-5493	23	16	,	,	PUNCT
ejpam-5493	23	17	12	12	NUM
ejpam-5493	23	18	]	]	PUNCT
ejpam-5493	23	19	.	.	PUNCT
ejpam-5493	24	1	in	in	ADP
ejpam-5493	24	2	[	[	X
ejpam-5493	24	3	2	2	NUM
ejpam-5493	24	4	]	]	PUNCT
ejpam-5493	24	5	,	,	PUNCT
ejpam-5493	24	6	authors	author	NOUN
ejpam-5493	24	7	investigated	investigate	VERB
ejpam-5493	24	8	the	the	DET
ejpam-5493	24	9	idea	idea	NOUN
ejpam-5493	24	10	of	of	ADP
ejpam-5493	24	11	jordan	jordan	PROPN
ejpam-5493	24	12	∗-derivations	∗-derivations	PROPN
ejpam-5493	24	13	on	on	ADP
ejpam-5493	24	14	standard	standard	ADJ
ejpam-5493	24	15	operator	operator	NOUN
ejpam-5493	24	16	algebras	algebra	NOUN
ejpam-5493	24	17	.	.	PUNCT
ejpam-5493	25	1	the	the	DET
ejpam-5493	25	2	study	study	NOUN
ejpam-5493	25	3	of	of	ADP
ejpam-5493	25	4	hopf	hopf	ADJ
ejpam-5493	25	5	algebras	algebra	NOUN
ejpam-5493	25	6	,	,	PUNCT
ejpam-5493	25	7	representation	representation	NOUN
ejpam-5493	25	8	theory	theory	NOUN
ejpam-5493	25	9	of	of	ADP
ejpam-5493	25	10	banach	banach	NOUN
ejpam-5493	25	11	algebras	algebra	NOUN
ejpam-5493	25	12	,	,	PUNCT
ejpam-5493	25	13	the	the	DET
ejpam-5493	25	14	study	study	NOUN
ejpam-5493	25	15	of	of	ADP
ejpam-5493	25	16	banach	banach	NOUN
ejpam-5493	25	17	modules	module	NOUN
ejpam-5493	25	18	,	,	PUNCT
ejpam-5493	25	19	the	the	DET
ejpam-5493	25	20	theory	theory	NOUN
ejpam-5493	25	21	of	of	ADP
ejpam-5493	25	22	singular	singular	ADJ
ejpam-5493	25	23	integrals	integral	NOUN
ejpam-5493	25	24	,	,	PUNCT
ejpam-5493	25	25	interpolation	interpolation	NOUN
ejpam-5493	25	26	theory	theory	NOUN
ejpam-5493	25	27	,	,	PUNCT
ejpam-5493	25	28	stochastic	stochastic	NOUN
ejpam-5493	25	29	processes	process	NOUN
ejpam-5493	25	30	,	,	PUNCT
ejpam-5493	25	31	the	the	DET
ejpam-5493	25	32	theory	theory	NOUN
ejpam-5493	25	33	of	of	ADP
ejpam-5493	25	34	semigroups	semigroup	NOUN
ejpam-5493	25	35	of	of	ADP
ejpam-5493	25	36	operators	operator	NOUN
ejpam-5493	25	37	,	,	PUNCT
ejpam-5493	25	38	partial	partial	ADJ
ejpam-5493	25	39	differential	differential	NOUN
ejpam-5493	25	40	equations	equation	NOUN
ejpam-5493	25	41	,	,	PUNCT
ejpam-5493	25	42	and	and	CCONJ
ejpam-5493	25	43	the	the	DET
ejpam-5493	25	44	study	study	NOUN
ejpam-5493	25	45	of	of	ADP
ejpam-5493	25	46	approximation	approximation	NOUN
ejpam-5493	25	47	problems	problem	NOUN
ejpam-5493	25	48	are	be	AUX
ejpam-5493	25	49	just	just	ADV
ejpam-5493	25	50	a	a	DET
ejpam-5493	25	51	few	few	ADJ
ejpam-5493	25	52	of	of	ADP
ejpam-5493	25	53	the	the	DET
ejpam-5493	25	54	fields	field	NOUN
ejpam-5493	25	55	in	in	ADP
ejpam-5493	25	56	which	which	PRON
ejpam-5493	25	57	centralizers	centralizer	NOUN
ejpam-5493	25	58	have	have	AUX
ejpam-5493	25	59	also	also	ADV
ejpam-5493	25	60	been	be	AUX
ejpam-5493	25	61	used	use	VERB
ejpam-5493	25	62	(	(	PUNCT
ejpam-5493	25	63	for	for	ADP
ejpam-5493	25	64	more	more	ADJ
ejpam-5493	25	65	information	information	NOUN
ejpam-5493	25	66	,	,	PUNCT
ejpam-5493	25	67	see	see	VERB
ejpam-5493	25	68	larsen	larsen	PROPN
ejpam-5493	25	69	[	[	X
ejpam-5493	25	70	11	11	NUM
ejpam-5493	25	71	]	]	NUM
ejpam-5493	25	72	)	)	PUNCT
ejpam-5493	25	73	.	.	PUNCT
ejpam-5493	26	1	an	an	DET
ejpam-5493	26	2	additive	additive	ADJ
ejpam-5493	26	3	mapping	mapping	NOUN
ejpam-5493	26	4	h	h	NOUN
ejpam-5493	26	5	:	:	PUNCT
ejpam-5493	26	6	r	r	NOUN
ejpam-5493	26	7	→	→	SYM
ejpam-5493	26	8	r	r	NOUN
ejpam-5493	26	9	is	be	AUX
ejpam-5493	26	10	said	say	VERB
ejpam-5493	26	11	to	to	PART
ejpam-5493	26	12	be	be	AUX
ejpam-5493	26	13	a	a	DET
ejpam-5493	26	14	left	left	ADJ
ejpam-5493	26	15	(	(	PUNCT
ejpam-5493	26	16	right	right	ADJ
ejpam-5493	26	17	)	)	PUNCT
ejpam-5493	26	18	centralizer	centralizer	NOUN
ejpam-5493	26	19	if	if	SCONJ
ejpam-5493	26	20	it	it	PRON
ejpam-5493	26	21	holds	hold	VERB
ejpam-5493	26	22	h(rt	h(rt	NOUN
ejpam-5493	26	23	)	)	PUNCT
ejpam-5493	26	24	=	=	SYM
ejpam-5493	26	25	h(r)t	h(r)t	PROPN
ejpam-5493	26	26	(	(	PUNCT
ejpam-5493	26	27	respectively	respectively	ADV
ejpam-5493	26	28	,	,	PUNCT
ejpam-5493	26	29	h(rt	h(rt	NOUN
ejpam-5493	26	30	)	)	PUNCT
ejpam-5493	26	31	=	=	PRON
ejpam-5493	26	32	rh(t	rh(t	X
ejpam-5493	26	33	)	)	PUNCT
ejpam-5493	26	34	)	)	PUNCT
ejpam-5493	26	35	for	for	ADP
ejpam-5493	26	36	all	all	DET
ejpam-5493	26	37	r	r	NOUN
ejpam-5493	26	38	,	,	PUNCT
ejpam-5493	26	39	t	t	PROPN
ejpam-5493	26	40	∈	∈	PROPN
ejpam-5493	26	41	r	r	NOUN
ejpam-5493	26	42	and	and	CCONJ
ejpam-5493	26	43	it	it	PRON
ejpam-5493	26	44	is	be	AUX
ejpam-5493	26	45	known	know	VERB
ejpam-5493	26	46	as	as	ADP
ejpam-5493	26	47	a	a	DET
ejpam-5493	26	48	jordan	jordan	PROPN
ejpam-5493	26	49	right	right	PROPN
ejpam-5493	26	50	(	(	PUNCT
ejpam-5493	26	51	jordan	jordan	PROPN
ejpam-5493	26	52	left	leave	VERB
ejpam-5493	26	53	)	)	PUNCT
ejpam-5493	26	54	centralizer	centralizer	NOUN
ejpam-5493	26	55	if	if	SCONJ
ejpam-5493	26	56	h(r2	h(r2	NOUN
ejpam-5493	26	57	)	)	PUNCT
ejpam-5493	26	58	=	=	SYM
ejpam-5493	26	59	rh(r	rh(r	NOUN
ejpam-5493	26	60	)	)	PUNCT
ejpam-5493	26	61	(	(	PUNCT
ejpam-5493	26	62	respectively	respectively	ADV
ejpam-5493	26	63	,	,	PUNCT
ejpam-5493	26	64	h(r2	h(r2	NOUN
ejpam-5493	26	65	)	)	PUNCT
ejpam-5493	27	1	=	=	SYM
ejpam-5493	27	2	h(r)r	h(r)r	PROPN
ejpam-5493	27	3	)	)	PUNCT
ejpam-5493	27	4	for	for	ADP
ejpam-5493	27	5	all	all	DET
ejpam-5493	27	6	r	r	PROPN
ejpam-5493	27	7	∈	∈	PROPN
ejpam-5493	27	8	r.	r.	NOUN
ejpam-5493	27	9	in	in	ADP
ejpam-5493	27	10	recognizing	recognize	VERB
ejpam-5493	27	11	that	that	SCONJ
ejpam-5493	27	12	this	this	DET
ejpam-5493	27	13	mapping	mapping	NOUN
ejpam-5493	27	14	h	h	NOUN
ejpam-5493	27	15	is	be	AUX
ejpam-5493	27	16	both	both	CCONJ
ejpam-5493	27	17	a	a	DET
ejpam-5493	27	18	right	right	ADJ
ejpam-5493	27	19	centralizer	centralizer	NOUN
ejpam-5493	27	20	and	and	CCONJ
ejpam-5493	27	21	a	a	DET
ejpam-5493	27	22	left	left	ADJ
ejpam-5493	27	23	centralizer	centralizer	NOUN
ejpam-5493	27	24	,	,	PUNCT
ejpam-5493	27	25	we	we	PRON
ejpam-5493	27	26	refer	refer	VERB
ejpam-5493	27	27	to	to	ADP
ejpam-5493	27	28	it	it	PRON
ejpam-5493	27	29	as	as	ADP
ejpam-5493	27	30	a	a	DET
ejpam-5493	27	31	centralizer	centralizer	NOUN
ejpam-5493	27	32	.	.	PUNCT
ejpam-5493	28	1	as	as	ADP
ejpam-5493	28	2	a	a	DET
ejpam-5493	28	3	result	result	NOUN
ejpam-5493	28	4	of	of	ADP
ejpam-5493	28	5	albas	albas	PROPN
ejpam-5493	28	6	[	[	X
ejpam-5493	28	7	1	1	NUM
ejpam-5493	28	8	]	]	PUNCT
ejpam-5493	28	9	,	,	PUNCT
ejpam-5493	28	10	h	h	NOUN
ejpam-5493	28	11	:	:	PUNCT
ejpam-5493	28	12	r	r	NOUN
ejpam-5493	28	13	→	→	SYM
ejpam-5493	28	14	r	r	NOUN
ejpam-5493	28	15	is	be	AUX
ejpam-5493	28	16	called	call	VERB
ejpam-5493	28	17	as	as	ADP
ejpam-5493	28	18	a	a	DET
ejpam-5493	28	19	left	left	ADJ
ejpam-5493	28	20	(	(	PUNCT
ejpam-5493	28	21	right	right	ADJ
ejpam-5493	28	22	)	)	PUNCT
ejpam-5493	28	23	φ	φ	NOUN
ejpam-5493	28	24	-	-	PUNCT
ejpam-5493	28	25	centralizer	centralizer	NOUN
ejpam-5493	28	26	if	if	SCONJ
ejpam-5493	28	27	h(rt	h(rt	NOUN
ejpam-5493	28	28	)	)	PUNCT
ejpam-5493	28	29	=	=	SYM
ejpam-5493	28	30	h(r)φ(t	h(r)φ(t	NUM
ejpam-5493	28	31	)	)	PUNCT
ejpam-5493	28	32	(	(	PUNCT
ejpam-5493	28	33	h(rt	h(rt	NOUN
ejpam-5493	28	34	)	)	PUNCT
ejpam-5493	28	35	=	=	PUNCT
ejpam-5493	28	36	φ(r)h(t	φ(r)h(t	X
ejpam-5493	28	37	)	)	PUNCT
ejpam-5493	28	38	)	)	PUNCT
ejpam-5493	29	1	and	and	CCONJ
ejpam-5493	29	2	it	it	PRON
ejpam-5493	29	3	is	be	AUX
ejpam-5493	29	4	additive	additive	ADJ
ejpam-5493	29	5	,	,	PUNCT
ejpam-5493	29	6	for	for	ADP
ejpam-5493	29	7	all	all	DET
ejpam-5493	29	8	r	r	NOUN
ejpam-5493	29	9	,	,	PUNCT
ejpam-5493	29	10	t	t	PROPN
ejpam-5493	29	11	∈	∈	PROPN
ejpam-5493	29	12	r	r	NOUN
ejpam-5493	29	13	and	and	CCONJ
ejpam-5493	29	14	is	be	AUX
ejpam-5493	29	15	known	know	VERB
ejpam-5493	29	16	as	as	ADP
ejpam-5493	29	17	a	a	DET
ejpam-5493	29	18	jordan	jordan	PROPN
ejpam-5493	29	19	right	right	PROPN
ejpam-5493	29	20	(	(	PUNCT
ejpam-5493	29	21	jordan	jordan	PROPN
ejpam-5493	29	22	left	leave	VERB
ejpam-5493	29	23	)	)	PUNCT
ejpam-5493	29	24	φ	φ	NUM
ejpam-5493	29	25	-	-	PUNCT
ejpam-5493	29	26	centralizer	centralizer	NOUN
ejpam-5493	29	27	if	if	SCONJ
ejpam-5493	29	28	h(r2	h(r2	NOUN
ejpam-5493	29	29	)	)	PUNCT
ejpam-5493	29	30	=	=	SYM
ejpam-5493	29	31	φ(r)h(r	φ(r)h(r	NOUN
ejpam-5493	29	32	)	)	PUNCT
ejpam-5493	29	33	(	(	PUNCT
ejpam-5493	29	34	h(r2	h(r2	NOUN
ejpam-5493	29	35	)	)	PUNCT
ejpam-5493	29	36	=	=	SYM
ejpam-5493	29	37	h(r)φ(r	h(r)φ(r	NOUN
ejpam-5493	29	38	)	)	PUNCT
ejpam-5493	29	39	)	)	PUNCT
ejpam-5493	29	40	for	for	ADP
ejpam-5493	29	41	all	all	DET
ejpam-5493	29	42	r	r	NOUN
ejpam-5493	29	43	∈	∈	NOUN
ejpam-5493	29	44	r	r	NOUN
ejpam-5493	29	45	,	,	PUNCT
ejpam-5493	29	46	where	where	SCONJ
ejpam-5493	29	47	φ	φ	PROPN
ejpam-5493	29	48	is	be	AUX
ejpam-5493	29	49	an	an	DET
ejpam-5493	29	50	endomorphism	endomorphism	NOUN
ejpam-5493	29	51	on	on	ADP
ejpam-5493	29	52	r.	r.	PROPN
ejpam-5493	29	53	an	an	DET
ejpam-5493	29	54	additive	additive	ADJ
ejpam-5493	29	55	mapping	mapping	NOUN
ejpam-5493	29	56	h	h	NOUN
ejpam-5493	29	57	is	be	AUX
ejpam-5493	29	58	recognised	recognise	VERB
ejpam-5493	29	59	as	as	ADP
ejpam-5493	29	60	a	a	DET
ejpam-5493	29	61	φ	φ	NOUN
ejpam-5493	29	62	-	-	PUNCT
ejpam-5493	29	63	centralizer	centralizer	NOUN
ejpam-5493	29	64	,	,	PUNCT
ejpam-5493	29	65	if	if	SCONJ
ejpam-5493	29	66	h	h	NOUN
ejpam-5493	29	67	is	be	AUX
ejpam-5493	29	68	both	both	PRON
ejpam-5493	29	69	left	leave	VERB
ejpam-5493	29	70	as	as	ADV
ejpam-5493	29	71	well	well	ADV
ejpam-5493	29	72	as	as	ADP
ejpam-5493	29	73	right	right	ADJ
ejpam-5493	29	74	φ	φ	NOUN
ejpam-5493	29	75	-	-	PUNCT
ejpam-5493	29	76	centralizer	centralizer	NOUN
ejpam-5493	29	77	.	.	PUNCT
ejpam-5493	30	1	every	every	DET
ejpam-5493	30	2	jordan	jordan	PROPN
ejpam-5493	30	3	φ	φ	PROPN
ejpam-5493	30	4	-	-	PUNCT
ejpam-5493	30	5	centralizer	centralizer	NOUN
ejpam-5493	30	6	is	be	AUX
ejpam-5493	30	7	a	a	DET
ejpam-5493	30	8	φ	φ	NOUN
ejpam-5493	30	9	-	-	PUNCT
ejpam-5493	30	10	centralizer	centralizer	NOUN
ejpam-5493	30	11	.	.	PUNCT
ejpam-5493	31	1	however	however	ADV
ejpam-5493	31	2	,	,	PUNCT
ejpam-5493	31	3	this	this	PRON
ejpam-5493	31	4	is	be	AUX
ejpam-5493	31	5	n’t	not	PART
ejpam-5493	31	6	usually	usually	ADV
ejpam-5493	31	7	the	the	DET
ejpam-5493	31	8	case	case	NOUN
ejpam-5493	31	9	.	.	PUNCT
ejpam-5493	32	1	under	under	ADP
ejpam-5493	32	2	appropriate	appropriate	ADJ
ejpam-5493	32	3	torsion	torsion	NOUN
ejpam-5493	32	4	restrictions	restriction	NOUN
ejpam-5493	32	5	,	,	PUNCT
ejpam-5493	32	6	the	the	DET
ejpam-5493	32	7	converse	converse	NOUN
ejpam-5493	32	8	of	of	ADP
ejpam-5493	32	9	this	this	DET
ejpam-5493	32	10	statement	statement	NOUN
ejpam-5493	32	11	is	be	AUX
ejpam-5493	32	12	also	also	ADV
ejpam-5493	32	13	true	true	ADJ
ejpam-5493	32	14	for	for	ADP
ejpam-5493	32	15	a	a	DET
ejpam-5493	32	16	semiprime	semiprime	NOUN
ejpam-5493	32	17	ring	ring	NOUN
ejpam-5493	32	18	provided	provide	VERB
ejpam-5493	32	19	in	in	ADP
ejpam-5493	32	20	[	[	X
ejpam-5493	32	21	1	1	NUM
ejpam-5493	32	22	]	]	PUNCT
ejpam-5493	32	23	.	.	PUNCT
ejpam-5493	33	1	motivated	motivate	VERB
ejpam-5493	33	2	by	by	ADP
ejpam-5493	33	3	previous	previous	ADJ
ejpam-5493	33	4	literature	literature	PROPN
ejpam-5493	33	5	review	review	NOUN
ejpam-5493	33	6	,	,	PUNCT
ejpam-5493	33	7	in	in	ADP
ejpam-5493	33	8	the	the	DET
ejpam-5493	33	9	present	present	ADJ
ejpam-5493	33	10	paper	paper	NOUN
ejpam-5493	33	11	,	,	PUNCT
ejpam-5493	33	12	authors	author	NOUN
ejpam-5493	33	13	presented	present	VERB
ejpam-5493	33	14	an	an	DET
ejpam-5493	33	15	extension	extension	NOUN
ejpam-5493	33	16	of	of	ADP
ejpam-5493	33	17	this	this	DET
ejpam-5493	33	18	mathematical	mathematical	ADJ
ejpam-5493	33	19	statement	statement	NOUN
ejpam-5493	33	20	.	.	PUNCT
ejpam-5493	34	1	specifically	specifically	ADV
ejpam-5493	34	2	,	,	PUNCT
ejpam-5493	34	3	h	h	NOUN
ejpam-5493	34	4	:	:	PUNCT
ejpam-5493	34	5	r	r	NOUN
ejpam-5493	34	6	→	→	SYM
ejpam-5493	34	7	r	r	NOUN
ejpam-5493	34	8	is	be	AUX
ejpam-5493	34	9	a	a	DET
ejpam-5493	34	10	φ	φ	NOUN
ejpam-5493	34	11	-	-	PUNCT
ejpam-5493	34	12	centralizer	centralizer	NOUN
ejpam-5493	34	13	,	,	PUNCT
ejpam-5493	34	14	if	if	SCONJ
ejpam-5493	34	15	h	h	NOUN
ejpam-5493	34	16	fulfills	fulfill	VERB
ejpam-5493	34	17	any	any	DET
ejpam-5493	34	18	one	one	NUM
ejpam-5493	34	19	of	of	ADP
ejpam-5493	34	20	the	the	DET
ejpam-5493	34	21	following	follow	VERB
ejpam-5493	34	22	3h(r3p	3h(r3p	NUM
ejpam-5493	34	23	)	)	PUNCT
ejpam-5493	34	24	=	=	SYM
ejpam-5493	34	25	h(rp)φ(r2p	h(rp)φ(r2p	NOUN
ejpam-5493	34	26	)	)	PUNCT
ejpam-5493	35	1	+	+	PUNCT
ejpam-5493	35	2	φ(rp)h(rp)φ(rp	φ(rp)h(rp)φ(rp	PROPN
ejpam-5493	35	3	)	)	PUNCT
ejpam-5493	35	4	+	+	NOUN
ejpam-5493	35	5	φ(r2p)h(rp	φ(r2p)h(rp	PROPN
ejpam-5493	35	6	)	)	PUNCT
ejpam-5493	35	7	,	,	PUNCT
ejpam-5493	35	8	2h(r2p	2h(r2p	NUM
ejpam-5493	35	9	)	)	PUNCT
ejpam-5493	35	10	=	=	PUNCT
ejpam-5493	35	11	h(rp)φ(rp	h(rp)φ(rp	PROPN
ejpam-5493	35	12	)	)	PUNCT
ejpam-5493	35	13	+	+	CCONJ
ejpam-5493	35	14	φ(rp)h(rp	φ(rp)h(rp	PROPN
ejpam-5493	35	15	)	)	PUNCT
ejpam-5493	35	16	and	and	CCONJ
ejpam-5493	35	17	h(r3p	h(r3p	NOUN
ejpam-5493	35	18	)	)	PUNCT
ejpam-5493	35	19	=	=	SYM
ejpam-5493	35	20	φ(rp)h(rp)φ(rp	φ(rp)h(rp)φ(rp	PROPN
ejpam-5493	35	21	)	)	PUNCT
ejpam-5493	35	22	for	for	ADP
ejpam-5493	35	23	every	every	DET
ejpam-5493	35	24	r	r	NOUN
ejpam-5493	35	25	in	in	ADP
ejpam-5493	35	26	a	a	DET
ejpam-5493	35	27	semiprime	semiprime	NOUN
ejpam-5493	35	28	ring	ring	NOUN
ejpam-5493	35	29	r	r	NOUN
ejpam-5493	35	30	that	that	PRON
ejpam-5493	35	31	is	be	AUX
ejpam-5493	35	32	specifically	specifically	ADV
ejpam-5493	35	33	torsion	torsion	NOUN
ejpam-5493	35	34	restricted	restrict	VERB
ejpam-5493	35	35	.	.	PUNCT
ejpam-5493	36	1	2	2	X
ejpam-5493	36	2	.	.	X
ejpam-5493	36	3	on	on	ADP
ejpam-5493	36	4	φ	φ	NOUN
ejpam-5493	36	5	-	-	PUNCT
ejpam-5493	36	6	centralizer	centralizer	NOUN
ejpam-5493	36	7	the	the	DET
ejpam-5493	36	8	following	follow	VERB
ejpam-5493	36	9	outcome	outcome	NOUN
ejpam-5493	36	10	is	be	AUX
ejpam-5493	36	11	required	require	VERB
ejpam-5493	36	12	to	to	PART
ejpam-5493	36	13	validate	validate	VERB
ejpam-5493	36	14	the	the	DET
ejpam-5493	36	15	basic	basic	ADJ
ejpam-5493	36	16	theorems	theorem	NOUN
ejpam-5493	36	17	:	:	PUNCT
ejpam-5493	36	18	lemma	lemma	PROPN
ejpam-5493	36	19	1	1	NUM
ejpam-5493	36	20	(	(	PUNCT
ejpam-5493	36	21	[	[	X
ejpam-5493	36	22	4	4	NUM
ejpam-5493	36	23	,	,	PUNCT
ejpam-5493	36	24	theorem	theorem	VERB
ejpam-5493	36	25	1.2	1.2	NUM
ejpam-5493	36	26	]	]	PUNCT
ejpam-5493	36	27	)	)	PUNCT
ejpam-5493	36	28	.	.	PUNCT
ejpam-5493	37	1	if	if	SCONJ
ejpam-5493	37	2	φ	φ	PROPN
ejpam-5493	37	3	is	be	AUX
ejpam-5493	37	4	a	a	DET
ejpam-5493	37	5	surjective	surjective	ADJ
ejpam-5493	37	6	endomorphism	endomorphism	NOUN
ejpam-5493	37	7	on	on	ADP
ejpam-5493	37	8	a	a	DET
ejpam-5493	37	9	semiprime	semiprime	NOUN
ejpam-5493	37	10	ring	ring	NOUN
ejpam-5493	37	11	r	r	NOUN
ejpam-5493	37	12	with	with	ADP
ejpam-5493	37	13	2	2	NUM
ejpam-5493	37	14	torsion	torsion	NOUN
ejpam-5493	37	15	free	free	ADJ
ejpam-5493	37	16	condition	condition	NOUN
ejpam-5493	37	17	and	and	CCONJ
ejpam-5493	37	18	h	h	NOUN
ejpam-5493	37	19	:	:	PUNCT
ejpam-5493	37	20	r	r	NOUN
ejpam-5493	37	21	→	→	SYM
ejpam-5493	37	22	r	r	NOUN
ejpam-5493	37	23	is	be	AUX
ejpam-5493	37	24	an	an	DET
ejpam-5493	37	25	additive	additive	ADJ
ejpam-5493	37	26	mapping	mapping	NOUN
ejpam-5493	37	27	that	that	PRON
ejpam-5493	37	28	satisfies	satisfy	VERB
ejpam-5493	37	29	2h(r2	2h(r2	NUM
ejpam-5493	37	30	)	)	PUNCT
ejpam-5493	37	31	=	=	SYM
ejpam-5493	37	32	h(r)φ(r	h(r)φ(r	X
ejpam-5493	37	33	)	)	PUNCT
ejpam-5493	37	34	+	+	CCONJ
ejpam-5493	37	35	φ(r)h(r	φ(r)h(r	NOUN
ejpam-5493	37	36	)	)	PUNCT
ejpam-5493	37	37	for	for	ADP
ejpam-5493	37	38	all	all	DET
ejpam-5493	37	39	r	r	PROPN
ejpam-5493	37	40	∈	∈	PROPN
ejpam-5493	37	41	r.	r.	NOUN
ejpam-5493	37	42	then	then	ADV
ejpam-5493	37	43	h	h	PROPN
ejpam-5493	37	44	is	be	AUX
ejpam-5493	37	45	a	a	DET
ejpam-5493	37	46	φ	φ	NOUN
ejpam-5493	37	47	-	-	PUNCT
ejpam-5493	37	48	centralizer	centralizer	NOUN
ejpam-5493	37	49	on	on	ADP
ejpam-5493	37	50	r.	r.	PROPN
ejpam-5493	37	51	we	we	PRON
ejpam-5493	37	52	start	start	VERB
ejpam-5493	37	53	with	with	ADP
ejpam-5493	37	54	the	the	DET
ejpam-5493	37	55	study	study	NOUN
ejpam-5493	37	56	considering	consider	VERB
ejpam-5493	37	57	the	the	DET
ejpam-5493	37	58	following	follow	VERB
ejpam-5493	37	59	problem	problem	NOUN
ejpam-5493	37	60	:	:	PUNCT
ejpam-5493	37	61	theorem	theorem	NOUN
ejpam-5493	37	62	1	1	NUM
ejpam-5493	37	63	.	.	PUNCT
ejpam-5493	38	1	if	if	SCONJ
ejpam-5493	38	2	φ	φ	PROPN
ejpam-5493	38	3	is	be	AUX
ejpam-5493	38	4	a	a	DET
ejpam-5493	38	5	surjective	surjective	ADJ
ejpam-5493	38	6	endomorphism	endomorphism	NOUN
ejpam-5493	38	7	on	on	ADP
ejpam-5493	38	8	a	a	DET
ejpam-5493	38	9	semiprime	semiprime	NOUN
ejpam-5493	38	10	ring	ring	NOUN
ejpam-5493	38	11	r	r	NOUN
ejpam-5493	38	12	with	with	ADP
ejpam-5493	38	13	(	(	PUNCT
ejpam-5493	38	14	3p	3p	NUM
ejpam-5493	38	15	−	−	NOUN
ejpam-5493	38	16	1	1	NUM
ejpam-5493	38	17	)	)	PUNCT
ejpam-5493	38	18	!	!	PUNCT
ejpam-5493	39	1	torsion	torsion	NOUN
ejpam-5493	39	2	free	free	ADJ
ejpam-5493	39	3	condition	condition	NOUN
ejpam-5493	39	4	and	and	CCONJ
ejpam-5493	39	5	h	h	NOUN
ejpam-5493	39	6	:	:	PUNCT
ejpam-5493	39	7	r	r	NOUN
ejpam-5493	39	8	→	→	SYM
ejpam-5493	39	9	r	r	NOUN
ejpam-5493	39	10	is	be	AUX
ejpam-5493	39	11	an	an	DET
ejpam-5493	39	12	additive	additive	ADJ
ejpam-5493	39	13	mapping	mapping	NOUN
ejpam-5493	39	14	that	that	PRON
ejpam-5493	39	15	satisfies	satisfy	VERB
ejpam-5493	39	16	3h(r3p	3h(r3p	NUM
ejpam-5493	39	17	)	)	PUNCT
ejpam-5493	39	18	=	=	SYM
ejpam-5493	39	19	h(rp)φ(r2p	h(rp)φ(r2p	NOUN
ejpam-5493	39	20	)	)	PUNCT
ejpam-5493	40	1	+	+	PUNCT
ejpam-5493	40	2	φ(rp)h(rp)φ(rp	φ(rp)h(rp)φ(rp	PROPN
ejpam-5493	40	3	)	)	PUNCT
ejpam-5493	40	4	+	+	CCONJ
ejpam-5493	40	5	φ(r2p)h(rp	φ(r2p)h(rp	PROPN
ejpam-5493	40	6	)	)	PUNCT
ejpam-5493	40	7	for	for	ADP
ejpam-5493	40	8	all	all	DET
ejpam-5493	40	9	r	r	NOUN
ejpam-5493	40	10	∈	∈	NOUN
ejpam-5493	40	11	r	r	NOUN
ejpam-5493	40	12	,	,	PUNCT
ejpam-5493	40	13	(	(	PUNCT
ejpam-5493	40	14	1	1	X
ejpam-5493	40	15	)	)	PUNCT
ejpam-5493	40	16	a.	a.	NOUN
ejpam-5493	40	17	z.	z.	PROPN
ejpam-5493	40	18	ansari	ansari	PROPN
ejpam-5493	40	19	et	et	PROPN
ejpam-5493	40	20	al	al	PROPN
ejpam-5493	40	21	.	.	PUNCT
ejpam-5493	40	22	/	/	SYM
ejpam-5493	40	23	eur	eur	PROPN
ejpam-5493	40	24	.	.	PUNCT
ejpam-5493	41	1	j.	j.	PROPN
ejpam-5493	41	2	pure	pure	PROPN
ejpam-5493	41	3	appl	appl	PROPN
ejpam-5493	41	4	.	.	PROPN
ejpam-5493	41	5	math	math	PROPN
ejpam-5493	41	6	,	,	PUNCT
ejpam-5493	41	7	18	18	NUM
ejpam-5493	41	8	(	(	PUNCT
ejpam-5493	41	9	1	1	NUM
ejpam-5493	41	10	)	)	PUNCT
ejpam-5493	41	11	(	(	PUNCT
ejpam-5493	41	12	2025	2025	NUM
ejpam-5493	41	13	)	)	PUNCT
ejpam-5493	41	14	,	,	PUNCT
ejpam-5493	41	15	5493	5493	NUM
ejpam-5493	41	16	3	3	NUM
ejpam-5493	41	17	of	of	ADP
ejpam-5493	41	18	10	10	NUM
ejpam-5493	41	19	then	then	ADV
ejpam-5493	41	20	h	h	PROPN
ejpam-5493	41	21	is	be	AUX
ejpam-5493	41	22	a	a	DET
ejpam-5493	41	23	φ	φ	NOUN
ejpam-5493	41	24	-	-	PUNCT
ejpam-5493	41	25	centralizer	centralizer	NOUN
ejpam-5493	41	26	on	on	ADP
ejpam-5493	41	27	r	r	NOUN
ejpam-5493	41	28	,	,	PUNCT
ejpam-5493	41	29	where	where	SCONJ
ejpam-5493	41	30	p	p	NOUN
ejpam-5493	41	31	is	be	AUX
ejpam-5493	41	32	a	a	DET
ejpam-5493	41	33	fixed	fix	VERB
ejpam-5493	41	34	integer	integer	NOUN
ejpam-5493	41	35	greater	great	ADJ
ejpam-5493	41	36	than	than	ADP
ejpam-5493	41	37	or	or	CCONJ
ejpam-5493	41	38	equal	equal	ADJ
ejpam-5493	41	39	to	to	ADP
ejpam-5493	41	40	1	1	NUM
ejpam-5493	41	41	.	.	PUNCT
ejpam-5493	42	1	proof	proof	NOUN
ejpam-5493	42	2	.	.	PUNCT
ejpam-5493	43	1	we	we	PRON
ejpam-5493	43	2	commence	commence	VERB
ejpam-5493	43	3	with	with	ADP
ejpam-5493	43	4	the	the	DET
ejpam-5493	43	5	equation	equation	NOUN
ejpam-5493	43	6	(	(	PUNCT
ejpam-5493	43	7	1	1	NUM
ejpam-5493	43	8	)	)	PUNCT
ejpam-5493	43	9	by	by	ADP
ejpam-5493	43	10	replacing	replace	VERB
ejpam-5493	43	11	r	r	NOUN
ejpam-5493	43	12	by	by	ADP
ejpam-5493	43	13	r	r	NOUN
ejpam-5493	43	14	+	+	SYM
ejpam-5493	43	15	kt	kt	PROPN
ejpam-5493	43	16	,	,	PUNCT
ejpam-5493	43	17	we	we	PRON
ejpam-5493	43	18	get	get	VERB
ejpam-5493	43	19	the	the	DET
ejpam-5493	43	20	following	following	NOUN
ejpam-5493	43	21	for	for	ADP
ejpam-5493	43	22	k	k	PROPN
ejpam-5493	43	23	being	be	AUX
ejpam-5493	43	24	a	a	DET
ejpam-5493	43	25	positive	positive	ADJ
ejpam-5493	43	26	integer	integer	NOUN
ejpam-5493	43	27	and	and	CCONJ
ejpam-5493	43	28	t	t	NOUN
ejpam-5493	43	29	∈	∈	PROPN
ejpam-5493	43	30	r	r	NOUN
ejpam-5493	43	31	3h(r3p+	3h(r3p+	NUM
ejpam-5493	43	32	(	(	PUNCT
ejpam-5493	43	33	3p	3p	NUM
ejpam-5493	43	34	1	1	NUM
ejpam-5493	43	35	)	)	PUNCT
ejpam-5493	43	36	(	(	PUNCT
ejpam-5493	44	1	r3p−1)kt+	r3p−1)kt+	NOUN
ejpam-5493	44	2	(	(	PUNCT
ejpam-5493	44	3	3p	3p	NUM
ejpam-5493	44	4	2	2	NUM
ejpam-5493	44	5	)	)	PUNCT
ejpam-5493	44	6	r3p−2k2t2	r3p−2k2t2	NOUN
ejpam-5493	44	7	+	+	CCONJ
ejpam-5493	44	8	...	...	PUNCT
ejpam-5493	45	1	+	+	ADJ
ejpam-5493	45	2	k3pt3p	k3pt3p	NOUN
ejpam-5493	45	3	)	)	PUNCT
ejpam-5493	45	4	=	=	VERB
ejpam-5493	45	5	h(rp+	h(rp+	X
ejpam-5493	45	6	(	(	PUNCT
ejpam-5493	45	7	p	p	NOUN
ejpam-5493	45	8	1	1	X
ejpam-5493	45	9	)	)	PUNCT
ejpam-5493	45	10	rp−1kt+	rp−1kt+	NOUN
ejpam-5493	45	11	(	(	PUNCT
ejpam-5493	45	12	p	p	NOUN
ejpam-5493	45	13	2	2	X
ejpam-5493	45	14	)	)	PUNCT
ejpam-5493	45	15	rp−2k2t2	rp−2k2t2	PROPN
ejpam-5493	45	16	+	+	NUM
ejpam-5493	45	17	...	...	PUNCT
ejpam-5493	46	1	+	+	X
ejpam-5493	46	2	kptp)·φ(r2p+	kptp)·φ(r2p+	X
ejpam-5493	46	3	(	(	PUNCT
ejpam-5493	46	4	2p	2p	NUM
ejpam-5493	46	5	1	1	NUM
ejpam-5493	46	6	)	)	PUNCT
ejpam-5493	46	7	r2p−1kt+	r2p−1kt+	NOUN
ejpam-5493	46	8	(	(	PUNCT
ejpam-5493	46	9	2p	2p	NUM
ejpam-5493	46	10	2	2	NUM
ejpam-5493	46	11	)	)	PUNCT
ejpam-5493	46	12	r2p−2k2t2+	r2p−2k2t2+	NOUN
ejpam-5493	46	13	...	...	PUNCT
ejpam-5493	46	14	+k2pt2p)+φ(rp+	+k2pt2p)+φ(rp+	NUM
ejpam-5493	46	15	(	(	PUNCT
ejpam-5493	46	16	p	p	NOUN
ejpam-5493	46	17	1	1	X
ejpam-5493	46	18	)	)	PUNCT
ejpam-5493	46	19	rp−1kt+	rp−1kt+	NOUN
ejpam-5493	46	20	(	(	PUNCT
ejpam-5493	46	21	p	p	NOUN
ejpam-5493	46	22	2	2	X
ejpam-5493	46	23	)	)	PUNCT
ejpam-5493	46	24	rp−2k2t2	rp−2k2t2	PROPN
ejpam-5493	46	25	+	+	CCONJ
ejpam-5493	46	26	...	...	PUNCT
ejpam-5493	47	1	+	+	ADJ
ejpam-5493	47	2	kptp	kptp	NOUN
ejpam-5493	47	3	)	)	PUNCT
ejpam-5493	47	4	·	·	PUNCT
ejpam-5493	47	5	h(rp+	h(rp+	X
ejpam-5493	47	6	(	(	PUNCT
ejpam-5493	47	7	p	p	NOUN
ejpam-5493	47	8	1	1	X
ejpam-5493	47	9	)	)	PUNCT
ejpam-5493	47	10	rp−1kt+	rp−1kt+	NOUN
ejpam-5493	47	11	(	(	PUNCT
ejpam-5493	47	12	p	p	NOUN
ejpam-5493	47	13	2	2	X
ejpam-5493	47	14	)	)	PUNCT
ejpam-5493	47	15	rp−2k2t2	rp−2k2t2	PROPN
ejpam-5493	47	16	+	+	CCONJ
ejpam-5493	47	17	...	...	PUNCT
ejpam-5493	48	1	+	+	ADJ
ejpam-5493	48	2	kptp	kptp	NOUN
ejpam-5493	48	3	)	)	PUNCT
ejpam-5493	48	4	·	·	PUNCT
ejpam-5493	48	5	φ(rp+	φ(rp+	X
ejpam-5493	48	6	(	(	PUNCT
ejpam-5493	48	7	p	p	NOUN
ejpam-5493	48	8	1	1	X
ejpam-5493	48	9	)	)	PUNCT
ejpam-5493	48	10	rp−1kt+	rp−1kt+	NOUN
ejpam-5493	48	11	(	(	PUNCT
ejpam-5493	48	12	p	p	NOUN
ejpam-5493	48	13	2	2	X
ejpam-5493	48	14	)	)	PUNCT
ejpam-5493	48	15	rp−2k2t2	rp−2k2t2	PROPN
ejpam-5493	48	16	+	+	NOUN
ejpam-5493	48	17	...	...	PUNCT
ejpam-5493	49	1	+	+	NUM
ejpam-5493	49	2	kptp)+φ(r2p+	kptp)+φ(r2p+	NOUN
ejpam-5493	49	3	(	(	PUNCT
ejpam-5493	49	4	2p	2p	NUM
ejpam-5493	49	5	1	1	NUM
ejpam-5493	49	6	)	)	PUNCT
ejpam-5493	49	7	r2p−1kt+	r2p−1kt+	NOUN
ejpam-5493	49	8	(	(	PUNCT
ejpam-5493	49	9	2p	2p	NUM
ejpam-5493	49	10	2	2	NUM
ejpam-5493	49	11	)	)	PUNCT
ejpam-5493	49	12	r2p−2k2t2	r2p−2k2t2	NOUN
ejpam-5493	49	13	+	+	CCONJ
ejpam-5493	49	14	...	...	PUNCT
ejpam-5493	49	15	+	+	ADJ
ejpam-5493	49	16	k2pt2p	k2pt2p	NOUN
ejpam-5493	49	17	)	)	PUNCT
ejpam-5493	49	18	·	·	PUNCT
ejpam-5493	49	19	h(rp+	h(rp+	X
ejpam-5493	49	20	(	(	PUNCT
ejpam-5493	49	21	p	p	NOUN
ejpam-5493	49	22	1	1	X
ejpam-5493	49	23	)	)	PUNCT
ejpam-5493	49	24	rp−1kt+	rp−1kt+	NOUN
ejpam-5493	49	25	(	(	PUNCT
ejpam-5493	49	26	p	p	NOUN
ejpam-5493	49	27	2	2	X
ejpam-5493	49	28	)	)	PUNCT
ejpam-5493	49	29	rp−2k2t2	rp−2k2t2	PROPN
ejpam-5493	49	30	+	+	NUM
ejpam-5493	49	31	...	...	PUNCT
ejpam-5493	49	32	+	+	NUM
ejpam-5493	49	33	kptp	kptp	NOUN
ejpam-5493	49	34	)	)	PUNCT
ejpam-5493	49	35	.	.	PUNCT
ejpam-5493	50	1	restate	restate	VERB
ejpam-5493	50	2	the	the	DET
ejpam-5493	50	3	preceding	precede	VERB
ejpam-5493	50	4	expression	expression	NOUN
ejpam-5493	50	5	using	use	VERB
ejpam-5493	50	6	(	(	PUNCT
ejpam-5493	50	7	1	1	NUM
ejpam-5493	50	8	)	)	PUNCT
ejpam-5493	50	9	as	as	ADP
ejpam-5493	50	10	ka1(r	ka1(r	PROPN
ejpam-5493	50	11	,	,	PUNCT
ejpam-5493	50	12	t	t	PROPN
ejpam-5493	50	13	)	)	PUNCT
ejpam-5493	51	1	+	+	CCONJ
ejpam-5493	52	1	k2a2(r	k2a2(r	PROPN
ejpam-5493	52	2	,	,	PUNCT
ejpam-5493	52	3	t	t	PROPN
ejpam-5493	52	4	)	)	PUNCT
ejpam-5493	52	5	+	+	CCONJ
ejpam-5493	52	6	...	...	PUNCT
ejpam-5493	53	1	+	+	NUM
ejpam-5493	53	2	k3p−1a3p−1(r	k3p−1a3p−1(r	PROPN
ejpam-5493	53	3	,	,	PUNCT
ejpam-5493	53	4	t	t	PROPN
ejpam-5493	53	5	)	)	PUNCT
ejpam-5493	53	6	=	=	SYM
ejpam-5493	54	1	0	0	NUM
ejpam-5493	54	2	,	,	PUNCT
ejpam-5493	54	3	where	where	SCONJ
ejpam-5493	54	4	the	the	DET
ejpam-5493	54	5	coefficients	coefficient	NOUN
ejpam-5493	54	6	of	of	ADP
ejpam-5493	54	7	ki	ki	PROPN
ejpam-5493	54	8	are	be	AUX
ejpam-5493	54	9	delimited	delimit	VERB
ejpam-5493	54	10	by	by	ADP
ejpam-5493	54	11	ai(r	ai(r	ADP
ejpam-5493	54	12	,	,	PUNCT
ejpam-5493	54	13	t	t	PROPN
ejpam-5493	54	14	)	)	PUNCT
ejpam-5493	54	15	for	for	ADP
ejpam-5493	54	16	all	all	DET
ejpam-5493	54	17	i	i	PRON
ejpam-5493	54	18	=	=	NOUN
ejpam-5493	54	19	1	1	NUM
ejpam-5493	54	20	,	,	PUNCT
ejpam-5493	54	21	2	2	NUM
ejpam-5493	54	22	,	,	PUNCT
ejpam-5493	54	23	...	...	PUNCT
ejpam-5493	54	24	,	,	PUNCT
ejpam-5493	54	25	(	(	PUNCT
ejpam-5493	54	26	3p−	3p−	PROPN
ejpam-5493	54	27	1	1	NUM
ejpam-5493	54	28	)	)	PUNCT
ejpam-5493	54	29	.	.	PUNCT
ejpam-5493	55	1	a	a	DET
ejpam-5493	55	2	system	system	NOUN
ejpam-5493	55	3	of	of	ADP
ejpam-5493	55	4	(	(	PUNCT
ejpam-5493	55	5	3p−	3p−	PROPN
ejpam-5493	55	6	1	1	NUM
ejpam-5493	55	7	)	)	PUNCT
ejpam-5493	55	8	homogeneous	homogeneous	ADJ
ejpam-5493	55	9	equations	equation	NOUN
ejpam-5493	55	10	can	can	AUX
ejpam-5493	55	11	be	be	AUX
ejpam-5493	55	12	obtained	obtain	VERB
ejpam-5493	55	13	if	if	SCONJ
ejpam-5493	55	14	we	we	PRON
ejpam-5493	55	15	substitute	substitute	VERB
ejpam-5493	55	16	1	1	NUM
ejpam-5493	55	17	,	,	PUNCT
ejpam-5493	55	18	2	2	NUM
ejpam-5493	55	19	,	,	PUNCT
ejpam-5493	55	20	...	...	PUNCT
ejpam-5493	55	21	,	,	PUNCT
ejpam-5493	55	22	(	(	PUNCT
ejpam-5493	55	23	3p−	3p−	PROPN
ejpam-5493	55	24	1	1	NUM
ejpam-5493	55	25	)	)	PUNCT
ejpam-5493	55	26	for	for	ADP
ejpam-5493	55	27	k	k	PROPN
ejpam-5493	55	28	one	one	NUM
ejpam-5493	55	29	by	by	ADP
ejpam-5493	55	30	one	one	NUM
ejpam-5493	55	31	,	,	PUNCT
ejpam-5493	55	32	it	it	PRON
ejpam-5493	55	33	provides	provide	VERB
ejpam-5493	55	34	a	a	DET
ejpam-5493	55	35	vandermonde	vandermonde	ADJ
ejpam-5493	55	36	matrix	matrix	ADJ
ejpam-5493	55	37	1	1	NUM
ejpam-5493	55	38	1	1	NUM
ejpam-5493	55	39	·	·	PUNCT
ejpam-5493	55	40	·	·	PUNCT
ejpam-5493	55	41	·	·	PUNCT
ejpam-5493	55	42	1	1	NUM
ejpam-5493	55	43	2	2	NUM
ejpam-5493	55	44	22	22	NUM
ejpam-5493	55	45	·	·	PUNCT
ejpam-5493	55	46	·	·	PUNCT
ejpam-5493	55	47	·	·	PUNCT
ejpam-5493	56	1	23p−1	23p−1	X
ejpam-5493	56	2	·	·	PUNCT
ejpam-5493	56	3	·	·	PUNCT
ejpam-5493	56	4	·	·	PUNCT
ejpam-5493	56	5	·	·	PUNCT
ejpam-5493	56	6	·	·	PUNCT
ejpam-5493	56	7	·	·	PUNCT
ejpam-5493	56	8	·	·	PUNCT
ejpam-5493	56	9	·	·	PUNCT
ejpam-5493	56	10	·	·	PUNCT
ejpam-5493	56	11	·	·	PUNCT
ejpam-5493	56	12	·	·	PUNCT
ejpam-5493	56	13	·	·	PUNCT
ejpam-5493	56	14	·	·	PUNCT
ejpam-5493	56	15	·	·	PUNCT
ejpam-5493	56	16	·	·	PUNCT
ejpam-5493	56	17	·	·	PUNCT
ejpam-5493	56	18	·	·	PUNCT
ejpam-5493	56	19	·	·	PUNCT
ejpam-5493	57	1	3p−	3p−	NUM
ejpam-5493	57	2	1	1	NUM
ejpam-5493	57	3	(	(	PUNCT
ejpam-5493	57	4	3p−	3p−	PROPN
ejpam-5493	57	5	1)2	1)2	NUM
ejpam-5493	57	6	·	·	PUNCT
ejpam-5493	57	7	·	·	PUNCT
ejpam-5493	57	8	·	·	PUNCT
ejpam-5493	57	9	(	(	PUNCT
ejpam-5493	57	10	3p−	3p−	PROPN
ejpam-5493	57	11	1)3p−1	1)3p−1	NUM
ejpam-5493	57	12			NUM
ejpam-5493	57	13	.	.	PUNCT
ejpam-5493	58	1	which	which	PRON
ejpam-5493	58	2	yields	yield	VERB
ejpam-5493	58	3	that	that	PRON
ejpam-5493	58	4	ai(r	ai(r	ADV
ejpam-5493	58	5	,	,	PUNCT
ejpam-5493	58	6	t	t	PROPN
ejpam-5493	58	7	)	)	PUNCT
ejpam-5493	58	8	=	=	SYM
ejpam-5493	58	9	0	0	NUM
ejpam-5493	58	10	for	for	ADP
ejpam-5493	58	11	all	all	DET
ejpam-5493	58	12	r	r	NOUN
ejpam-5493	58	13	,	,	PUNCT
ejpam-5493	58	14	t	t	PROPN
ejpam-5493	58	15	∈	∈	PROPN
ejpam-5493	58	16	r	r	NOUN
ejpam-5493	58	17	and	and	CCONJ
ejpam-5493	58	18	for	for	ADP
ejpam-5493	58	19	i	i	PRON
ejpam-5493	58	20	=	=	SYM
ejpam-5493	58	21	1	1	NUM
ejpam-5493	58	22	,	,	PUNCT
ejpam-5493	58	23	2	2	NUM
ejpam-5493	58	24	,	,	PUNCT
ejpam-5493	58	25	..	..	PUNCT
ejpam-5493	58	26	,	,	PUNCT
ejpam-5493	58	27	(	(	PUNCT
ejpam-5493	58	28	3p−1	3p−1	NUM
ejpam-5493	58	29	)	)	PUNCT
ejpam-5493	58	30	.	.	PUNCT
ejpam-5493	59	1	in	in	ADP
ejpam-5493	59	2	particular	particular	ADJ
ejpam-5493	59	3	,	,	PUNCT
ejpam-5493	59	4	we	we	PRON
ejpam-5493	59	5	have	have	VERB
ejpam-5493	59	6	a1(r	a1(r	NOUN
ejpam-5493	59	7	,	,	PUNCT
ejpam-5493	59	8	t	t	PROPN
ejpam-5493	59	9	)	)	PUNCT
ejpam-5493	59	10	=	=	SYM
ejpam-5493	60	1	0	0	NUM
ejpam-5493	60	2	implies	imply	VERB
ejpam-5493	60	3	that	that	SCONJ
ejpam-5493	60	4	3	3	X
ejpam-5493	60	5	(	(	PUNCT
ejpam-5493	60	6	3p	3p	NUM
ejpam-5493	60	7	1	1	NUM
ejpam-5493	60	8	)	)	PUNCT
ejpam-5493	60	9	h(r3p−1	h(r3p−1	PROPN
ejpam-5493	60	10	t	t	NOUN
ejpam-5493	60	11	)	)	PUNCT
ejpam-5493	60	12	=	=	PUNCT
ejpam-5493	61	1	(	(	PUNCT
ejpam-5493	61	2	2p	2p	NUM
ejpam-5493	61	3	1	1	NUM
ejpam-5493	61	4	)	)	PUNCT
ejpam-5493	61	5	h(rp)φ(r2p−1	h(rp)φ(r2p−1	PROPN
ejpam-5493	61	6	t	t	PROPN
ejpam-5493	61	7	)	)	PUNCT
ejpam-5493	61	8	+	+	CCONJ
ejpam-5493	61	9	(	(	PUNCT
ejpam-5493	61	10	p	p	NOUN
ejpam-5493	61	11	1	1	NUM
ejpam-5493	61	12	)	)	PUNCT
ejpam-5493	61	13	h(rp−1t)φ(r2p	h(rp−1t)φ(r2p	PROPN
ejpam-5493	61	14	)	)	PUNCT
ejpam-5493	62	1	+	+	CCONJ
ejpam-5493	62	2	(	(	PUNCT
ejpam-5493	62	3	p	p	NOUN
ejpam-5493	62	4	1	1	NUM
ejpam-5493	62	5	)	)	PUNCT
ejpam-5493	62	6	φ(rp−1t)h(rp)φ(rp	φ(rp−1t)h(rp)φ(rp	PROPN
ejpam-5493	62	7	)	)	PUNCT
ejpam-5493	63	1	+	+	CCONJ
ejpam-5493	63	2	(	(	PUNCT
ejpam-5493	63	3	p	p	NOUN
ejpam-5493	63	4	1	1	X
ejpam-5493	63	5	)	)	PUNCT
ejpam-5493	63	6	φ(rp)h(rp−1t)φ(rp	φ(rp)h(rp−1t)φ(rp	PROPN
ejpam-5493	63	7	)	)	PUNCT
ejpam-5493	63	8	+	+	CCONJ
ejpam-5493	63	9	(	(	PUNCT
ejpam-5493	63	10	p	p	NOUN
ejpam-5493	63	11	1	1	X
ejpam-5493	63	12	)	)	PUNCT
ejpam-5493	63	13	φ(rp)h(rp)φ(rp−1	φ(rp)h(rp)φ(rp−1	PROPN
ejpam-5493	63	14	t	t	PROPN
ejpam-5493	63	15	)	)	PUNCT
ejpam-5493	64	1	+	+	CCONJ
ejpam-5493	64	2	(	(	PUNCT
ejpam-5493	64	3	2p	2p	NUM
ejpam-5493	64	4	1	1	NUM
ejpam-5493	64	5	)	)	PUNCT
ejpam-5493	64	6	φ(r2p−1t)h(rp	φ(r2p−1t)h(rp	NOUN
ejpam-5493	64	7	)	)	PUNCT
ejpam-5493	64	8	for	for	ADP
ejpam-5493	64	9	each	each	DET
ejpam-5493	64	10	r	r	NOUN
ejpam-5493	64	11	,	,	PUNCT
ejpam-5493	64	12	t	t	PROPN
ejpam-5493	64	13	∈	∈	PROPN
ejpam-5493	64	14	r.	r.	PROPN
ejpam-5493	64	15	if	if	SCONJ
ejpam-5493	64	16	we	we	PRON
ejpam-5493	64	17	put	put	VERB
ejpam-5493	64	18	e	e	NOUN
ejpam-5493	64	19	in	in	ADP
ejpam-5493	64	20	place	place	NOUN
ejpam-5493	64	21	of	of	ADP
ejpam-5493	64	22	r	r	NOUN
ejpam-5493	64	23	in	in	ADP
ejpam-5493	64	24	above	above	ADP
ejpam-5493	64	25	expression	expression	NOUN
ejpam-5493	64	26	,	,	PUNCT
ejpam-5493	64	27	then	then	ADV
ejpam-5493	64	28	we	we	PRON
ejpam-5493	64	29	find	find	VERB
ejpam-5493	64	30	9ph(t	9ph(t	NUM
ejpam-5493	64	31	)	)	PUNCT
ejpam-5493	65	1	=	=	SYM
ejpam-5493	65	2	2ph(e)t	2ph(e)t	PROPN
ejpam-5493	65	3	+	+	CCONJ
ejpam-5493	65	4	2pth(e	2pth(e	NUM
ejpam-5493	65	5	)	)	PUNCT
ejpam-5493	65	6	+	+	X
ejpam-5493	65	7	3ph(t	3ph(t	NUM
ejpam-5493	65	8	)	)	PUNCT
ejpam-5493	66	1	+	+	CCONJ
ejpam-5493	66	2	ph(e)t	ph(e)t	PROPN
ejpam-5493	66	3	+	+	NUM
ejpam-5493	66	4	pth(e	pth(e	NOUN
ejpam-5493	66	5	)	)	PUNCT
ejpam-5493	66	6	,	,	PUNCT
ejpam-5493	66	7	for	for	SCONJ
ejpam-5493	66	8	each	each	DET
ejpam-5493	66	9	t	t	PROPN
ejpam-5493	66	10	∈	∈	PROPN
ejpam-5493	66	11	r.	r.	NOUN
ejpam-5493	66	12	making	make	VERB
ejpam-5493	66	13	use	use	NOUN
ejpam-5493	66	14	of	of	ADP
ejpam-5493	66	15	torsion	torsion	NOUN
ejpam-5493	66	16	restrictions	restriction	NOUN
ejpam-5493	66	17	on	on	ADP
ejpam-5493	66	18	r	r	NOUN
ejpam-5493	66	19	to	to	PART
ejpam-5493	66	20	obtain	obtain	VERB
ejpam-5493	66	21	2h(t	2h(t	NUM
ejpam-5493	66	22	)	)	PUNCT
ejpam-5493	66	23	=	=	SYM
ejpam-5493	66	24	h(e)φ(t	h(e)φ(t	NUM
ejpam-5493	66	25	)	)	PUNCT
ejpam-5493	66	26	+	+	CCONJ
ejpam-5493	66	27	φ(t)h(e	φ(t)h(e	NOUN
ejpam-5493	66	28	)	)	PUNCT
ejpam-5493	66	29	,	,	PUNCT
ejpam-5493	66	30	for	for	ADP
ejpam-5493	66	31	all	all	DET
ejpam-5493	66	32	t	t	PROPN
ejpam-5493	66	33	∈	∈	PROPN
ejpam-5493	66	34	r.	r.	PROPN
ejpam-5493	66	35	(	(	PUNCT
ejpam-5493	66	36	2	2	NUM
ejpam-5493	66	37	)	)	PUNCT
ejpam-5493	66	38	next	next	ADJ
ejpam-5493	66	39	,	,	PUNCT
ejpam-5493	66	40	a2(r	a2(r	PROPN
ejpam-5493	66	41	,	,	PUNCT
ejpam-5493	66	42	t	t	PROPN
ejpam-5493	66	43	)	)	PUNCT
ejpam-5493	66	44	=	=	SYM
ejpam-5493	66	45	0	0	NUM
ejpam-5493	66	46	implies	imply	VERB
ejpam-5493	66	47	that	that	SCONJ
ejpam-5493	66	48	3	3	X
ejpam-5493	66	49	(	(	PUNCT
ejpam-5493	66	50	3p	3p	NUM
ejpam-5493	66	51	2	2	NUM
ejpam-5493	66	52	)	)	PUNCT
ejpam-5493	66	53	h(r3p−2t2	h(r3p−2t2	PROPN
ejpam-5493	66	54	)	)	PUNCT
ejpam-5493	66	55	=	=	SYM
ejpam-5493	66	56	(	(	PUNCT
ejpam-5493	66	57	2p	2p	NUM
ejpam-5493	66	58	2	2	NUM
ejpam-5493	66	59	)	)	PUNCT
ejpam-5493	66	60	h(rp)φ(r2p−2t2	h(rp)φ(r2p−2t2	NOUN
ejpam-5493	66	61	)	)	PUNCT
ejpam-5493	67	1	+	+	CCONJ
ejpam-5493	67	2	(	(	PUNCT
ejpam-5493	67	3	p	p	NOUN
ejpam-5493	67	4	1	1	NUM
ejpam-5493	67	5	)	)	PUNCT
ejpam-5493	67	6	(	(	PUNCT
ejpam-5493	67	7	2p	2p	NUM
ejpam-5493	67	8	1	1	NUM
ejpam-5493	67	9	)	)	PUNCT
ejpam-5493	67	10	h(rp−1t)φ(r2p−1	h(rp−1t)φ(r2p−1	PROPN
ejpam-5493	67	11	t	t	PROPN
ejpam-5493	67	12	)	)	PUNCT
ejpam-5493	67	13	+	+	CCONJ
ejpam-5493	67	14	(	(	PUNCT
ejpam-5493	67	15	p	p	NOUN
ejpam-5493	67	16	2	2	NUM
ejpam-5493	67	17	)	)	PUNCT
ejpam-5493	67	18	h(rp−2t2)φ(r2p	h(rp−2t2)φ(r2p	NOUN
ejpam-5493	67	19	)	)	PUNCT
ejpam-5493	68	1	+	+	CCONJ
ejpam-5493	68	2	(	(	PUNCT
ejpam-5493	68	3	p	p	NOUN
ejpam-5493	68	4	2	2	NUM
ejpam-5493	68	5	)	)	PUNCT
ejpam-5493	68	6	φ(rp)h(rp)φ(rp−2t2	φ(rp)h(rp)φ(rp−2t2	NOUN
ejpam-5493	68	7	)	)	PUNCT
ejpam-5493	69	1	+	+	CCONJ
ejpam-5493	69	2	(	(	PUNCT
ejpam-5493	69	3	p	p	NOUN
ejpam-5493	69	4	1	1	NUM
ejpam-5493	69	5	)	)	PUNCT
ejpam-5493	69	6	(	(	PUNCT
ejpam-5493	69	7	p	p	NOUN
ejpam-5493	69	8	1	1	NUM
ejpam-5493	69	9	)	)	PUNCT
ejpam-5493	69	10	φ(rp−1t)h(rp)φ(rp−1	φ(rp−1t)h(rp)φ(rp−1	NUM
ejpam-5493	69	11	t	t	NOUN
ejpam-5493	69	12	)	)	PUNCT
ejpam-5493	69	13	+	+	CCONJ
ejpam-5493	69	14	(	(	PUNCT
ejpam-5493	69	15	p	p	NOUN
ejpam-5493	69	16	1	1	NUM
ejpam-5493	69	17	)	)	PUNCT
ejpam-5493	69	18	(	(	PUNCT
ejpam-5493	69	19	p	p	NOUN
ejpam-5493	69	20	1	1	X
ejpam-5493	69	21	)	)	PUNCT
ejpam-5493	69	22	φ(rp)h(rp−1t)φ(rp−1	φ(rp)h(rp−1t)φ(rp−1	PROPN
ejpam-5493	69	23	t	t	PROPN
ejpam-5493	69	24	)	)	PUNCT
ejpam-5493	69	25	+	+	CCONJ
ejpam-5493	69	26	(	(	PUNCT
ejpam-5493	69	27	p	p	NOUN
ejpam-5493	69	28	2	2	X
ejpam-5493	69	29	)	)	PUNCT
ejpam-5493	69	30	φ(rp)h(rp−2t2)φ(rp	φ(rp)h(rp−2t2)φ(rp	PROPN
ejpam-5493	69	31	)	)	PUNCT
ejpam-5493	70	1	+	+	CCONJ
ejpam-5493	70	2	(	(	PUNCT
ejpam-5493	70	3	p	p	NOUN
ejpam-5493	70	4	1	1	NUM
ejpam-5493	70	5	)	)	PUNCT
ejpam-5493	70	6	(	(	PUNCT
ejpam-5493	70	7	p	p	NOUN
ejpam-5493	70	8	1	1	X
ejpam-5493	70	9	)	)	PUNCT
ejpam-5493	70	10	φ(rp−1t)h(rp−1t)φ(rp	φ(rp−1t)h(rp−1t)φ(rp	PROPN
ejpam-5493	70	11	)	)	PUNCT
ejpam-5493	70	12	+	+	CCONJ
ejpam-5493	70	13	(	(	PUNCT
ejpam-5493	70	14	p	p	NOUN
ejpam-5493	70	15	2	2	NUM
ejpam-5493	70	16	)	)	PUNCT
ejpam-5493	70	17	φ(rp−2t2)h(rp)φ(rp	φ(rp−2t2)h(rp)φ(rp	PROPN
ejpam-5493	70	18	)	)	PUNCT
ejpam-5493	71	1	+	+	CCONJ
ejpam-5493	71	2	(	(	PUNCT
ejpam-5493	71	3	p	p	NOUN
ejpam-5493	71	4	2	2	NUM
ejpam-5493	71	5	)	)	PUNCT
ejpam-5493	71	6	φ(r2p)h(rp−2t2	φ(r2p)h(rp−2t2	PROPN
ejpam-5493	71	7	)	)	PUNCT
ejpam-5493	72	1	+	+	CCONJ
ejpam-5493	72	2	(	(	PUNCT
ejpam-5493	72	3	2p	2p	NUM
ejpam-5493	72	4	1	1	NUM
ejpam-5493	72	5	)	)	PUNCT
ejpam-5493	72	6	(	(	PUNCT
ejpam-5493	72	7	p	p	NOUN
ejpam-5493	72	8	1	1	NUM
ejpam-5493	72	9	)	)	PUNCT
ejpam-5493	72	10	φ(r2p−1t)h(rp−1	φ(r2p−1t)h(rp−1	PROPN
ejpam-5493	72	11	t	t	PROPN
ejpam-5493	72	12	)	)	PUNCT
ejpam-5493	72	13	+	+	CCONJ
ejpam-5493	72	14	(	(	PUNCT
ejpam-5493	72	15	2p	2p	NUM
ejpam-5493	72	16	2	2	NUM
ejpam-5493	72	17	)	)	PUNCT
ejpam-5493	72	18	φ(r2p−2t2)h(rp	φ(r2p−2t2)h(rp	PROPN
ejpam-5493	72	19	)	)	PUNCT
ejpam-5493	72	20	.	.	PUNCT
ejpam-5493	73	1	a.	a.	PROPN
ejpam-5493	73	2	z.	z.	PROPN
ejpam-5493	73	3	ansari	ansari	PROPN
ejpam-5493	73	4	et	et	PROPN
ejpam-5493	73	5	al	al	PROPN
ejpam-5493	73	6	.	.	PUNCT
ejpam-5493	73	7	/	/	SYM
ejpam-5493	73	8	eur	eur	PROPN
ejpam-5493	73	9	.	.	PUNCT
ejpam-5493	74	1	j.	j.	PROPN
ejpam-5493	74	2	pure	pure	PROPN
ejpam-5493	74	3	appl	appl	PROPN
ejpam-5493	74	4	.	.	PROPN
ejpam-5493	74	5	math	math	PROPN
ejpam-5493	74	6	,	,	PUNCT
ejpam-5493	74	7	18	18	NUM
ejpam-5493	74	8	(	(	PUNCT
ejpam-5493	74	9	1	1	NUM
ejpam-5493	74	10	)	)	PUNCT
ejpam-5493	74	11	(	(	PUNCT
ejpam-5493	74	12	2025	2025	NUM
ejpam-5493	74	13	)	)	PUNCT
ejpam-5493	74	14	,	,	PUNCT
ejpam-5493	74	15	5493	5493	NUM
ejpam-5493	74	16	4	4	NUM
ejpam-5493	74	17	of	of	ADP
ejpam-5493	74	18	10	10	NUM
ejpam-5493	74	19	reword	reword	NOUN
ejpam-5493	74	20	the	the	DET
ejpam-5493	74	21	above	above	ADJ
ejpam-5493	74	22	expression	expression	NOUN
ejpam-5493	74	23	by	by	ADP
ejpam-5493	74	24	putting	put	VERB
ejpam-5493	74	25	e	e	NOUN
ejpam-5493	74	26	in	in	ADP
ejpam-5493	74	27	place	place	NOUN
ejpam-5493	74	28	of	of	ADP
ejpam-5493	74	29	r	r	NOUN
ejpam-5493	74	30	,	,	PUNCT
ejpam-5493	74	31	we	we	PRON
ejpam-5493	74	32	have	have	VERB
ejpam-5493	74	33	33p(3p−1	33p(3p−1	NUM
ejpam-5493	74	34	)	)	PUNCT
ejpam-5493	74	35	2	2	NUM
ejpam-5493	74	36	h(t2	h(t2	NOUN
ejpam-5493	74	37	)	)	PUNCT
ejpam-5493	74	38	=	=	SYM
ejpam-5493	75	1	2p(2p−1	2p(2p−1	NUM
ejpam-5493	75	2	)	)	PUNCT
ejpam-5493	75	3	2	2	NUM
ejpam-5493	75	4	h(e)φ(t2	h(e)φ(t2	NOUN
ejpam-5493	75	5	)	)	PUNCT
ejpam-5493	75	6	+	+	CCONJ
ejpam-5493	75	7	2p2h(t)φ(t	2p2h(t)φ(t	NUM
ejpam-5493	75	8	)	)	PUNCT
ejpam-5493	75	9	+	+	NUM
ejpam-5493	75	10	p(p−1	p(p−1	NOUN
ejpam-5493	75	11	)	)	PUNCT
ejpam-5493	75	12	2	2	NUM
ejpam-5493	75	13	h(t2	h(t2	NOUN
ejpam-5493	75	14	)	)	PUNCT
ejpam-5493	76	1	+	+	NOUN
ejpam-5493	76	2	p(p−1	p(p−1	NOUN
ejpam-5493	76	3	)	)	PUNCT
ejpam-5493	76	4	2	2	NUM
ejpam-5493	76	5	h(e)φ(t2	h(e)φ(t2	NOUN
ejpam-5493	76	6	)	)	PUNCT
ejpam-5493	76	7	+	+	SYM
ejpam-5493	76	8	p2φ(t)h(e)φ(t	p2φ(t)h(e)φ(t	X
ejpam-5493	76	9	)	)	PUNCT
ejpam-5493	77	1	+	+	CCONJ
ejpam-5493	77	2	p(p−1	p(p−1	NOUN
ejpam-5493	77	3	)	)	PUNCT
ejpam-5493	77	4	2	2	NUM
ejpam-5493	77	5	h(t2	h(t2	NOUN
ejpam-5493	77	6	)	)	PUNCT
ejpam-5493	77	7	+	+	NOUN
ejpam-5493	77	8	p2φ(t)h(e)φ(t	p2φ(t)h(e)φ(t	NUM
ejpam-5493	77	9	)	)	PUNCT
ejpam-5493	77	10	+	+	CCONJ
ejpam-5493	77	11	p2φ(t)h(t	p2φ(t)h(t	NOUN
ejpam-5493	77	12	)	)	PUNCT
ejpam-5493	77	13	+	+	CCONJ
ejpam-5493	77	14	p(p−1	p(p−1	NOUN
ejpam-5493	77	15	)	)	PUNCT
ejpam-5493	77	16	2	2	NUM
ejpam-5493	77	17	φ(t2)h(e	φ(t2)h(e	NOUN
ejpam-5493	77	18	)	)	PUNCT
ejpam-5493	77	19	+	+	NOUN
ejpam-5493	77	20	p(p−1	p(p−1	NOUN
ejpam-5493	77	21	)	)	PUNCT
ejpam-5493	77	22	2	2	NUM
ejpam-5493	77	23	h(t2	h(t2	NOUN
ejpam-5493	77	24	)	)	PUNCT
ejpam-5493	77	25	+	+	X
ejpam-5493	77	26	2p2φ(t)h(t	2p2φ(t)h(t	X
ejpam-5493	77	27	)	)	PUNCT
ejpam-5493	78	1	+	+	CCONJ
ejpam-5493	78	2	2p(2p−1	2p(2p−1	X
ejpam-5493	78	3	)	)	PUNCT
ejpam-5493	78	4	2	2	NUM
ejpam-5493	78	5	φ(t2)h(e	φ(t2)h(e	NOUN
ejpam-5493	78	6	)	)	PUNCT
ejpam-5493	78	7	simplify	simplify	VERB
ejpam-5493	78	8	the	the	DET
ejpam-5493	78	9	above	above	ADJ
ejpam-5493	78	10	expression	expression	NOUN
ejpam-5493	78	11	to	to	PART
ejpam-5493	78	12	find	find	VERB
ejpam-5493	78	13	9p(3p−	9p(3p−	NUM
ejpam-5493	78	14	1)h(t2	1)h(t2	NUM
ejpam-5493	78	15	)	)	PUNCT
ejpam-5493	78	16	=	=	SYM
ejpam-5493	78	17	2p(2p−	2p(2p−	NUM
ejpam-5493	78	18	1)h(e)φ(t2	1)h(e)φ(t2	NUM
ejpam-5493	78	19	)	)	PUNCT
ejpam-5493	78	20	+	+	CCONJ
ejpam-5493	78	21	4p2h(t)φ(t	4p2h(t)φ(t	NUM
ejpam-5493	78	22	)	)	PUNCT
ejpam-5493	79	1	+	+	CCONJ
ejpam-5493	79	2	p(p−	p(p−	VERB
ejpam-5493	79	3	1)h(t2	1)h(t2	NUM
ejpam-5493	79	4	)	)	PUNCT
ejpam-5493	80	1	+	+	VERB
ejpam-5493	80	2	p(p−	p(p−	VERB
ejpam-5493	80	3	1)h(e)φ(t2	1)h(e)φ(t2	NUM
ejpam-5493	80	4	)	)	PUNCT
ejpam-5493	80	5	+	+	NOUN
ejpam-5493	80	6	2p2h(t)φ(t	2p2h(t)φ(t	NUM
ejpam-5493	80	7	)	)	PUNCT
ejpam-5493	80	8	+	+	CCONJ
ejpam-5493	80	9	p(p−	p(p−	VERB
ejpam-5493	80	10	1)h(t2	1)h(t2	NUM
ejpam-5493	80	11	)	)	PUNCT
ejpam-5493	80	12	+2p2φ(t)h(e)φ(t	+2p2φ(t)h(e)φ(t	PROPN
ejpam-5493	80	13	)	)	PUNCT
ejpam-5493	81	1	+	+	CCONJ
ejpam-5493	81	2	2p2φ(t)h(t	2p2φ(t)h(t	X
ejpam-5493	81	3	)	)	PUNCT
ejpam-5493	81	4	+	+	CCONJ
ejpam-5493	81	5	p(p−	p(p−	NOUN
ejpam-5493	81	6	1)φ(t2)h(e	1)φ(t2)h(e	NUM
ejpam-5493	81	7	)	)	PUNCT
ejpam-5493	82	1	+	+	VERB
ejpam-5493	82	2	p(p−	p(p−	VERB
ejpam-5493	82	3	1)h(t2	1)h(t2	NOUN
ejpam-5493	82	4	)	)	PUNCT
ejpam-5493	82	5	+	+	X
ejpam-5493	82	6	4p2φ(t)h(t	4p2φ(t)h(t	NUM
ejpam-5493	82	7	)	)	PUNCT
ejpam-5493	82	8	+	+	CCONJ
ejpam-5493	82	9	2p(2p−	2p(2p−	NUM
ejpam-5493	82	10	1)φ(t2)h(e	1)φ(t2)h(e	NUM
ejpam-5493	82	11	)	)	PUNCT
ejpam-5493	82	12	collect	collect	VERB
ejpam-5493	82	13	the	the	DET
ejpam-5493	82	14	like	like	ADJ
ejpam-5493	82	15	terms	term	NOUN
ejpam-5493	82	16	in	in	ADP
ejpam-5493	82	17	above	above	ADP
ejpam-5493	82	18	expression	expression	NOUN
ejpam-5493	82	19	and	and	CCONJ
ejpam-5493	82	20	make	make	VERB
ejpam-5493	82	21	them	they	PRON
ejpam-5493	82	22	more	more	ADV
ejpam-5493	82	23	comprehensible	comprehensible	ADJ
ejpam-5493	82	24	as	as	ADP
ejpam-5493	82	25	(	(	PUNCT
ejpam-5493	82	26	24p2	24p2	NUM
ejpam-5493	82	27	−	−	PROPN
ejpam-5493	82	28	6p)h(t2	6p)h(t2	NUM
ejpam-5493	82	29	)	)	PUNCT
ejpam-5493	82	30	=	=	PUNCT
ejpam-5493	83	1	(	(	PUNCT
ejpam-5493	83	2	5p2	5p2	NUM
ejpam-5493	83	3	−	−	NOUN
ejpam-5493	83	4	3p)2h(t2	3p)2h(t2	NUM
ejpam-5493	83	5	)	)	PUNCT
ejpam-5493	83	6	+	+	CCONJ
ejpam-5493	83	7	6p2(h(t)φ(t	6p2(h(t)φ(t	NUM
ejpam-5493	83	8	)	)	PUNCT
ejpam-5493	84	1	+	+	NOUN
ejpam-5493	84	2	φ(t)h(t	φ(t)h(t	NUM
ejpam-5493	84	3	)	)	PUNCT
ejpam-5493	84	4	)	)	PUNCT
ejpam-5493	85	1	+	+	PUNCT
ejpam-5493	85	2	2p2φ(t)h(e)φ(t	2p2φ(t)h(e)φ(t	NUM
ejpam-5493	85	3	)	)	PUNCT
ejpam-5493	85	4	,	,	PUNCT
ejpam-5493	85	5	for	for	ADP
ejpam-5493	85	6	all	all	DET
ejpam-5493	85	7	t	t	PROPN
ejpam-5493	85	8	∈	∈	PROPN
ejpam-5493	85	9	r.	r.	PROPN
ejpam-5493	85	10	again	again	ADV
ejpam-5493	85	11	comparing	compare	VERB
ejpam-5493	85	12	the	the	DET
ejpam-5493	85	13	like	like	ADJ
ejpam-5493	85	14	terms	term	NOUN
ejpam-5493	85	15	both	both	PRON
ejpam-5493	85	16	side	side	NOUN
ejpam-5493	85	17	and	and	CCONJ
ejpam-5493	85	18	using	use	VERB
ejpam-5493	85	19	equation	equation	NOUN
ejpam-5493	85	20	(	(	PUNCT
ejpam-5493	85	21	2	2	NUM
ejpam-5493	85	22	)	)	PUNCT
ejpam-5493	85	23	,	,	PUNCT
ejpam-5493	85	24	we	we	PRON
ejpam-5493	85	25	come	come	VERB
ejpam-5493	85	26	up	up	ADP
ejpam-5493	85	27	with	with	ADP
ejpam-5493	85	28	14p2h(t2	14p2h(t2	NUM
ejpam-5493	85	29	)	)	PUNCT
ejpam-5493	85	30	=	=	SYM
ejpam-5493	86	1	6p2(h(t)φ(t	6p2(h(t)φ(t	NUM
ejpam-5493	86	2	)	)	PUNCT
ejpam-5493	87	1	+	+	NOUN
ejpam-5493	87	2	φ(t)h(t	φ(t)h(t	NUM
ejpam-5493	87	3	)	)	PUNCT
ejpam-5493	87	4	)	)	PUNCT
ejpam-5493	88	1	+	+	PUNCT
ejpam-5493	88	2	2p2φ(t)h(e)φ(t	2p2φ(t)h(e)φ(t	NUM
ejpam-5493	88	3	)	)	PUNCT
ejpam-5493	88	4	,	,	PUNCT
ejpam-5493	88	5	for	for	ADP
ejpam-5493	88	6	all	all	DET
ejpam-5493	88	7	t	t	PROPN
ejpam-5493	88	8	∈	∈	PROPN
ejpam-5493	88	9	r.	r.	PROPN
ejpam-5493	88	10	hence	hence	ADV
ejpam-5493	88	11	,	,	PUNCT
ejpam-5493	88	12	we	we	PRON
ejpam-5493	88	13	get	get	VERB
ejpam-5493	88	14	by	by	ADP
ejpam-5493	88	15	applying	apply	VERB
ejpam-5493	88	16	the	the	DET
ejpam-5493	88	17	torsion	torsion	NOUN
ejpam-5493	88	18	freeness	freeness	NOUN
ejpam-5493	88	19	of	of	ADP
ejpam-5493	88	20	r	r	PROPN
ejpam-5493	88	21	14h(t2	14h(t2	NUM
ejpam-5493	88	22	)	)	PUNCT
ejpam-5493	88	23	=	=	SYM
ejpam-5493	88	24	6	6	NUM
ejpam-5493	88	25	(	(	PUNCT
ejpam-5493	88	26	h(t)φ(t	h(t)φ(t	NOUN
ejpam-5493	88	27	)	)	PUNCT
ejpam-5493	88	28	+	+	CCONJ
ejpam-5493	88	29	φ(t)h(t	φ(t)h(t	NUM
ejpam-5493	88	30	)	)	PUNCT
ejpam-5493	88	31	)	)	PUNCT
ejpam-5493	89	1	+	+	CCONJ
ejpam-5493	89	2	2φ(t)h(e)φ(t	2φ(t)h(e)φ(t	NUM
ejpam-5493	89	3	)	)	PUNCT
ejpam-5493	89	4	,	,	PUNCT
ejpam-5493	89	5	for	for	ADP
ejpam-5493	89	6	every	every	DET
ejpam-5493	89	7	t	t	PROPN
ejpam-5493	89	8	∈	∈	PROPN
ejpam-5493	89	9	r.	r.	PROPN
ejpam-5493	89	10	(	(	PUNCT
ejpam-5493	89	11	3	3	X
ejpam-5493	89	12	)	)	PUNCT
ejpam-5493	89	13	multiplying	multiply	VERB
ejpam-5493	89	14	from	from	ADP
ejpam-5493	89	15	right	right	ADJ
ejpam-5493	89	16	side	side	NOUN
ejpam-5493	89	17	by	by	ADP
ejpam-5493	89	18	φ(r	φ(r	NOUN
ejpam-5493	89	19	)	)	PUNCT
ejpam-5493	89	20	to	to	ADP
ejpam-5493	89	21	(	(	PUNCT
ejpam-5493	89	22	2	2	NUM
ejpam-5493	89	23	)	)	PUNCT
ejpam-5493	89	24	,	,	PUNCT
ejpam-5493	89	25	we	we	PRON
ejpam-5493	89	26	obtain	obtain	VERB
ejpam-5493	89	27	2h(r)φ(r	2h(r)φ(r	NUM
ejpam-5493	89	28	)	)	PUNCT
ejpam-5493	89	29	=	=	SYM
ejpam-5493	89	30	h(e)φ(r2	h(e)φ(r2	NOUN
ejpam-5493	89	31	)	)	PUNCT
ejpam-5493	89	32	+	+	CCONJ
ejpam-5493	90	1	φ(r)h(e)φ(r	φ(r)h(e)φ(r	NOUN
ejpam-5493	90	2	)	)	PUNCT
ejpam-5493	90	3	for	for	ADP
ejpam-5493	90	4	all	all	DET
ejpam-5493	90	5	r	r	PROPN
ejpam-5493	90	6	∈	∈	PROPN
ejpam-5493	90	7	r.	r.	NOUN
ejpam-5493	90	8	multiply	multiply	NOUN
ejpam-5493	90	9	from	from	ADP
ejpam-5493	90	10	left	left	ADJ
ejpam-5493	90	11	side	side	NOUN
ejpam-5493	90	12	by	by	ADP
ejpam-5493	90	13	φ(r	φ(r	ADJ
ejpam-5493	90	14	)	)	PUNCT
ejpam-5493	90	15	to	to	ADP
ejpam-5493	90	16	(	(	PUNCT
ejpam-5493	90	17	2	2	X
ejpam-5493	90	18	)	)	PUNCT
ejpam-5493	90	19	to	to	PART
ejpam-5493	90	20	get	get	VERB
ejpam-5493	90	21	2φ(r)h(r	2φ(r)h(r	NUM
ejpam-5493	90	22	)	)	PUNCT
ejpam-5493	91	1	=	=	PUNCT
ejpam-5493	91	2	φ(r)h(e)φ(r	φ(r)h(e)φ(r	ADJ
ejpam-5493	91	3	)	)	PUNCT
ejpam-5493	91	4	+	+	CCONJ
ejpam-5493	91	5	φ(r2)h(e	φ(r2)h(e	NOUN
ejpam-5493	91	6	)	)	PUNCT
ejpam-5493	91	7	for	for	ADP
ejpam-5493	91	8	all	all	DET
ejpam-5493	91	9	r	r	PROPN
ejpam-5493	91	10	∈	∈	PROPN
ejpam-5493	91	11	r.	r.	NOUN
ejpam-5493	91	12	adding	add	VERB
ejpam-5493	91	13	these	these	DET
ejpam-5493	91	14	equations	equation	NOUN
ejpam-5493	91	15	,	,	PUNCT
ejpam-5493	91	16	we	we	PRON
ejpam-5493	91	17	find	find	VERB
ejpam-5493	91	18	2(h(r)φ(r	2(h(r)φ(r	NUM
ejpam-5493	91	19	)	)	PUNCT
ejpam-5493	92	1	+	+	NUM
ejpam-5493	92	2	φ(r)h(r	φ(r)h(r	NOUN
ejpam-5493	92	3	)	)	PUNCT
ejpam-5493	92	4	)	)	PUNCT
ejpam-5493	93	1	=	=	PUNCT
ejpam-5493	93	2	2φ(r)h(e)φ(r	2φ(r)h(e)φ(r	NUM
ejpam-5493	93	3	)	)	PUNCT
ejpam-5493	93	4	+	+	NUM
ejpam-5493	93	5	2h(r2	2h(r2	NUM
ejpam-5493	93	6	)	)	PUNCT
ejpam-5493	93	7	,	,	PUNCT
ejpam-5493	93	8	which	which	PRON
ejpam-5493	93	9	implies	imply	VERB
ejpam-5493	93	10	that	that	SCONJ
ejpam-5493	93	11	2φ(r)h(e)φ(r	2φ(r)h(e)φ(r	NUM
ejpam-5493	93	12	)	)	PUNCT
ejpam-5493	93	13	=	=	SYM
ejpam-5493	93	14	2(h(r)φ(r	2(h(r)φ(r	NUM
ejpam-5493	93	15	)	)	PUNCT
ejpam-5493	94	1	+	+	CCONJ
ejpam-5493	95	1	φ(r)h(r))−	φ(r)h(r))−	NUM
ejpam-5493	95	2	2h(r2	2h(r2	NUM
ejpam-5493	95	3	)	)	PUNCT
ejpam-5493	95	4	for	for	ADP
ejpam-5493	95	5	all	all	DET
ejpam-5493	95	6	r	r	PROPN
ejpam-5493	95	7	∈	∈	PROPN
ejpam-5493	95	8	r.	r.	NOUN
ejpam-5493	95	9	using	use	VERB
ejpam-5493	95	10	this	this	DET
ejpam-5493	95	11	equation	equation	NOUN
ejpam-5493	95	12	in	in	ADP
ejpam-5493	95	13	(	(	PUNCT
ejpam-5493	95	14	3	3	NUM
ejpam-5493	95	15	)	)	PUNCT
ejpam-5493	95	16	,	,	PUNCT
ejpam-5493	95	17	we	we	PRON
ejpam-5493	95	18	have	have	VERB
ejpam-5493	95	19	14h(r2	14h(r2	NUM
ejpam-5493	95	20	)	)	PUNCT
ejpam-5493	95	21	=	=	SYM
ejpam-5493	95	22	6	6	NUM
ejpam-5493	95	23	(	(	PUNCT
ejpam-5493	95	24	h(r)φ(r	h(r)φ(r	NOUN
ejpam-5493	95	25	)	)	PUNCT
ejpam-5493	96	1	+	+	NUM
ejpam-5493	96	2	φ(r)h(r	φ(r)h(r	NOUN
ejpam-5493	96	3	)	)	PUNCT
ejpam-5493	96	4	)	)	PUNCT
ejpam-5493	97	1	+	+	CCONJ
ejpam-5493	97	2	2	2	NUM
ejpam-5493	97	3	(	(	PUNCT
ejpam-5493	97	4	h(r)φ(r	h(r)φ(r	NOUN
ejpam-5493	97	5	)	)	PUNCT
ejpam-5493	97	6	+	+	NUM
ejpam-5493	97	7	φ(r)h(r	φ(r)h(r	NOUN
ejpam-5493	97	8	)	)	PUNCT
ejpam-5493	97	9	)	)	PUNCT
ejpam-5493	98	1	−	−	ADP
ejpam-5493	98	2	2h(r2	2h(r2	NUM
ejpam-5493	98	3	)	)	PUNCT
ejpam-5493	98	4	for	for	ADP
ejpam-5493	98	5	all	all	DET
ejpam-5493	98	6	r	r	PROPN
ejpam-5493	98	7	∈	∈	PROPN
ejpam-5493	98	8	r.	r.	PROPN
ejpam-5493	98	9	a.	a.	PROPN
ejpam-5493	98	10	z.	z.	PROPN
ejpam-5493	98	11	ansari	ansari	PROPN
ejpam-5493	98	12	et	et	PROPN
ejpam-5493	98	13	al	al	PROPN
ejpam-5493	98	14	.	.	PUNCT
ejpam-5493	98	15	/	/	SYM
ejpam-5493	98	16	eur	eur	PROPN
ejpam-5493	98	17	.	.	PUNCT
ejpam-5493	99	1	j.	j.	PROPN
ejpam-5493	99	2	pure	pure	PROPN
ejpam-5493	99	3	appl	appl	PROPN
ejpam-5493	99	4	.	.	PROPN
ejpam-5493	99	5	math	math	PROPN
ejpam-5493	99	6	,	,	PUNCT
ejpam-5493	99	7	18	18	NUM
ejpam-5493	99	8	(	(	PUNCT
ejpam-5493	99	9	1	1	NUM
ejpam-5493	99	10	)	)	PUNCT
ejpam-5493	99	11	(	(	PUNCT
ejpam-5493	99	12	2025	2025	NUM
ejpam-5493	99	13	)	)	PUNCT
ejpam-5493	99	14	,	,	PUNCT
ejpam-5493	99	15	5493	5493	NUM
ejpam-5493	99	16	5	5	NUM
ejpam-5493	99	17	of	of	ADP
ejpam-5493	99	18	10	10	NUM
ejpam-5493	99	19	using	use	VERB
ejpam-5493	99	20	torsion	torsion	NOUN
ejpam-5493	99	21	restrictions	restriction	NOUN
ejpam-5493	99	22	on	on	ADP
ejpam-5493	99	23	r	r	NOUN
ejpam-5493	99	24	,	,	PUNCT
ejpam-5493	99	25	we	we	PRON
ejpam-5493	99	26	get	get	VERB
ejpam-5493	99	27	2h(r2	2h(r2	NOUN
ejpam-5493	99	28	)	)	PUNCT
ejpam-5493	99	29	=	=	SYM
ejpam-5493	100	1	h(r)φ(r	h(r)φ(r	X
ejpam-5493	100	2	)	)	PUNCT
ejpam-5493	100	3	+	+	CCONJ
ejpam-5493	100	4	φ(r)h(r	φ(r)h(r	NOUN
ejpam-5493	100	5	)	)	PUNCT
ejpam-5493	100	6	for	for	ADP
ejpam-5493	100	7	all	all	DET
ejpam-5493	100	8	r	r	NOUN
ejpam-5493	100	9	∈	∈	PROPN
ejpam-5493	100	10	r.	r.	NOUN
ejpam-5493	100	11	using	use	VERB
ejpam-5493	100	12	lemma	lemma	PROPN
ejpam-5493	100	13	1	1	NUM
ejpam-5493	100	14	,	,	PUNCT
ejpam-5493	100	15	we	we	PRON
ejpam-5493	100	16	obtained	obtain	VERB
ejpam-5493	100	17	the	the	DET
ejpam-5493	100	18	required	require	VERB
ejpam-5493	100	19	outcome	outcome	NOUN
ejpam-5493	100	20	.	.	PUNCT
ejpam-5493	101	1	theorem	theorem	NOUN
ejpam-5493	101	2	2	2	NUM
ejpam-5493	101	3	.	.	PUNCT
ejpam-5493	102	1	if	if	SCONJ
ejpam-5493	102	2	φ	φ	PROPN
ejpam-5493	102	3	is	be	AUX
ejpam-5493	102	4	a	a	DET
ejpam-5493	102	5	surjective	surjective	ADJ
ejpam-5493	102	6	endomorphism	endomorphism	NOUN
ejpam-5493	102	7	on	on	ADP
ejpam-5493	102	8	a	a	DET
ejpam-5493	102	9	semiprime	semiprime	NOUN
ejpam-5493	102	10	ring	ring	NOUN
ejpam-5493	102	11	r	r	NOUN
ejpam-5493	102	12	with	with	ADP
ejpam-5493	102	13	(	(	PUNCT
ejpam-5493	102	14	2p	2p	NUM
ejpam-5493	102	15	−	−	NOUN
ejpam-5493	102	16	1	1	NUM
ejpam-5493	102	17	)	)	PUNCT
ejpam-5493	102	18	!	!	PUNCT
ejpam-5493	103	1	torsion	torsion	NOUN
ejpam-5493	103	2	free	free	ADJ
ejpam-5493	103	3	condition	condition	NOUN
ejpam-5493	103	4	and	and	CCONJ
ejpam-5493	103	5	h	h	NOUN
ejpam-5493	103	6	:	:	PUNCT
ejpam-5493	103	7	r	r	NOUN
ejpam-5493	103	8	→	→	SYM
ejpam-5493	103	9	r	r	NOUN
ejpam-5493	103	10	is	be	AUX
ejpam-5493	103	11	an	an	DET
ejpam-5493	103	12	additive	additive	ADJ
ejpam-5493	103	13	mapping	mapping	NOUN
ejpam-5493	103	14	that	that	PRON
ejpam-5493	103	15	satisfies	satisfy	VERB
ejpam-5493	103	16	2h(r2p	2h(r2p	NUM
ejpam-5493	103	17	)	)	PUNCT
ejpam-5493	103	18	=	=	PUNCT
ejpam-5493	103	19	h(rp)φ(rp	h(rp)φ(rp	PROPN
ejpam-5493	103	20	)	)	PUNCT
ejpam-5493	103	21	+	+	CCONJ
ejpam-5493	103	22	φ(rp)h(rp	φ(rp)h(rp	PROPN
ejpam-5493	103	23	)	)	PUNCT
ejpam-5493	103	24	for	for	ADP
ejpam-5493	103	25	all	all	DET
ejpam-5493	103	26	r	r	NOUN
ejpam-5493	103	27	∈	∈	NOUN
ejpam-5493	103	28	r	r	NOUN
ejpam-5493	103	29	,	,	PUNCT
ejpam-5493	103	30	(	(	PUNCT
ejpam-5493	103	31	4	4	X
ejpam-5493	103	32	)	)	PUNCT
ejpam-5493	103	33	then	then	ADV
ejpam-5493	103	34	h	h	PROPN
ejpam-5493	103	35	is	be	AUX
ejpam-5493	103	36	a	a	DET
ejpam-5493	103	37	φ	φ	NOUN
ejpam-5493	103	38	-	-	PUNCT
ejpam-5493	103	39	centralizer	centralizer	NOUN
ejpam-5493	103	40	on	on	ADP
ejpam-5493	103	41	r	r	NOUN
ejpam-5493	103	42	,	,	PUNCT
ejpam-5493	103	43	where	where	SCONJ
ejpam-5493	103	44	p	p	NOUN
ejpam-5493	103	45	is	be	AUX
ejpam-5493	103	46	a	a	DET
ejpam-5493	103	47	fixed	fix	VERB
ejpam-5493	103	48	integer	integer	NOUN
ejpam-5493	103	49	greater	great	ADJ
ejpam-5493	103	50	than	than	ADP
ejpam-5493	103	51	or	or	CCONJ
ejpam-5493	103	52	equal	equal	ADJ
ejpam-5493	103	53	to	to	ADP
ejpam-5493	103	54	1	1	NUM
ejpam-5493	103	55	.	.	PUNCT
ejpam-5493	104	1	proof	proof	NOUN
ejpam-5493	104	2	.	.	PUNCT
ejpam-5493	105	1	we	we	PRON
ejpam-5493	105	2	proceed	proceed	VERB
ejpam-5493	105	3	with	with	ADP
ejpam-5493	105	4	(	(	PUNCT
ejpam-5493	105	5	4	4	NUM
ejpam-5493	105	6	)	)	PUNCT
ejpam-5493	105	7	and	and	CCONJ
ejpam-5493	105	8	replace	replace	VERB
ejpam-5493	105	9	r	r	NOUN
ejpam-5493	105	10	by	by	ADP
ejpam-5493	105	11	r	r	NOUN
ejpam-5493	105	12	+	+	X
ejpam-5493	105	13	kt	kt	PROPN
ejpam-5493	105	14	for	for	ADP
ejpam-5493	105	15	k	k	PROPN
ejpam-5493	105	16	≥	≥	PROPN
ejpam-5493	105	17	1	1	NUM
ejpam-5493	105	18	and	and	CCONJ
ejpam-5493	105	19	t	t	NOUN
ejpam-5493	105	20	∈	∈	PROPN
ejpam-5493	105	21	r	r	NOUN
ejpam-5493	105	22	,	,	PUNCT
ejpam-5493	105	23	to	to	PART
ejpam-5493	105	24	get	get	VERB
ejpam-5493	105	25	2h(r2p+	2h(r2p+	NUM
ejpam-5493	105	26	(	(	PUNCT
ejpam-5493	105	27	2p	2p	NUM
ejpam-5493	105	28	1	1	NUM
ejpam-5493	105	29	)	)	PUNCT
ejpam-5493	105	30	(	(	PUNCT
ejpam-5493	105	31	r2p−1)kt+	r2p−1)kt+	NOUN
ejpam-5493	105	32	(	(	PUNCT
ejpam-5493	105	33	2p	2p	NUM
ejpam-5493	105	34	2	2	NUM
ejpam-5493	105	35	)	)	PUNCT
ejpam-5493	105	36	r2p−2k2t2	r2p−2k2t2	NOUN
ejpam-5493	105	37	+	+	CCONJ
ejpam-5493	105	38	...	...	PUNCT
ejpam-5493	106	1	+	+	NOUN
ejpam-5493	106	2	k2pt2p	k2pt2p	NOUN
ejpam-5493	106	3	)	)	PUNCT
ejpam-5493	106	4	=	=	VERB
ejpam-5493	107	1	h(rp+	h(rp+	X
ejpam-5493	107	2	(	(	PUNCT
ejpam-5493	107	3	p	p	NOUN
ejpam-5493	107	4	1	1	X
ejpam-5493	107	5	)	)	PUNCT
ejpam-5493	107	6	rp−1kt+	rp−1kt+	NOUN
ejpam-5493	107	7	(	(	PUNCT
ejpam-5493	107	8	p	p	NOUN
ejpam-5493	107	9	2	2	X
ejpam-5493	107	10	)	)	PUNCT
ejpam-5493	107	11	rp−2k2t2	rp−2k2t2	PROPN
ejpam-5493	107	12	+	+	CCONJ
ejpam-5493	107	13	...	...	PUNCT
ejpam-5493	108	1	+	+	ADJ
ejpam-5493	108	2	kptp	kptp	NOUN
ejpam-5493	108	3	)	)	PUNCT
ejpam-5493	108	4	·	·	PUNCT
ejpam-5493	108	5	φ(rp	φ(rp	PROPN
ejpam-5493	108	6	+	+	X
ejpam-5493	108	7	(	(	PUNCT
ejpam-5493	108	8	p	p	NOUN
ejpam-5493	108	9	1	1	X
ejpam-5493	108	10	)	)	PUNCT
ejpam-5493	108	11	rp−1kt+	rp−1kt+	NOUN
ejpam-5493	108	12	(	(	PUNCT
ejpam-5493	108	13	p	p	NOUN
ejpam-5493	108	14	2	2	X
ejpam-5493	108	15	)	)	PUNCT
ejpam-5493	108	16	rp−2k2t2	rp−2k2t2	PROPN
ejpam-5493	109	1	+	+	CCONJ
ejpam-5493	110	1	...	...	PUNCT
ejpam-5493	110	2	+	+	ADJ
ejpam-5493	110	3	kptp	kptp	NOUN
ejpam-5493	110	4	)	)	PUNCT
ejpam-5493	111	1	+	+	ADP
ejpam-5493	111	2	φ(rp	φ(rp	ADJ
ejpam-5493	111	3	+	+	PUNCT
ejpam-5493	111	4	(	(	PUNCT
ejpam-5493	111	5	p	p	NOUN
ejpam-5493	111	6	1	1	X
ejpam-5493	111	7	)	)	PUNCT
ejpam-5493	111	8	rp−1kt+	rp−1kt+	NOUN
ejpam-5493	111	9	(	(	PUNCT
ejpam-5493	111	10	p	p	NOUN
ejpam-5493	111	11	2	2	X
ejpam-5493	111	12	)	)	PUNCT
ejpam-5493	111	13	rp−2k2t2	rp−2k2t2	PROPN
ejpam-5493	112	1	+	+	CCONJ
ejpam-5493	112	2	...	...	PUNCT
ejpam-5493	112	3	+	+	NUM
ejpam-5493	112	4	kptp	kptp	NOUN
ejpam-5493	112	5	)	)	PUNCT
ejpam-5493	112	6	·	·	PUNCT
ejpam-5493	113	1	h(rp	h(rp	PROPN
ejpam-5493	113	2	+	+	CCONJ
ejpam-5493	113	3	(	(	PUNCT
ejpam-5493	113	4	p	p	NOUN
ejpam-5493	113	5	1	1	NUM
ejpam-5493	113	6	)	)	PUNCT
ejpam-5493	113	7	rp−1kt+	rp−1kt+	NOUN
ejpam-5493	113	8	(	(	PUNCT
ejpam-5493	113	9	p	p	NOUN
ejpam-5493	113	10	2	2	X
ejpam-5493	113	11	)	)	PUNCT
ejpam-5493	113	12	rp−2k2t2	rp−2k2t2	PROPN
ejpam-5493	113	13	+	+	CCONJ
ejpam-5493	113	14	...	...	PUNCT
ejpam-5493	113	15	+	+	NUM
ejpam-5493	113	16	kptp	kptp	NOUN
ejpam-5493	113	17	)	)	PUNCT
ejpam-5493	113	18	for	for	ADP
ejpam-5493	113	19	all	all	DET
ejpam-5493	113	20	r	r	NOUN
ejpam-5493	113	21	,	,	PUNCT
ejpam-5493	113	22	t	t	PROPN
ejpam-5493	113	23	∈	∈	PROPN
ejpam-5493	113	24	r	r	NOUN
ejpam-5493	113	25	and	and	CCONJ
ejpam-5493	113	26	k	k	PROPN
ejpam-5493	113	27	≥	≥	PROPN
ejpam-5493	113	28	1	1	NUM
ejpam-5493	113	29	.	.	PUNCT
ejpam-5493	113	30	rewrite	rewrite	VERB
ejpam-5493	113	31	the	the	DET
ejpam-5493	113	32	above	above	ADJ
ejpam-5493	113	33	expression	expression	NOUN
ejpam-5493	113	34	by	by	ADP
ejpam-5493	113	35	using	use	VERB
ejpam-5493	113	36	(	(	PUNCT
ejpam-5493	113	37	4	4	NUM
ejpam-5493	113	38	)	)	PUNCT
ejpam-5493	113	39	as	as	ADP
ejpam-5493	113	40	kq1(r	kq1(r	PROPN
ejpam-5493	113	41	,	,	PUNCT
ejpam-5493	113	42	t	t	PROPN
ejpam-5493	113	43	)	)	PUNCT
ejpam-5493	114	1	+	+	CCONJ
ejpam-5493	114	2	k2q2(r	k2q2(r	PROPN
ejpam-5493	114	3	,	,	PUNCT
ejpam-5493	114	4	t	t	PROPN
ejpam-5493	114	5	)	)	PUNCT
ejpam-5493	114	6	+	+	CCONJ
ejpam-5493	114	7	...	...	PUNCT
ejpam-5493	115	1	+	+	CCONJ
ejpam-5493	115	2	k2p−1q2p−1(r	k2p−1q2p−1(r	ADJ
ejpam-5493	115	3	,	,	PUNCT
ejpam-5493	115	4	t	t	PROPN
ejpam-5493	115	5	)	)	PUNCT
ejpam-5493	115	6	=	=	NOUN
ejpam-5493	116	1	0	0	X
ejpam-5493	116	2	.	.	PUNCT
ejpam-5493	117	1	a	a	DET
ejpam-5493	117	2	system	system	NOUN
ejpam-5493	117	3	of	of	ADP
ejpam-5493	117	4	(	(	PUNCT
ejpam-5493	117	5	2p	2p	NUM
ejpam-5493	117	6	−	−	NOUN
ejpam-5493	117	7	1	1	NUM
ejpam-5493	117	8	)	)	PUNCT
ejpam-5493	117	9	homogeneous	homogeneous	ADJ
ejpam-5493	117	10	equations	equation	NOUN
ejpam-5493	117	11	can	can	AUX
ejpam-5493	117	12	be	be	AUX
ejpam-5493	117	13	identified	identify	VERB
ejpam-5493	117	14	if	if	SCONJ
ejpam-5493	117	15	k	k	PROPN
ejpam-5493	117	16	is	be	AUX
ejpam-5493	117	17	substituted	substitute	VERB
ejpam-5493	117	18	by	by	ADP
ejpam-5493	117	19	1	1	NUM
ejpam-5493	117	20	,	,	PUNCT
ejpam-5493	117	21	2	2	NUM
ejpam-5493	117	22	,	,	PUNCT
ejpam-5493	117	23	...	...	PUNCT
ejpam-5493	117	24	,	,	PUNCT
ejpam-5493	117	25	(	(	PUNCT
ejpam-5493	117	26	2p	2p	NUM
ejpam-5493	117	27	−	−	NOUN
ejpam-5493	117	28	1	1	NUM
ejpam-5493	117	29	)	)	PUNCT
ejpam-5493	117	30	in	in	ADP
ejpam-5493	117	31	turn	turn	NOUN
ejpam-5493	117	32	.	.	PUNCT
ejpam-5493	118	1	it	it	PRON
ejpam-5493	118	2	provides	provide	VERB
ejpam-5493	118	3	a	a	DET
ejpam-5493	118	4	vandermonde	vandermonde	ADJ
ejpam-5493	118	5	matrix	matrix	NOUN
ejpam-5493	118	6	of	of	ADP
ejpam-5493	118	7	type	type	NOUN
ejpam-5493	118	8	(	(	PUNCT
ejpam-5493	118	9	2p	2p	NUM
ejpam-5493	118	10	−	−	NOUN
ejpam-5493	118	11	1	1	NUM
ejpam-5493	118	12	)	)	PUNCT
ejpam-5493	118	13	×	×	NOUN
ejpam-5493	118	14	(	(	PUNCT
ejpam-5493	118	15	2p	2p	NUM
ejpam-5493	118	16	−	−	NOUN
ejpam-5493	118	17	1	1	NUM
ejpam-5493	118	18	)	)	PUNCT
ejpam-5493	118	19	,	,	PUNCT
ejpam-5493	118	20	then	then	ADV
ejpam-5493	118	21	for	for	ADP
ejpam-5493	118	22	i	i	PROPN
ejpam-5493	118	23	=	=	SYM
ejpam-5493	118	24	1	1	NUM
ejpam-5493	118	25	,	,	PUNCT
ejpam-5493	118	26	2	2	NUM
ejpam-5493	118	27	,	,	PUNCT
ejpam-5493	118	28	..	..	PUNCT
ejpam-5493	118	29	,	,	PUNCT
ejpam-5493	118	30	(	(	PUNCT
ejpam-5493	118	31	2p−	2p−	NOUN
ejpam-5493	118	32	1	1	NUM
ejpam-5493	118	33	)	)	PUNCT
ejpam-5493	118	34	,	,	PUNCT
ejpam-5493	118	35	qi(r	qi(r	NUM
ejpam-5493	118	36	,	,	PUNCT
ejpam-5493	118	37	t	t	PROPN
ejpam-5493	118	38	)	)	PUNCT
ejpam-5493	118	39	=	=	SYM
ejpam-5493	118	40	0	0	NUM
ejpam-5493	118	41	for	for	ADP
ejpam-5493	118	42	all	all	DET
ejpam-5493	118	43	r	r	NOUN
ejpam-5493	118	44	,	,	PUNCT
ejpam-5493	118	45	t	t	PROPN
ejpam-5493	118	46	∈	∈	PROPN
ejpam-5493	118	47	r.	r.	PROPN
ejpam-5493	118	48	particularly	particularly	ADV
ejpam-5493	118	49	,	,	PUNCT
ejpam-5493	118	50	q1(r	q1(r	PROPN
ejpam-5493	118	51	,	,	PUNCT
ejpam-5493	118	52	t	t	PROPN
ejpam-5493	118	53	)	)	PUNCT
ejpam-5493	118	54	=	=	SYM
ejpam-5493	118	55	0	0	NUM
ejpam-5493	118	56	suggests	suggest	VERB
ejpam-5493	118	57	2	2	NUM
ejpam-5493	118	58	(	(	PUNCT
ejpam-5493	118	59	2p	2p	NUM
ejpam-5493	118	60	1	1	NUM
ejpam-5493	118	61	)	)	PUNCT
ejpam-5493	118	62	h(r2p−1kt	h(r2p−1kt	NOUN
ejpam-5493	118	63	)	)	PUNCT
ejpam-5493	119	1	=	=	PRON
ejpam-5493	120	1	(	(	PUNCT
ejpam-5493	120	2	p	p	NOUN
ejpam-5493	120	3	1	1	X
ejpam-5493	120	4	)	)	PUNCT
ejpam-5493	120	5	h(rp)φ(rp−1	h(rp)φ(rp−1	NOUN
ejpam-5493	120	6	t	t	PROPN
ejpam-5493	120	7	)	)	PUNCT
ejpam-5493	120	8	+	+	CCONJ
ejpam-5493	120	9	(	(	PUNCT
ejpam-5493	120	10	p	p	NOUN
ejpam-5493	120	11	1	1	NUM
ejpam-5493	120	12	)	)	PUNCT
ejpam-5493	120	13	h(rp−1)φ(trp	h(rp−1)φ(trp	NUM
ejpam-5493	120	14	)	)	PUNCT
ejpam-5493	121	1	+	+	CCONJ
ejpam-5493	121	2	(	(	PUNCT
ejpam-5493	121	3	p	p	NOUN
ejpam-5493	121	4	1	1	NUM
ejpam-5493	121	5	)	)	PUNCT
ejpam-5493	121	6	φ(rp)h(rp−1	φ(rp)h(rp−1	PROPN
ejpam-5493	121	7	t	t	PROPN
ejpam-5493	121	8	)	)	PUNCT
ejpam-5493	121	9	+	+	CCONJ
ejpam-5493	121	10	(	(	PUNCT
ejpam-5493	121	11	p	p	NOUN
ejpam-5493	121	12	1	1	NUM
ejpam-5493	121	13	)	)	PUNCT
ejpam-5493	121	14	φ(rp−1t)h(rp	φ(rp−1t)h(rp	NOUN
ejpam-5493	121	15	)	)	PUNCT
ejpam-5493	121	16	(	(	PUNCT
ejpam-5493	121	17	5	5	X
ejpam-5493	121	18	)	)	PUNCT
ejpam-5493	121	19	reinstate	reinstate	VERB
ejpam-5493	121	20	the	the	DET
ejpam-5493	121	21	above	above	ADJ
ejpam-5493	121	22	equation	equation	NOUN
ejpam-5493	121	23	by	by	ADP
ejpam-5493	121	24	putting	put	VERB
ejpam-5493	121	25	e	e	NOUN
ejpam-5493	121	26	in	in	ADP
ejpam-5493	121	27	place	place	NOUN
ejpam-5493	121	28	of	of	ADP
ejpam-5493	121	29	r	r	NOUN
ejpam-5493	121	30	to	to	PART
ejpam-5493	121	31	have	have	VERB
ejpam-5493	121	32	4ph(t	4ph(t	NUM
ejpam-5493	121	33	)	)	PUNCT
ejpam-5493	121	34	=	=	SYM
ejpam-5493	121	35	ph(e)φ(t	ph(e)φ(t	PROPN
ejpam-5493	121	36	)	)	PUNCT
ejpam-5493	121	37	+	+	NUM
ejpam-5493	121	38	ph(t	ph(t	X
ejpam-5493	121	39	)	)	PUNCT
ejpam-5493	121	40	+	+	CCONJ
ejpam-5493	121	41	ph(t	ph(t	X
ejpam-5493	121	42	)	)	PUNCT
ejpam-5493	122	1	+	+	CCONJ
ejpam-5493	122	2	pφ(t)h(e	pφ(t)h(e	ADJ
ejpam-5493	122	3	)	)	PUNCT
ejpam-5493	122	4	.	.	PUNCT
ejpam-5493	123	1	on	on	ADP
ejpam-5493	123	2	simplifying	simplify	VERB
ejpam-5493	123	3	the	the	DET
ejpam-5493	123	4	last	last	ADJ
ejpam-5493	123	5	relation	relation	NOUN
ejpam-5493	123	6	we	we	PRON
ejpam-5493	123	7	can	can	AUX
ejpam-5493	123	8	obtain	obtain	VERB
ejpam-5493	123	9	2ph(t	2ph(t	NUM
ejpam-5493	123	10	)	)	PUNCT
ejpam-5493	123	11	=	=	SYM
ejpam-5493	123	12	ph(e)φ(t	ph(e)φ(t	PROPN
ejpam-5493	123	13	)	)	PUNCT
ejpam-5493	123	14	+	+	CCONJ
ejpam-5493	123	15	pφ(t)h(e	pφ(t)h(e	ADJ
ejpam-5493	123	16	)	)	PUNCT
ejpam-5493	123	17	for	for	ADP
ejpam-5493	123	18	all	all	DET
ejpam-5493	123	19	t	t	PROPN
ejpam-5493	123	20	∈	∈	PROPN
ejpam-5493	123	21	r.	r.	PROPN
ejpam-5493	123	22	a	a	DET
ejpam-5493	123	23	torsion	torsion	NOUN
ejpam-5493	123	24	restriction	restriction	NOUN
ejpam-5493	123	25	given	give	VERB
ejpam-5493	123	26	in	in	ADP
ejpam-5493	123	27	the	the	DET
ejpam-5493	123	28	hypothesis	hypothesis	NOUN
ejpam-5493	123	29	enable	enable	VERB
ejpam-5493	123	30	us	we	PRON
ejpam-5493	123	31	to	to	PART
ejpam-5493	123	32	write	write	VERB
ejpam-5493	123	33	2h(t	2h(t	NUM
ejpam-5493	123	34	)	)	PUNCT
ejpam-5493	124	1	=	=	SYM
ejpam-5493	124	2	h(e)φ(t	h(e)φ(t	NUM
ejpam-5493	124	3	)	)	PUNCT
ejpam-5493	125	1	+	+	CCONJ
ejpam-5493	125	2	φ(t)h(e	φ(t)h(e	NOUN
ejpam-5493	125	3	)	)	PUNCT
ejpam-5493	125	4	,	,	PUNCT
ejpam-5493	125	5	for	for	ADP
ejpam-5493	125	6	all	all	DET
ejpam-5493	125	7	t	t	PROPN
ejpam-5493	125	8	∈	∈	PROPN
ejpam-5493	125	9	r.	r.	PROPN
ejpam-5493	125	10	(	(	PUNCT
ejpam-5493	125	11	6	6	NUM
ejpam-5493	125	12	)	)	PUNCT
ejpam-5493	125	13	now	now	ADV
ejpam-5493	125	14	consider	consider	VERB
ejpam-5493	125	15	the	the	DET
ejpam-5493	125	16	following	follow	VERB
ejpam-5493	125	17	q2(r	q2(r	PROPN
ejpam-5493	125	18	,	,	PUNCT
ejpam-5493	125	19	t	t	PROPN
ejpam-5493	125	20	)	)	PUNCT
ejpam-5493	125	21	=	=	SYM
ejpam-5493	126	1	0	0	NUM
ejpam-5493	126	2	,	,	PUNCT
ejpam-5493	126	3	we	we	PRON
ejpam-5493	126	4	have	have	VERB
ejpam-5493	126	5	2	2	NUM
ejpam-5493	126	6	(	(	PUNCT
ejpam-5493	126	7	2p	2p	NUM
ejpam-5493	126	8	2	2	NUM
ejpam-5493	126	9	)	)	PUNCT
ejpam-5493	126	10	h(r2p−2t2	h(r2p−2t2	PROPN
ejpam-5493	126	11	)	)	PUNCT
ejpam-5493	126	12	=	=	SYM
ejpam-5493	127	1	(	(	PUNCT
ejpam-5493	127	2	p	p	NOUN
ejpam-5493	127	3	2	2	X
ejpam-5493	127	4	)	)	PUNCT
ejpam-5493	127	5	h(rp)φ(rp−2t2	h(rp)φ(rp−2t2	NOUN
ejpam-5493	127	6	)	)	PUNCT
ejpam-5493	128	1	+	+	CCONJ
ejpam-5493	128	2	(	(	PUNCT
ejpam-5493	128	3	p	p	NOUN
ejpam-5493	128	4	1	1	NUM
ejpam-5493	128	5	)	)	PUNCT
ejpam-5493	128	6	(	(	PUNCT
ejpam-5493	128	7	p	p	NOUN
ejpam-5493	128	8	1	1	NUM
ejpam-5493	128	9	)	)	PUNCT
ejpam-5493	128	10	h(rp−1t)φ(rp−1	h(rp−1t)φ(rp−1	NOUN
ejpam-5493	128	11	t	t	NOUN
ejpam-5493	128	12	)	)	PUNCT
ejpam-5493	128	13	+	+	CCONJ
ejpam-5493	128	14	(	(	PUNCT
ejpam-5493	128	15	p	p	NOUN
ejpam-5493	128	16	2	2	NUM
ejpam-5493	128	17	)	)	PUNCT
ejpam-5493	128	18	h(rp−2t2)φ(rp	h(rp−2t2)φ(rp	NOUN
ejpam-5493	128	19	)	)	PUNCT
ejpam-5493	129	1	+	+	CCONJ
ejpam-5493	129	2	(	(	PUNCT
ejpam-5493	129	3	p	p	NOUN
ejpam-5493	129	4	2	2	NUM
ejpam-5493	129	5	)	)	PUNCT
ejpam-5493	129	6	φ(rp)h(rp−2t2	φ(rp)h(rp−2t2	PROPN
ejpam-5493	129	7	)	)	PUNCT
ejpam-5493	130	1	+	+	CCONJ
ejpam-5493	130	2	(	(	PUNCT
ejpam-5493	130	3	p	p	NOUN
ejpam-5493	130	4	1	1	NUM
ejpam-5493	130	5	)	)	PUNCT
ejpam-5493	130	6	(	(	PUNCT
ejpam-5493	130	7	p	p	NOUN
ejpam-5493	130	8	1	1	NUM
ejpam-5493	130	9	)	)	PUNCT
ejpam-5493	130	10	φ(rp−1t)h(rp−1	φ(rp−1t)h(rp−1	NOUN
ejpam-5493	130	11	t	t	PROPN
ejpam-5493	130	12	)	)	PUNCT
ejpam-5493	130	13	+	+	CCONJ
ejpam-5493	130	14	(	(	PUNCT
ejpam-5493	130	15	p	p	NOUN
ejpam-5493	130	16	2	2	NUM
ejpam-5493	130	17	)	)	PUNCT
ejpam-5493	130	18	φ(rp−2t2)h(rp	φ(rp−2t2)h(rp	NOUN
ejpam-5493	130	19	)	)	PUNCT
ejpam-5493	130	20	substitute	substitute	NOUN
ejpam-5493	130	21	e	e	NOUN
ejpam-5493	130	22	for	for	ADP
ejpam-5493	130	23	r	r	NOUN
ejpam-5493	130	24	in	in	ADP
ejpam-5493	130	25	above	above	ADP
ejpam-5493	130	26	expression	expression	NOUN
ejpam-5493	130	27	to	to	PART
ejpam-5493	130	28	obtain	obtain	VERB
ejpam-5493	130	29	22p(2p−1	22p(2p−1	NUM
ejpam-5493	130	30	)	)	PUNCT
ejpam-5493	130	31	2	2	NUM
ejpam-5493	130	32	h(t2	h(t2	NOUN
ejpam-5493	130	33	)	)	PUNCT
ejpam-5493	130	34	=	=	SYM
ejpam-5493	130	35	p(p−1	p(p−1	NOUN
ejpam-5493	130	36	)	)	PUNCT
ejpam-5493	130	37	2	2	NUM
ejpam-5493	130	38	h(e)φ(t2	h(e)φ(t2	NOUN
ejpam-5493	130	39	)	)	PUNCT
ejpam-5493	130	40	+	+	SYM
ejpam-5493	130	41	p2h(t)φ(t	p2h(t)φ(t	NOUN
ejpam-5493	130	42	)	)	PUNCT
ejpam-5493	130	43	+	+	CCONJ
ejpam-5493	130	44	p(p−1	p(p−1	NOUN
ejpam-5493	130	45	)	)	PUNCT
ejpam-5493	130	46	2	2	NUM
ejpam-5493	130	47	h(t2	h(t2	NOUN
ejpam-5493	130	48	)	)	PUNCT
ejpam-5493	130	49	+	+	NOUN
ejpam-5493	130	50	p(p−1	p(p−1	NOUN
ejpam-5493	130	51	)	)	PUNCT
ejpam-5493	130	52	2	2	NUM
ejpam-5493	130	53	h(t2	h(t2	NOUN
ejpam-5493	130	54	)	)	PUNCT
ejpam-5493	130	55	+	+	SYM
ejpam-5493	130	56	p2φ(t)h(t	p2φ(t)h(t	NOUN
ejpam-5493	130	57	)	)	PUNCT
ejpam-5493	130	58	+	+	CCONJ
ejpam-5493	130	59	p(p−1	p(p−1	NOUN
ejpam-5493	130	60	)	)	PUNCT
ejpam-5493	130	61	2	2	NUM
ejpam-5493	130	62	φ(t2)h(e	φ(t2)h(e	NOUN
ejpam-5493	130	63	)	)	PUNCT
ejpam-5493	130	64	a.	a.	NOUN
ejpam-5493	130	65	z.	z.	PROPN
ejpam-5493	130	66	ansari	ansari	PROPN
ejpam-5493	130	67	et	et	PROPN
ejpam-5493	130	68	al	al	PROPN
ejpam-5493	130	69	.	.	PUNCT
ejpam-5493	130	70	/	/	SYM
ejpam-5493	130	71	eur	eur	PROPN
ejpam-5493	130	72	.	.	PUNCT
ejpam-5493	131	1	j.	j.	PROPN
ejpam-5493	131	2	pure	pure	PROPN
ejpam-5493	131	3	appl	appl	PROPN
ejpam-5493	131	4	.	.	PROPN
ejpam-5493	131	5	math	math	PROPN
ejpam-5493	131	6	,	,	PUNCT
ejpam-5493	131	7	18	18	NUM
ejpam-5493	131	8	(	(	PUNCT
ejpam-5493	131	9	1	1	NUM
ejpam-5493	131	10	)	)	PUNCT
ejpam-5493	131	11	(	(	PUNCT
ejpam-5493	131	12	2025	2025	NUM
ejpam-5493	131	13	)	)	PUNCT
ejpam-5493	131	14	,	,	PUNCT
ejpam-5493	131	15	5493	5493	NUM
ejpam-5493	131	16	6	6	NUM
ejpam-5493	131	17	of	of	ADP
ejpam-5493	131	18	10	10	NUM
ejpam-5493	131	19	a	a	DET
ejpam-5493	131	20	simple	simple	ADJ
ejpam-5493	131	21	manipulation	manipulation	NOUN
ejpam-5493	131	22	yields	yield	VERB
ejpam-5493	131	23	that	that	SCONJ
ejpam-5493	131	24	2p2h(t2	2p2h(t2	NUM
ejpam-5493	131	25	)	)	PUNCT
ejpam-5493	131	26	=	=	SYM
ejpam-5493	131	27	p2(h(t)φ(t	p2(h(t)φ(t	NOUN
ejpam-5493	131	28	)	)	PUNCT
ejpam-5493	131	29	+	+	CCONJ
ejpam-5493	131	30	φ(t)h(t	φ(t)h(t	NUM
ejpam-5493	131	31	)	)	PUNCT
ejpam-5493	131	32	)	)	PUNCT
ejpam-5493	131	33	.	.	PUNCT
ejpam-5493	132	1	by	by	ADP
ejpam-5493	132	2	utilizing	utilize	VERB
ejpam-5493	132	3	the	the	DET
ejpam-5493	132	4	torsion	torsion	NOUN
ejpam-5493	132	5	-	-	PUNCT
ejpam-5493	132	6	freeness	freeness	NOUN
ejpam-5493	132	7	of	of	ADP
ejpam-5493	132	8	r	r	PROPN
ejpam-5493	132	9	,	,	PUNCT
ejpam-5493	132	10	we	we	PRON
ejpam-5493	132	11	achieved	achieve	VERB
ejpam-5493	132	12	2h(t2	2h(t2	NUM
ejpam-5493	132	13	)	)	PUNCT
ejpam-5493	132	14	=	=	SYM
ejpam-5493	132	15	h(t)φ(t	h(t)φ(t	X
ejpam-5493	132	16	)	)	PUNCT
ejpam-5493	132	17	+	+	NOUN
ejpam-5493	132	18	φ(t)h(t	φ(t)h(t	NUM
ejpam-5493	132	19	)	)	PUNCT
ejpam-5493	132	20	for	for	ADP
ejpam-5493	132	21	all	all	DET
ejpam-5493	132	22	t	t	PROPN
ejpam-5493	132	23	∈	∈	PROPN
ejpam-5493	132	24	r.	r.	PROPN
ejpam-5493	132	25	hence	hence	ADV
ejpam-5493	132	26	h	h	PROPN
ejpam-5493	132	27	is	be	AUX
ejpam-5493	132	28	carry	carry	VERB
ejpam-5493	132	29	oneself	oneself	PRON
ejpam-5493	132	30	like	like	ADP
ejpam-5493	132	31	φ	φ	NOUN
ejpam-5493	132	32	-	-	PUNCT
ejpam-5493	132	33	centralizer	centralizer	NOUN
ejpam-5493	132	34	,	,	PUNCT
ejpam-5493	132	35	as	as	SCONJ
ejpam-5493	132	36	desired	desire	VERB
ejpam-5493	132	37	.	.	PUNCT
ejpam-5493	133	1	theorem	theorem	NOUN
ejpam-5493	133	2	3	3	NUM
ejpam-5493	133	3	.	.	PUNCT
ejpam-5493	134	1	if	if	SCONJ
ejpam-5493	134	2	φ	φ	PROPN
ejpam-5493	134	3	is	be	AUX
ejpam-5493	134	4	a	a	DET
ejpam-5493	134	5	surjective	surjective	ADJ
ejpam-5493	134	6	endomorphism	endomorphism	NOUN
ejpam-5493	134	7	on	on	ADP
ejpam-5493	134	8	a	a	DET
ejpam-5493	134	9	semiprime	semiprime	NOUN
ejpam-5493	134	10	ring	ring	NOUN
ejpam-5493	134	11	r	r	NOUN
ejpam-5493	134	12	with	with	ADP
ejpam-5493	134	13	(	(	PUNCT
ejpam-5493	134	14	3p	3p	NUM
ejpam-5493	134	15	−	−	NOUN
ejpam-5493	134	16	1	1	NUM
ejpam-5493	134	17	)	)	PUNCT
ejpam-5493	134	18	!	!	PUNCT
ejpam-5493	135	1	torsion	torsion	NOUN
ejpam-5493	135	2	free	free	ADJ
ejpam-5493	135	3	condition	condition	NOUN
ejpam-5493	135	4	and	and	CCONJ
ejpam-5493	135	5	h	h	NOUN
ejpam-5493	135	6	:	:	PUNCT
ejpam-5493	135	7	r	r	NOUN
ejpam-5493	135	8	→	→	SYM
ejpam-5493	135	9	r	r	NOUN
ejpam-5493	135	10	is	be	AUX
ejpam-5493	135	11	an	an	DET
ejpam-5493	135	12	additive	additive	ADJ
ejpam-5493	135	13	mapping	mapping	NOUN
ejpam-5493	135	14	that	that	PRON
ejpam-5493	135	15	satisfies	satisfy	VERB
ejpam-5493	135	16	h(r3p	h(r3p	X
ejpam-5493	135	17	)	)	PUNCT
ejpam-5493	135	18	=	=	SYM
ejpam-5493	135	19	φ(rp)hφ((rp))rp	φ(rp)hφ((rp))rp	NOUN
ejpam-5493	135	20	for	for	ADP
ejpam-5493	135	21	all	all	DET
ejpam-5493	135	22	r	r	PROPN
ejpam-5493	135	23	∈	∈	PROPN
ejpam-5493	135	24	r.	r.	NOUN
ejpam-5493	135	25	(	(	PUNCT
ejpam-5493	135	26	7	7	NUM
ejpam-5493	135	27	)	)	PUNCT
ejpam-5493	135	28	then	then	ADV
ejpam-5493	135	29	h	h	PROPN
ejpam-5493	135	30	is	be	AUX
ejpam-5493	135	31	a	a	DET
ejpam-5493	135	32	φ	φ	NOUN
ejpam-5493	135	33	-	-	PUNCT
ejpam-5493	135	34	centralizer	centralizer	NOUN
ejpam-5493	135	35	on	on	ADP
ejpam-5493	135	36	r	r	NOUN
ejpam-5493	135	37	,	,	PUNCT
ejpam-5493	135	38	where	where	SCONJ
ejpam-5493	135	39	p	p	NOUN
ejpam-5493	135	40	is	be	AUX
ejpam-5493	135	41	a	a	DET
ejpam-5493	135	42	fixed	fix	VERB
ejpam-5493	135	43	integer	integer	NOUN
ejpam-5493	135	44	greater	great	ADJ
ejpam-5493	135	45	than	than	ADP
ejpam-5493	135	46	or	or	CCONJ
ejpam-5493	135	47	equal	equal	ADJ
ejpam-5493	135	48	to	to	ADP
ejpam-5493	135	49	1	1	NUM
ejpam-5493	135	50	.	.	PUNCT
ejpam-5493	136	1	proof	proof	NOUN
ejpam-5493	136	2	.	.	PUNCT
ejpam-5493	137	1	replacing	replace	VERB
ejpam-5493	137	2	r	r	NOUN
ejpam-5493	137	3	by	by	ADP
ejpam-5493	137	4	r	r	NOUN
ejpam-5493	137	5	+	+	CCONJ
ejpam-5493	137	6	kt	kt	X
ejpam-5493	137	7	in	in	ADP
ejpam-5493	137	8	(	(	PUNCT
ejpam-5493	137	9	7	7	NUM
ejpam-5493	137	10	)	)	PUNCT
ejpam-5493	137	11	,	,	PUNCT
ejpam-5493	137	12	we	we	PRON
ejpam-5493	137	13	obtain	obtain	VERB
ejpam-5493	137	14	h(r3p+	h(r3p+	NOUN
ejpam-5493	137	15	(	(	PUNCT
ejpam-5493	137	16	3p	3p	NUM
ejpam-5493	137	17	1	1	NUM
ejpam-5493	137	18	)	)	PUNCT
ejpam-5493	137	19	(	(	PUNCT
ejpam-5493	137	20	r3p−1)kt+	r3p−1)kt+	NOUN
ejpam-5493	137	21	(	(	PUNCT
ejpam-5493	137	22	3p	3p	NUM
ejpam-5493	137	23	2	2	NUM
ejpam-5493	137	24	)	)	PUNCT
ejpam-5493	137	25	r3p−2k2t2+	r3p−2k2t2+	ADJ
ejpam-5493	137	26	...	...	PUNCT
ejpam-5493	137	27	+k3pt3p	+k3pt3p	NUM
ejpam-5493	137	28	)	)	PUNCT
ejpam-5493	137	29	=	=	PUNCT
ejpam-5493	137	30	φ(rp+	φ(rp+	NOUN
ejpam-5493	137	31	(	(	PUNCT
ejpam-5493	137	32	p	p	NOUN
ejpam-5493	137	33	1	1	X
ejpam-5493	137	34	)	)	PUNCT
ejpam-5493	137	35	rp−1kt+	rp−1kt+	NOUN
ejpam-5493	137	36	(	(	PUNCT
ejpam-5493	137	37	p	p	NOUN
ejpam-5493	137	38	2	2	X
ejpam-5493	137	39	)	)	PUNCT
ejpam-5493	137	40	rp−2k2t2+	rp−2k2t2+	NOUN
ejpam-5493	137	41	...	...	PUNCT
ejpam-5493	138	1	+	+	NUM
ejpam-5493	138	2	kptp	kptp	NOUN
ejpam-5493	138	3	)	)	PUNCT
ejpam-5493	138	4	·	·	PUNCT
ejpam-5493	138	5	h(rp+	h(rp+	X
ejpam-5493	138	6	(	(	PUNCT
ejpam-5493	138	7	p	p	NOUN
ejpam-5493	138	8	1	1	X
ejpam-5493	138	9	)	)	PUNCT
ejpam-5493	138	10	rp−1kt+	rp−1kt+	NOUN
ejpam-5493	138	11	(	(	PUNCT
ejpam-5493	138	12	p	p	NOUN
ejpam-5493	138	13	2	2	X
ejpam-5493	138	14	)	)	PUNCT
ejpam-5493	138	15	rp−2k2t2	rp−2k2t2	PROPN
ejpam-5493	138	16	+	+	NOUN
ejpam-5493	138	17	...	...	PUNCT
ejpam-5493	139	1	+	+	ADJ
ejpam-5493	139	2	kptp)φ(rp+	kptp)φ(rp+	ADJ
ejpam-5493	139	3	(	(	PUNCT
ejpam-5493	139	4	p	p	NOUN
ejpam-5493	139	5	1	1	X
ejpam-5493	139	6	)	)	PUNCT
ejpam-5493	139	7	rp−1kt+	rp−1kt+	NOUN
ejpam-5493	139	8	(	(	PUNCT
ejpam-5493	139	9	p	p	NOUN
ejpam-5493	139	10	2	2	X
ejpam-5493	139	11	)	)	PUNCT
ejpam-5493	139	12	rp−2k2t2	rp−2k2t2	PROPN
ejpam-5493	139	13	+	+	CCONJ
ejpam-5493	139	14	...	...	PUNCT
ejpam-5493	140	1	+	+	ADJ
ejpam-5493	140	2	kptp	kptp	NOUN
ejpam-5493	140	3	)	)	PUNCT
ejpam-5493	140	4	,	,	PUNCT
ejpam-5493	140	5	where	where	SCONJ
ejpam-5493	140	6	k	k	PROPN
ejpam-5493	140	7	is	be	AUX
ejpam-5493	140	8	a	a	DET
ejpam-5493	140	9	positive	positive	ADJ
ejpam-5493	140	10	integer	integer	NOUN
ejpam-5493	140	11	.	.	PUNCT
ejpam-5493	141	1	rewrite	rewrite	VERB
ejpam-5493	141	2	the	the	DET
ejpam-5493	141	3	above	above	ADJ
ejpam-5493	141	4	expression	expression	NOUN
ejpam-5493	141	5	by	by	ADP
ejpam-5493	141	6	using	use	VERB
ejpam-5493	141	7	(	(	PUNCT
ejpam-5493	141	8	7	7	NUM
ejpam-5493	141	9	)	)	PUNCT
ejpam-5493	141	10	as	as	ADP
ejpam-5493	141	11	kr1(r	kr1(r	PROPN
ejpam-5493	141	12	,	,	PUNCT
ejpam-5493	141	13	t	t	PROPN
ejpam-5493	141	14	)	)	PUNCT
ejpam-5493	142	1	+	+	CCONJ
ejpam-5493	142	2	k2r2(r	k2r2(r	PROPN
ejpam-5493	142	3	,	,	PUNCT
ejpam-5493	142	4	t	t	PROPN
ejpam-5493	142	5	)	)	PUNCT
ejpam-5493	143	1	+	+	CCONJ
ejpam-5493	143	2	...	...	PUNCT
ejpam-5493	144	1	+	+	CCONJ
ejpam-5493	144	2	k3p−1r3p−1(r	k3p−1r3p−1(r	ADJ
ejpam-5493	144	3	,	,	PUNCT
ejpam-5493	144	4	t	t	PROPN
ejpam-5493	144	5	)	)	PUNCT
ejpam-5493	144	6	=	=	SYM
ejpam-5493	144	7	0	0	NUM
ejpam-5493	144	8	,	,	PUNCT
ejpam-5493	144	9	where	where	SCONJ
ejpam-5493	144	10	ri(r	ri(r	NOUN
ejpam-5493	144	11	,	,	PUNCT
ejpam-5493	144	12	t	t	PROPN
ejpam-5493	144	13	)	)	PUNCT
ejpam-5493	144	14	signifies	signifie	NOUN
ejpam-5493	144	15	for	for	ADP
ejpam-5493	144	16	the	the	DET
ejpam-5493	144	17	coefficients	coefficient	NOUN
ejpam-5493	144	18	of	of	ADP
ejpam-5493	144	19	power	power	NOUN
ejpam-5493	144	20	of	of	ADP
ejpam-5493	144	21	k	k	PROPN
ejpam-5493	144	22	up	up	ADP
ejpam-5493	144	23	to	to	ADP
ejpam-5493	144	24	(	(	PUNCT
ejpam-5493	144	25	3p	3p	NUM
ejpam-5493	144	26	−	−	NOUN
ejpam-5493	144	27	1	1	NUM
ejpam-5493	144	28	)	)	PUNCT
ejpam-5493	144	29	.	.	PUNCT
ejpam-5493	145	1	replacing	replace	VERB
ejpam-5493	145	2	k	k	PRON
ejpam-5493	145	3	by	by	ADP
ejpam-5493	145	4	1	1	NUM
ejpam-5493	145	5	,	,	PUNCT
ejpam-5493	145	6	2	2	NUM
ejpam-5493	145	7	,	,	PUNCT
ejpam-5493	145	8	...	...	PUNCT
ejpam-5493	145	9	,	,	PUNCT
ejpam-5493	145	10	(	(	PUNCT
ejpam-5493	145	11	3p	3p	NUM
ejpam-5493	145	12	−	−	NOUN
ejpam-5493	145	13	1	1	NUM
ejpam-5493	145	14	)	)	PUNCT
ejpam-5493	145	15	in	in	ADP
ejpam-5493	145	16	turn	turn	NOUN
ejpam-5493	145	17	,	,	PUNCT
ejpam-5493	145	18	we	we	PRON
ejpam-5493	145	19	obtain	obtain	VERB
ejpam-5493	145	20	a	a	DET
ejpam-5493	145	21	system	system	NOUN
ejpam-5493	145	22	of	of	ADP
ejpam-5493	145	23	(	(	PUNCT
ejpam-5493	145	24	3p	3p	NUM
ejpam-5493	145	25	−	−	NOUN
ejpam-5493	145	26	1	1	NUM
ejpam-5493	145	27	)	)	PUNCT
ejpam-5493	145	28	homogeneous	homogeneous	ADJ
ejpam-5493	145	29	equations	equation	NOUN
ejpam-5493	145	30	that	that	PRON
ejpam-5493	145	31	provides	provide	VERB
ejpam-5493	145	32	a	a	DET
ejpam-5493	145	33	vander	vander	NOUN
ejpam-5493	145	34	monde	monde	NOUN
ejpam-5493	145	35	matrix	matrix	NOUN
ejpam-5493	145	36	of	of	ADP
ejpam-5493	145	37	(	(	PUNCT
ejpam-5493	145	38	3p	3p	NUM
ejpam-5493	145	39	−	−	NOUN
ejpam-5493	145	40	1	1	NUM
ejpam-5493	145	41	)	)	PUNCT
ejpam-5493	145	42	by	by	ADP
ejpam-5493	145	43	(	(	PUNCT
ejpam-5493	145	44	3p	3p	NUM
ejpam-5493	145	45	−	−	NOUN
ejpam-5493	145	46	1	1	NUM
ejpam-5493	145	47	)	)	PUNCT
ejpam-5493	145	48	that	that	PRON
ejpam-5493	145	49	implies	imply	VERB
ejpam-5493	145	50	that	that	SCONJ
ejpam-5493	145	51	for	for	ADP
ejpam-5493	145	52	all	all	DET
ejpam-5493	145	53	r	r	NOUN
ejpam-5493	145	54	,	,	PUNCT
ejpam-5493	145	55	t	t	NOUN
ejpam-5493	145	56	∈	∈	PROPN
ejpam-5493	145	57	r	r	PROPN
ejpam-5493	145	58	,	,	PUNCT
ejpam-5493	145	59	ri(r	ri(r	NUM
ejpam-5493	145	60	,	,	PUNCT
ejpam-5493	145	61	t	t	PROPN
ejpam-5493	145	62	)	)	PUNCT
ejpam-5493	145	63	=	=	SYM
ejpam-5493	146	1	0	0	NUM
ejpam-5493	146	2	,	,	PUNCT
ejpam-5493	146	3	where	where	SCONJ
ejpam-5493	146	4	i	i	PRON
ejpam-5493	146	5	=	=	NOUN
ejpam-5493	146	6	1	1	NUM
ejpam-5493	146	7	,	,	PUNCT
ejpam-5493	146	8	2	2	NUM
ejpam-5493	146	9	,	,	PUNCT
ejpam-5493	146	10	..	..	PUNCT
ejpam-5493	146	11	,	,	PUNCT
ejpam-5493	146	12	(	(	PUNCT
ejpam-5493	146	13	3p	3p	NUM
ejpam-5493	146	14	−	−	NOUN
ejpam-5493	146	15	1	1	NUM
ejpam-5493	146	16	)	)	PUNCT
ejpam-5493	146	17	.	.	PUNCT
ejpam-5493	147	1	in	in	ADP
ejpam-5493	147	2	particular	particular	ADJ
ejpam-5493	147	3	,	,	PUNCT
ejpam-5493	147	4	we	we	PRON
ejpam-5493	147	5	have	have	VERB
ejpam-5493	147	6	(	(	PUNCT
ejpam-5493	147	7	3p	3p	NUM
ejpam-5493	147	8	1	1	NUM
ejpam-5493	147	9	)	)	PUNCT
ejpam-5493	147	10	h(r3p−1	h(r3p−1	PROPN
ejpam-5493	147	11	t	t	PROPN
ejpam-5493	147	12	)	)	PUNCT
ejpam-5493	147	13	=(	=(	NOUN
ejpam-5493	147	14	p	p	NOUN
ejpam-5493	147	15	1	1	X
ejpam-5493	147	16	)	)	PUNCT
ejpam-5493	147	17	φ(rp)h(rp−1t)φ(rp	φ(rp)h(rp−1t)φ(rp	PROPN
ejpam-5493	147	18	)	)	PUNCT
ejpam-5493	147	19	+	+	CCONJ
ejpam-5493	148	1	(	(	PUNCT
ejpam-5493	148	2	p	p	NOUN
ejpam-5493	148	3	1	1	NUM
ejpam-5493	148	4	)	)	PUNCT
ejpam-5493	148	5	φ(rp)h(rp)φ(rp−1t)−	φ(rp)h(rp)φ(rp−1t)−	PUNCT
ejpam-5493	148	6	(	(	PUNCT
ejpam-5493	148	7	p	p	NOUN
ejpam-5493	148	8	1	1	NUM
ejpam-5493	148	9	)	)	PUNCT
ejpam-5493	148	10	φ(rp−1t)h(rp)φ(rp	φ(rp−1t)h(rp)φ(rp	PROPN
ejpam-5493	148	11	)	)	PUNCT
ejpam-5493	148	12	for	for	ADP
ejpam-5493	148	13	all	all	DET
ejpam-5493	148	14	r	r	NOUN
ejpam-5493	148	15	,	,	PUNCT
ejpam-5493	148	16	t	t	PROPN
ejpam-5493	148	17	∈	∈	PROPN
ejpam-5493	148	18	r.	r.	NOUN
ejpam-5493	148	19	replacing	replace	VERB
ejpam-5493	148	20	r	r	NOUN
ejpam-5493	148	21	by	by	ADP
ejpam-5493	148	22	e	e	NOUN
ejpam-5493	148	23	and	and	CCONJ
ejpam-5493	148	24	making	make	VERB
ejpam-5493	148	25	use	use	NOUN
ejpam-5493	148	26	of	of	ADP
ejpam-5493	148	27	torsion	torsion	NOUN
ejpam-5493	148	28	restriction	restriction	NOUN
ejpam-5493	148	29	on	on	ADP
ejpam-5493	148	30	r	r	NOUN
ejpam-5493	148	31	to	to	PART
ejpam-5493	148	32	get	get	VERB
ejpam-5493	148	33	2h(t	2h(t	NUM
ejpam-5493	148	34	)	)	PUNCT
ejpam-5493	148	35	=	=	SYM
ejpam-5493	149	1	h(e)φ(t	h(e)φ(t	NUM
ejpam-5493	149	2	)	)	PUNCT
ejpam-5493	150	1	+	+	CCONJ
ejpam-5493	150	2	φ(t)h(e	φ(t)h(e	NOUN
ejpam-5493	150	3	)	)	PUNCT
ejpam-5493	150	4	,	,	PUNCT
ejpam-5493	150	5	for	for	ADP
ejpam-5493	150	6	all	all	DET
ejpam-5493	150	7	t	t	PROPN
ejpam-5493	150	8	∈	∈	PROPN
ejpam-5493	150	9	r.	r.	PROPN
ejpam-5493	150	10	(	(	PUNCT
ejpam-5493	150	11	8)	8)	NUM
ejpam-5493	150	12	further	far	ADV
ejpam-5493	150	13	,	,	PUNCT
ejpam-5493	150	14	r2(r	r2(r	PROPN
ejpam-5493	150	15	,	,	PUNCT
ejpam-5493	150	16	t	t	PROPN
ejpam-5493	150	17	)	)	PUNCT
ejpam-5493	150	18	=	=	SYM
ejpam-5493	150	19	0	0	NUM
ejpam-5493	150	20	implies	imply	VERB
ejpam-5493	150	21	that	that	SCONJ
ejpam-5493	150	22	(	(	PUNCT
ejpam-5493	150	23	3p	3p	NUM
ejpam-5493	150	24	2	2	NUM
ejpam-5493	150	25	)	)	PUNCT
ejpam-5493	150	26	h(r3p−2t2	h(r3p−2t2	PROPN
ejpam-5493	150	27	)	)	PUNCT
ejpam-5493	150	28	=	=	PUNCT
ejpam-5493	151	1	(	(	PUNCT
ejpam-5493	151	2	p	p	NOUN
ejpam-5493	151	3	2	2	NUM
ejpam-5493	151	4	)	)	PUNCT
ejpam-5493	151	5	φ(rp)h(rp)φ(rp−2t2	φ(rp)h(rp)φ(rp−2t2	NOUN
ejpam-5493	151	6	)	)	PUNCT
ejpam-5493	152	1	+	+	CCONJ
ejpam-5493	152	2	(	(	PUNCT
ejpam-5493	152	3	p	p	NOUN
ejpam-5493	152	4	1	1	NUM
ejpam-5493	152	5	)	)	PUNCT
ejpam-5493	152	6	(	(	PUNCT
ejpam-5493	152	7	p	p	NOUN
ejpam-5493	152	8	1	1	NUM
ejpam-5493	152	9	)	)	PUNCT
ejpam-5493	152	10	φ(rp−1t)h(rp)φ(rp−1	φ(rp−1t)h(rp)φ(rp−1	NUM
ejpam-5493	152	11	t	t	NOUN
ejpam-5493	152	12	)	)	PUNCT
ejpam-5493	152	13	+	+	CCONJ
ejpam-5493	152	14	(	(	PUNCT
ejpam-5493	152	15	p	p	NOUN
ejpam-5493	152	16	1	1	NUM
ejpam-5493	152	17	)	)	PUNCT
ejpam-5493	152	18	(	(	PUNCT
ejpam-5493	152	19	p	p	NOUN
ejpam-5493	152	20	1	1	X
ejpam-5493	152	21	)	)	PUNCT
ejpam-5493	152	22	φ(rp)h(rp−1t)φ(rp−1	φ(rp)h(rp−1t)φ(rp−1	PROPN
ejpam-5493	152	23	t	t	PROPN
ejpam-5493	152	24	)	)	PUNCT
ejpam-5493	152	25	+	+	CCONJ
ejpam-5493	152	26	(	(	PUNCT
ejpam-5493	152	27	p	p	NOUN
ejpam-5493	152	28	2	2	X
ejpam-5493	152	29	)	)	PUNCT
ejpam-5493	152	30	φ(rp)h(rp−2t2)φ(rp	φ(rp)h(rp−2t2)φ(rp	PROPN
ejpam-5493	152	31	)	)	PUNCT
ejpam-5493	153	1	+	+	CCONJ
ejpam-5493	153	2	(	(	PUNCT
ejpam-5493	153	3	p	p	NOUN
ejpam-5493	153	4	1	1	NUM
ejpam-5493	153	5	)	)	PUNCT
ejpam-5493	153	6	(	(	PUNCT
ejpam-5493	153	7	p	p	NOUN
ejpam-5493	153	8	1	1	X
ejpam-5493	153	9	)	)	PUNCT
ejpam-5493	153	10	φ(rp−1t)h(rp−1t)φ(rp	φ(rp−1t)h(rp−1t)φ(rp	PROPN
ejpam-5493	153	11	)	)	PUNCT
ejpam-5493	153	12	+	+	CCONJ
ejpam-5493	153	13	(	(	PUNCT
ejpam-5493	153	14	p	p	NOUN
ejpam-5493	153	15	2	2	NUM
ejpam-5493	153	16	)	)	PUNCT
ejpam-5493	153	17	φ(rp−2t2)h(rp)φ(rp	φ(rp−2t2)h(rp)φ(rp	NOUN
ejpam-5493	153	18	)	)	PUNCT
ejpam-5493	153	19	.	.	PUNCT
ejpam-5493	154	1	reword	reword	VERB
ejpam-5493	154	2	the	the	DET
ejpam-5493	154	3	above	above	ADJ
ejpam-5493	154	4	expression	expression	NOUN
ejpam-5493	154	5	by	by	ADP
ejpam-5493	154	6	putting	put	VERB
ejpam-5493	154	7	e	e	NOUN
ejpam-5493	154	8	in	in	ADP
ejpam-5493	154	9	place	place	NOUN
ejpam-5493	154	10	of	of	ADP
ejpam-5493	154	11	r	r	NOUN
ejpam-5493	154	12	,	,	PUNCT
ejpam-5493	154	13	we	we	PRON
ejpam-5493	154	14	have	have	VERB
ejpam-5493	154	15	3p(3p−1	3p(3p−1	NUM
ejpam-5493	154	16	)	)	PUNCT
ejpam-5493	154	17	2	2	NUM
ejpam-5493	154	18	h(t2	h(t2	NOUN
ejpam-5493	154	19	)	)	PUNCT
ejpam-5493	155	1	=	=	PUNCT
ejpam-5493	155	2	(	(	PUNCT
ejpam-5493	155	3	p	p	NOUN
ejpam-5493	155	4	2	2	X
ejpam-5493	155	5	)	)	PUNCT
ejpam-5493	155	6	h(e)φ(t2	h(e)φ(t2	PROPN
ejpam-5493	155	7	)	)	PUNCT
ejpam-5493	156	1	+	+	CCONJ
ejpam-5493	156	2	(	(	PUNCT
ejpam-5493	156	3	p	p	NOUN
ejpam-5493	156	4	1	1	NUM
ejpam-5493	156	5	)	)	PUNCT
ejpam-5493	156	6	(	(	PUNCT
ejpam-5493	156	7	p	p	NOUN
ejpam-5493	156	8	1	1	X
ejpam-5493	156	9	)	)	PUNCT
ejpam-5493	156	10	φ(t)h(e)φ(t	φ(t)h(e)φ(t	PROPN
ejpam-5493	156	11	)	)	PUNCT
ejpam-5493	157	1	+	+	CCONJ
ejpam-5493	157	2	(	(	PUNCT
ejpam-5493	157	3	p	p	NOUN
ejpam-5493	157	4	1	1	NUM
ejpam-5493	157	5	)	)	PUNCT
ejpam-5493	157	6	(	(	PUNCT
ejpam-5493	157	7	p	p	NOUN
ejpam-5493	157	8	1	1	NUM
ejpam-5493	157	9	)	)	PUNCT
ejpam-5493	157	10	h(t)φ(t	h(t)φ(t	NUM
ejpam-5493	157	11	)	)	PUNCT
ejpam-5493	157	12	+	+	CCONJ
ejpam-5493	157	13	(	(	PUNCT
ejpam-5493	157	14	p	p	NOUN
ejpam-5493	157	15	2	2	X
ejpam-5493	157	16	)	)	PUNCT
ejpam-5493	157	17	h(t2	h(t2	NOUN
ejpam-5493	157	18	)	)	PUNCT
ejpam-5493	157	19	+	+	CCONJ
ejpam-5493	157	20	(	(	PUNCT
ejpam-5493	157	21	p	p	NOUN
ejpam-5493	157	22	1	1	NUM
ejpam-5493	157	23	)	)	PUNCT
ejpam-5493	157	24	(	(	PUNCT
ejpam-5493	157	25	p	p	NOUN
ejpam-5493	157	26	1	1	NUM
ejpam-5493	157	27	)	)	PUNCT
ejpam-5493	157	28	φ(t)h(t	φ(t)h(t	NUM
ejpam-5493	157	29	)	)	PUNCT
ejpam-5493	157	30	+	+	CCONJ
ejpam-5493	157	31	(	(	PUNCT
ejpam-5493	157	32	p	p	NOUN
ejpam-5493	157	33	2	2	NUM
ejpam-5493	157	34	)	)	PUNCT
ejpam-5493	157	35	φ(t2)h(e	φ(t2)h(e	PROPN
ejpam-5493	157	36	)	)	PUNCT
ejpam-5493	157	37	.	.	PUNCT
ejpam-5493	158	1	simplify	simplify	VERB
ejpam-5493	158	2	the	the	DET
ejpam-5493	158	3	above	above	ADJ
ejpam-5493	158	4	expression	expression	NOUN
ejpam-5493	158	5	using	use	VERB
ejpam-5493	158	6	the	the	DET
ejpam-5493	158	7	same	same	ADJ
ejpam-5493	158	8	steps	step	NOUN
ejpam-5493	158	9	as	as	SCONJ
ejpam-5493	158	10	we	we	PRON
ejpam-5493	158	11	did	do	VERB
ejpam-5493	158	12	in	in	ADP
ejpam-5493	158	13	last	last	ADJ
ejpam-5493	158	14	theorems	theorem	NOUN
ejpam-5493	158	15	to	to	PART
ejpam-5493	158	16	find	find	VERB
ejpam-5493	158	17	3p2h(t2	3p2h(t2	NUM
ejpam-5493	158	18	)	)	PUNCT
ejpam-5493	158	19	=	=	SYM
ejpam-5493	158	20	p2(h(t)φ(t	p2(h(t)φ(t	NOUN
ejpam-5493	158	21	)	)	PUNCT
ejpam-5493	158	22	+	+	CCONJ
ejpam-5493	158	23	φ(t)h(t	φ(t)h(t	NUM
ejpam-5493	158	24	)	)	PUNCT
ejpam-5493	158	25	)	)	PUNCT
ejpam-5493	159	1	+	+	CCONJ
ejpam-5493	159	2	p2φ(t)h(e)φ(t	p2φ(t)h(e)φ(t	NOUN
ejpam-5493	159	3	)	)	PUNCT
ejpam-5493	159	4	,	,	PUNCT
ejpam-5493	159	5	for	for	ADP
ejpam-5493	159	6	all	all	DET
ejpam-5493	159	7	t	t	PROPN
ejpam-5493	159	8	∈	∈	PROPN
ejpam-5493	159	9	r.	r.	PROPN
ejpam-5493	159	10	hence	hence	ADV
ejpam-5493	159	11	,	,	PUNCT
ejpam-5493	159	12	we	we	PRON
ejpam-5493	159	13	get	get	VERB
ejpam-5493	159	14	by	by	ADP
ejpam-5493	159	15	applying	apply	VERB
ejpam-5493	159	16	the	the	DET
ejpam-5493	159	17	torsion	torsion	NOUN
ejpam-5493	159	18	freeness	freeness	NOUN
ejpam-5493	159	19	of	of	ADP
ejpam-5493	159	20	r	r	NOUN
ejpam-5493	159	21	a.	a.	NOUN
ejpam-5493	159	22	z.	z.	PROPN
ejpam-5493	159	23	ansari	ansari	PROPN
ejpam-5493	159	24	et	et	PROPN
ejpam-5493	159	25	al	al	PROPN
ejpam-5493	159	26	.	.	PUNCT
ejpam-5493	159	27	/	/	SYM
ejpam-5493	159	28	eur	eur	PROPN
ejpam-5493	159	29	.	.	PUNCT
ejpam-5493	160	1	j.	j.	PROPN
ejpam-5493	160	2	pure	pure	PROPN
ejpam-5493	160	3	appl	appl	PROPN
ejpam-5493	160	4	.	.	PROPN
ejpam-5493	160	5	math	math	PROPN
ejpam-5493	160	6	,	,	PUNCT
ejpam-5493	160	7	18	18	NUM
ejpam-5493	160	8	(	(	PUNCT
ejpam-5493	160	9	1	1	NUM
ejpam-5493	160	10	)	)	PUNCT
ejpam-5493	160	11	(	(	PUNCT
ejpam-5493	160	12	2025	2025	NUM
ejpam-5493	160	13	)	)	PUNCT
ejpam-5493	160	14	,	,	PUNCT
ejpam-5493	160	15	5493	5493	NUM
ejpam-5493	160	16	7	7	NUM
ejpam-5493	160	17	of	of	ADP
ejpam-5493	160	18	10	10	NUM
ejpam-5493	160	19	3h(t2	3h(t2	NUM
ejpam-5493	160	20	)	)	PUNCT
ejpam-5493	160	21	=	=	SYM
ejpam-5493	160	22	(	(	PUNCT
ejpam-5493	160	23	h(t)φ(t	h(t)φ(t	NOUN
ejpam-5493	160	24	)	)	PUNCT
ejpam-5493	160	25	+	+	NUM
ejpam-5493	160	26	φ(t)h(t	φ(t)h(t	NUM
ejpam-5493	160	27	)	)	PUNCT
ejpam-5493	160	28	)	)	PUNCT
ejpam-5493	161	1	+	+	CCONJ
ejpam-5493	161	2	φ(t)h(e)φ(t	φ(t)h(e)φ(t	NUM
ejpam-5493	161	3	)	)	PUNCT
ejpam-5493	161	4	,	,	PUNCT
ejpam-5493	161	5	for	for	ADP
ejpam-5493	161	6	all	all	DET
ejpam-5493	161	7	t	t	PROPN
ejpam-5493	161	8	∈	∈	PROPN
ejpam-5493	161	9	r.	r.	PROPN
ejpam-5493	161	10	(	(	PUNCT
ejpam-5493	161	11	9	9	X
ejpam-5493	161	12	)	)	PUNCT
ejpam-5493	161	13	multiplying	multiply	VERB
ejpam-5493	161	14	from	from	ADP
ejpam-5493	161	15	right	right	ADJ
ejpam-5493	161	16	side	side	NOUN
ejpam-5493	161	17	by	by	ADP
ejpam-5493	161	18	φ(r	φ(r	NOUN
ejpam-5493	161	19	)	)	PUNCT
ejpam-5493	161	20	to	to	ADP
ejpam-5493	161	21	(	(	PUNCT
ejpam-5493	161	22	8)	8)	NUM
ejpam-5493	161	23	,	,	PUNCT
ejpam-5493	161	24	we	we	PRON
ejpam-5493	161	25	obtain	obtain	VERB
ejpam-5493	161	26	2h(r)φ(r	2h(r)φ(r	NUM
ejpam-5493	161	27	)	)	PUNCT
ejpam-5493	161	28	=	=	SYM
ejpam-5493	161	29	h(e)φ(r2	h(e)φ(r2	NOUN
ejpam-5493	161	30	)	)	PUNCT
ejpam-5493	161	31	+	+	CCONJ
ejpam-5493	162	1	φ(r)h(e)φ(r	φ(r)h(e)φ(r	NOUN
ejpam-5493	162	2	)	)	PUNCT
ejpam-5493	162	3	for	for	ADP
ejpam-5493	162	4	every	every	DET
ejpam-5493	162	5	r	r	NOUN
ejpam-5493	162	6	∈	∈	PROPN
ejpam-5493	162	7	r.	r.	NOUN
ejpam-5493	162	8	multiply	multiply	NOUN
ejpam-5493	162	9	from	from	ADP
ejpam-5493	162	10	left	left	ADJ
ejpam-5493	162	11	side	side	NOUN
ejpam-5493	162	12	by	by	ADP
ejpam-5493	162	13	φ(r	φ(r	ADJ
ejpam-5493	162	14	)	)	PUNCT
ejpam-5493	162	15	to	to	ADP
ejpam-5493	162	16	(	(	PUNCT
ejpam-5493	162	17	8)	8)	NUM
ejpam-5493	162	18	to	to	PART
ejpam-5493	162	19	get	get	VERB
ejpam-5493	162	20	2φ(r)h(r	2φ(r)h(r	NUM
ejpam-5493	162	21	)	)	PUNCT
ejpam-5493	163	1	=	=	PUNCT
ejpam-5493	163	2	φ(r)h(e)φ(r	φ(r)h(e)φ(r	ADJ
ejpam-5493	163	3	)	)	PUNCT
ejpam-5493	163	4	+	+	CCONJ
ejpam-5493	163	5	φ(r2)h(e	φ(r2)h(e	NOUN
ejpam-5493	163	6	)	)	PUNCT
ejpam-5493	163	7	for	for	ADP
ejpam-5493	163	8	every	every	DET
ejpam-5493	163	9	r	r	NOUN
ejpam-5493	163	10	∈	∈	PROPN
ejpam-5493	163	11	r.	r.	NOUN
ejpam-5493	163	12	adding	add	VERB
ejpam-5493	163	13	these	these	DET
ejpam-5493	163	14	equations	equation	NOUN
ejpam-5493	163	15	,	,	PUNCT
ejpam-5493	163	16	we	we	PRON
ejpam-5493	163	17	find	find	VERB
ejpam-5493	163	18	2(h(r)φ(r	2(h(r)φ(r	NUM
ejpam-5493	163	19	)	)	PUNCT
ejpam-5493	164	1	+	+	NUM
ejpam-5493	164	2	φ(r)h(r	φ(r)h(r	NOUN
ejpam-5493	164	3	)	)	PUNCT
ejpam-5493	164	4	)	)	PUNCT
ejpam-5493	165	1	=	=	PUNCT
ejpam-5493	165	2	2φ(r)h(e)φ(r	2φ(r)h(e)φ(r	NUM
ejpam-5493	165	3	)	)	PUNCT
ejpam-5493	165	4	+	+	NUM
ejpam-5493	165	5	2h(r2	2h(r2	NUM
ejpam-5493	165	6	)	)	PUNCT
ejpam-5493	165	7	,	,	PUNCT
ejpam-5493	165	8	which	which	PRON
ejpam-5493	165	9	implies	imply	VERB
ejpam-5493	165	10	that	that	SCONJ
ejpam-5493	165	11	φ(r)h(e)φ(r	φ(r)h(e)φ(r	ADJ
ejpam-5493	165	12	)	)	PUNCT
ejpam-5493	165	13	=	=	SYM
ejpam-5493	165	14	h(r)φ(r	h(r)φ(r	NOUN
ejpam-5493	165	15	)	)	PUNCT
ejpam-5493	165	16	+	+	X
ejpam-5493	165	17	φ(r)h(r)−h(r2	φ(r)h(r)−h(r2	NOUN
ejpam-5493	165	18	)	)	PUNCT
ejpam-5493	165	19	for	for	ADP
ejpam-5493	165	20	every	every	DET
ejpam-5493	165	21	r	r	NOUN
ejpam-5493	165	22	∈	∈	PROPN
ejpam-5493	165	23	r.	r.	NOUN
ejpam-5493	165	24	using	use	VERB
ejpam-5493	165	25	this	this	DET
ejpam-5493	165	26	equation	equation	NOUN
ejpam-5493	165	27	in	in	ADP
ejpam-5493	165	28	(	(	PUNCT
ejpam-5493	165	29	9	9	NUM
ejpam-5493	165	30	)	)	PUNCT
ejpam-5493	165	31	,	,	PUNCT
ejpam-5493	165	32	we	we	PRON
ejpam-5493	165	33	have	have	VERB
ejpam-5493	165	34	4h(r2	4h(r2	NOUN
ejpam-5493	165	35	)	)	PUNCT
ejpam-5493	165	36	=	=	SYM
ejpam-5493	166	1	2(h(r)φ(r	2(h(r)φ(r	NUM
ejpam-5493	166	2	)	)	PUNCT
ejpam-5493	167	1	+	+	NUM
ejpam-5493	167	2	φ(r)h(r	φ(r)h(r	NOUN
ejpam-5493	167	3	)	)	PUNCT
ejpam-5493	167	4	)	)	PUNCT
ejpam-5493	168	1	for	for	ADP
ejpam-5493	168	2	every	every	DET
ejpam-5493	168	3	r	r	NOUN
ejpam-5493	168	4	∈	∈	PROPN
ejpam-5493	168	5	r.	r.	NOUN
ejpam-5493	168	6	using	use	VERB
ejpam-5493	168	7	torsion	torsion	NOUN
ejpam-5493	168	8	restrictions	restriction	NOUN
ejpam-5493	168	9	on	on	ADP
ejpam-5493	168	10	r	r	NOUN
ejpam-5493	168	11	,	,	PUNCT
ejpam-5493	168	12	get	get	VERB
ejpam-5493	168	13	2h(r2	2h(r2	NOUN
ejpam-5493	168	14	)	)	PUNCT
ejpam-5493	169	1	=	=	VERB
ejpam-5493	169	2	h(r)φ(r)+φ(r)h(r	h(r)φ(r)+φ(r)h(r	ADV
ejpam-5493	169	3	)	)	PUNCT
ejpam-5493	169	4	for	for	ADP
ejpam-5493	169	5	every	every	DET
ejpam-5493	169	6	r	r	NOUN
ejpam-5493	169	7	∈	∈	PROPN
ejpam-5493	169	8	r.	r.	NOUN
ejpam-5493	169	9	using	use	VERB
ejpam-5493	169	10	lemma	lemma	PROPN
ejpam-5493	169	11	1	1	NUM
ejpam-5493	169	12	,	,	PUNCT
ejpam-5493	169	13	h	h	NOUN
ejpam-5493	169	14	is	be	AUX
ejpam-5493	169	15	a	a	DET
ejpam-5493	169	16	φ	φ	NOUN
ejpam-5493	169	17	-	-	PUNCT
ejpam-5493	169	18	centralizer	centralizer	NOUN
ejpam-5493	169	19	on	on	ADP
ejpam-5493	169	20	r.	r.	PROPN
ejpam-5493	169	21	the	the	DET
ejpam-5493	169	22	subsequent	subsequent	ADJ
ejpam-5493	169	23	illustration	illustration	NOUN
ejpam-5493	169	24	supports	support	VERB
ejpam-5493	169	25	our	our	PRON
ejpam-5493	169	26	theorems	theorem	NOUN
ejpam-5493	169	27	:	:	PUNCT
ejpam-5493	169	28	example	example	NOUN
ejpam-5493	169	29	1	1	X
ejpam-5493	169	30	.	.	PUNCT
ejpam-5493	170	1	let	let	VERB
ejpam-5493	170	2	r	r	NOUN
ejpam-5493	170	3	=	=	PRON
ejpam-5493	170	4	{	{	PUNCT
ejpam-5493	170	5	(	(	PUNCT
ejpam-5493	170	6	z1	z1	NOUN
ejpam-5493	170	7	0	0	NUM
ejpam-5493	170	8	0	0	NUM
ejpam-5493	170	9	z2	z2	PROPN
ejpam-5493	170	10	)	)	PUNCT
ejpam-5493	171	1	|	|	ADV
ejpam-5493	171	2	z1	z1	VERB
ejpam-5493	171	3	,	,	PUNCT
ejpam-5493	171	4	z2	z2	PROPN
ejpam-5493	171	5	∈	∈	PROPN
ejpam-5493	171	6	2z8	2z8	NUM
ejpam-5493	171	7	}	}	PUNCT
ejpam-5493	171	8	,	,	PUNCT
ejpam-5493	171	9	whereby	whereby	SCONJ
ejpam-5493	171	10	the	the	DET
ejpam-5493	171	11	meaning	meaning	NOUN
ejpam-5493	171	12	of	of	ADP
ejpam-5493	171	13	z8	z8	NOUN
ejpam-5493	171	14	is	be	AUX
ejpam-5493	171	15	as	as	ADV
ejpam-5493	171	16	usual	usual	ADJ
ejpam-5493	171	17	.	.	PUNCT
ejpam-5493	172	1	define	define	VERB
ejpam-5493	172	2	mappings	mapping	NOUN
ejpam-5493	172	3	h	h	NOUN
ejpam-5493	172	4	,	,	PUNCT
ejpam-5493	172	5	φ	φ	X
ejpam-5493	172	6	:	:	PUNCT
ejpam-5493	172	7	r	r	NOUN
ejpam-5493	172	8	→	→	SYM
ejpam-5493	172	9	r	r	NOUN
ejpam-5493	172	10	by	by	ADP
ejpam-5493	172	11	h(r	h(r	NOUN
ejpam-5493	172	12	)	)	PUNCT
ejpam-5493	172	13	=	=	PUNCT
ejpam-5493	173	1	(	(	PUNCT
ejpam-5493	173	2	0	0	NUM
ejpam-5493	173	3	0	0	NUM
ejpam-5493	173	4	0	0	NUM
ejpam-5493	173	5	z2	z2	PROPN
ejpam-5493	173	6	)	)	PUNCT
ejpam-5493	173	7	and	and	CCONJ
ejpam-5493	173	8	φ(r	φ(r	ADJ
ejpam-5493	173	9	)	)	PUNCT
ejpam-5493	173	10	=	=	SYM
ejpam-5493	173	11	(	(	PUNCT
ejpam-5493	173	12	z2	z2	NOUN
ejpam-5493	173	13	0	0	NUM
ejpam-5493	173	14	0	0	NUM
ejpam-5493	173	15	z1	z1	PROPN
ejpam-5493	173	16	)	)	PUNCT
ejpam-5493	173	17	for	for	ADP
ejpam-5493	173	18	all	all	DET
ejpam-5493	173	19	r	r	PROPN
ejpam-5493	173	20	∈	∈	PROPN
ejpam-5493	173	21	r.	r.	NOUN
ejpam-5493	173	22	clearly	clearly	ADV
ejpam-5493	173	23	,	,	PUNCT
ejpam-5493	173	24	r	r	NOUN
ejpam-5493	173	25	is	be	AUX
ejpam-5493	173	26	not	not	PART
ejpam-5493	173	27	a	a	DET
ejpam-5493	173	28	semiprime	semiprime	NOUN
ejpam-5493	173	29	ring	ring	NOUN
ejpam-5493	173	30	but	but	CCONJ
ejpam-5493	173	31	h	h	NOUN
ejpam-5493	173	32	satisfy	satisfy	VERB
ejpam-5493	173	33	the	the	DET
ejpam-5493	173	34	algebraic	algebraic	ADJ
ejpam-5493	173	35	identity	identity	NOUN
ejpam-5493	173	36	of	of	ADP
ejpam-5493	173	37	main	main	ADJ
ejpam-5493	173	38	theorems	theorem	NOUN
ejpam-5493	173	39	(	(	PUNCT
ejpam-5493	173	40	(	(	PUNCT
ejpam-5493	173	41	ii	ii	NOUN
ejpam-5493	173	42	)	)	PUNCT
ejpam-5493	174	1	p	p	NOUN
ejpam-5493	174	2	>	>	X
ejpam-5493	174	3	1	1	NUM
ejpam-5493	174	4	)	)	PUNCT
ejpam-5493	174	5	of	of	ADP
ejpam-5493	174	6	this	this	DET
ejpam-5493	174	7	section	section	NOUN
ejpam-5493	174	8	.	.	PUNCT
ejpam-5493	175	1	it	it	PRON
ejpam-5493	175	2	is	be	AUX
ejpam-5493	175	3	easy	easy	ADJ
ejpam-5493	175	4	to	to	PART
ejpam-5493	175	5	see	see	VERB
ejpam-5493	175	6	that	that	SCONJ
ejpam-5493	175	7	h	h	NOUN
ejpam-5493	175	8	is	be	AUX
ejpam-5493	175	9	not	not	PART
ejpam-5493	175	10	a	a	DET
ejpam-5493	175	11	φ	φ	NOUN
ejpam-5493	175	12	-	-	PUNCT
ejpam-5493	175	13	centralizer	centralizer	NOUN
ejpam-5493	175	14	.	.	PUNCT
ejpam-5493	176	1	therefore	therefore	ADV
ejpam-5493	176	2	semiprimeness	semiprimeness	NOUN
ejpam-5493	176	3	hypothesis	hypothesis	NOUN
ejpam-5493	176	4	is	be	AUX
ejpam-5493	176	5	crucial	crucial	ADJ
ejpam-5493	176	6	for	for	ADP
ejpam-5493	176	7	the	the	DET
ejpam-5493	176	8	above	above	ADJ
ejpam-5493	176	9	theorems	theorem	NOUN
ejpam-5493	176	10	.	.	PUNCT
ejpam-5493	177	1	3	3	X
ejpam-5493	177	2	.	.	X
ejpam-5493	177	3	on	on	ADP
ejpam-5493	177	4	involution	involution	NOUN
ejpam-5493	177	5	ring	ring	NOUN
ejpam-5493	177	6	next	next	ADV
ejpam-5493	177	7	,	,	PUNCT
ejpam-5493	177	8	an	an	DET
ejpam-5493	177	9	additive	additive	ADJ
ejpam-5493	177	10	mapping	mapping	NOUN
ejpam-5493	177	11	iv	iv	NUM
ejpam-5493	177	12	:	:	PUNCT
ejpam-5493	177	13	r	r	NOUN
ejpam-5493	177	14	→	→	SYM
ejpam-5493	177	15	r	r	NOUN
ejpam-5493	177	16	is	be	AUX
ejpam-5493	177	17	said	say	VERB
ejpam-5493	177	18	to	to	PART
ejpam-5493	177	19	be	be	AUX
ejpam-5493	177	20	an	an	DET
ejpam-5493	177	21	involution	involution	NOUN
ejpam-5493	177	22	if	if	SCONJ
ejpam-5493	177	23	it	it	PRON
ejpam-5493	177	24	satisfies	satisfy	VERB
ejpam-5493	177	25	iv(rt	iv(rt	NUM
ejpam-5493	177	26	)	)	PUNCT
ejpam-5493	177	27	=	=	SYM
ejpam-5493	177	28	iv(t)iv(r	iv(t)iv(r	NOUN
ejpam-5493	177	29	)	)	PUNCT
ejpam-5493	177	30	and	and	CCONJ
ejpam-5493	177	31	iv(iv(r	iv(iv(r	NUM
ejpam-5493	177	32	)	)	PUNCT
ejpam-5493	177	33	)	)	PUNCT
ejpam-5493	178	1	=	=	SYM
ejpam-5493	178	2	r	r	NOUN
ejpam-5493	178	3	for	for	ADP
ejpam-5493	178	4	all	all	DET
ejpam-5493	178	5	r	r	NOUN
ejpam-5493	178	6	,	,	PUNCT
ejpam-5493	178	7	t	t	PROPN
ejpam-5493	178	8	∈	∈	PROPN
ejpam-5493	178	9	r.	r.	PROPN
ejpam-5493	178	10	a	a	DET
ejpam-5493	178	11	ring	ring	NOUN
ejpam-5493	178	12	with	with	ADP
ejpam-5493	178	13	involution	involution	NOUN
ejpam-5493	178	14	is	be	AUX
ejpam-5493	178	15	a	a	DET
ejpam-5493	178	16	ring	ring	NOUN
ejpam-5493	178	17	that	that	PRON
ejpam-5493	178	18	possesses	possess	VERB
ejpam-5493	178	19	an	an	DET
ejpam-5493	178	20	involution	involution	NOUN
ejpam-5493	178	21	iv	iv	NUM
ejpam-5493	178	22	.	.	PUNCT
ejpam-5493	179	1	an	an	DET
ejpam-5493	179	2	additive	additive	ADJ
ejpam-5493	179	3	mappingh	mappingh	NOUN
ejpam-5493	179	4	:	:	PUNCT
ejpam-5493	179	5	r	r	NOUN
ejpam-5493	179	6	→	→	SYM
ejpam-5493	179	7	r	r	NOUN
ejpam-5493	179	8	is	be	AUX
ejpam-5493	179	9	termed	term	VERB
ejpam-5493	179	10	as	as	ADP
ejpam-5493	179	11	a	a	DET
ejpam-5493	179	12	right	right	NOUN
ejpam-5493	179	13	(	(	PUNCT
ejpam-5493	179	14	resp	resp	NOUN
ejpam-5493	179	15	.	.	PUNCT
ejpam-5493	180	1	left	leave	VERB
ejpam-5493	180	2	)	)	PUNCT
ejpam-5493	180	3	iv	iv	NOUN
ejpam-5493	180	4	-	-	PUNCT
ejpam-5493	180	5	centralizer	centralizer	NOUN
ejpam-5493	180	6	if	if	SCONJ
ejpam-5493	180	7	h(rt	h(rt	NOUN
ejpam-5493	180	8	)	)	PUNCT
ejpam-5493	180	9	=	=	SYM
ejpam-5493	180	10	iv(r)h(t	iv(r)h(t	NOUN
ejpam-5493	180	11	)	)	PUNCT
ejpam-5493	180	12	(	(	PUNCT
ejpam-5493	180	13	resp	resp	NOUN
ejpam-5493	180	14	.	.	PUNCT
ejpam-5493	181	1	h(rt	h(rt	NOUN
ejpam-5493	181	2	)	)	PUNCT
ejpam-5493	182	1	=	=	SYM
ejpam-5493	182	2	h(r)iv(t	h(r)iv(t	NOUN
ejpam-5493	182	3	)	)	PUNCT
ejpam-5493	182	4	)	)	PUNCT
ejpam-5493	182	5	holds	hold	VERB
ejpam-5493	182	6	for	for	ADP
ejpam-5493	182	7	all	all	DET
ejpam-5493	182	8	r	r	NOUN
ejpam-5493	182	9	,	,	PUNCT
ejpam-5493	182	10	t	t	PROPN
ejpam-5493	182	11	∈	∈	PROPN
ejpam-5493	182	12	r	r	NOUN
ejpam-5493	182	13	and	and	CCONJ
ejpam-5493	182	14	h	h	NOUN
ejpam-5493	182	15	is	be	AUX
ejpam-5493	182	16	termed	term	VERB
ejpam-5493	182	17	as	as	ADP
ejpam-5493	182	18	a	a	DET
ejpam-5493	182	19	right	right	NOUN
ejpam-5493	182	20	(	(	PUNCT
ejpam-5493	182	21	resp	resp	NOUN
ejpam-5493	182	22	.	.	PUNCT
ejpam-5493	183	1	left	left	PROPN
ejpam-5493	183	2	)	)	PUNCT
ejpam-5493	184	1	jordan	jordan	PROPN
ejpam-5493	184	2	iv	iv	PROPN
ejpam-5493	184	3	-	-	PUNCT
ejpam-5493	184	4	centralizer	centralizer	NOUN
ejpam-5493	184	5	if	if	SCONJ
ejpam-5493	184	6	for	for	ADP
ejpam-5493	184	7	all	all	DET
ejpam-5493	184	8	r	r	NOUN
ejpam-5493	184	9	∈	∈	NOUN
ejpam-5493	184	10	r	r	NOUN
ejpam-5493	184	11	,	,	PUNCT
ejpam-5493	184	12	h(r2	h(r2	NOUN
ejpam-5493	184	13	)	)	PUNCT
ejpam-5493	184	14	=	=	SYM
ejpam-5493	184	15	iv(r)h(r	iv(r)h(r	PROPN
ejpam-5493	184	16	)	)	PUNCT
ejpam-5493	184	17	(	(	PUNCT
ejpam-5493	184	18	resp	resp	NOUN
ejpam-5493	184	19	.	.	PUNCT
ejpam-5493	185	1	h(r2	h(r2	PROPN
ejpam-5493	185	2	)	)	PUNCT
ejpam-5493	186	1	=	=	SYM
ejpam-5493	186	2	h(r)iv(r	h(r)iv(r	NOUN
ejpam-5493	186	3	)	)	PUNCT
ejpam-5493	186	4	)	)	PUNCT
ejpam-5493	186	5	.	.	PUNCT
ejpam-5493	187	1	if	if	SCONJ
ejpam-5493	187	2	h	h	NOUN
ejpam-5493	187	3	is	be	AUX
ejpam-5493	187	4	both	both	ADV
ejpam-5493	187	5	right	right	ADJ
ejpam-5493	187	6	and	and	CCONJ
ejpam-5493	187	7	left	leave	VERB
ejpam-5493	187	8	(	(	PUNCT
ejpam-5493	187	9	jordan	jordan	PROPN
ejpam-5493	187	10	)	)	PUNCT
ejpam-5493	187	11	iv	iv	NOUN
ejpam-5493	187	12	-	-	PUNCT
ejpam-5493	187	13	centralizer	centralizer	NOUN
ejpam-5493	187	14	then	then	ADV
ejpam-5493	187	15	,	,	PUNCT
ejpam-5493	187	16	recognised	recognise	VERB
ejpam-5493	187	17	as	as	ADP
ejpam-5493	187	18	a	a	DET
ejpam-5493	187	19	(	(	PUNCT
ejpam-5493	187	20	jordan	jordan	PROPN
ejpam-5493	187	21	)	)	PUNCT
ejpam-5493	187	22	iv	iv	NOUN
ejpam-5493	187	23	-	-	PUNCT
ejpam-5493	187	24	centralizer	centralizer	NOUN
ejpam-5493	187	25	of	of	ADP
ejpam-5493	187	26	r.	r.	PROPN
ejpam-5493	187	27	let	let	VERB
ejpam-5493	187	28	φ	φ	PROPN
ejpam-5493	187	29	be	be	AUX
ejpam-5493	187	30	an	an	DET
ejpam-5493	187	31	endomorphism	endomorphism	NOUN
ejpam-5493	187	32	on	on	ADP
ejpam-5493	187	33	r.	r.	PROPN
ejpam-5493	187	34	an	an	DET
ejpam-5493	187	35	additive	additive	ADJ
ejpam-5493	187	36	mapping	mapping	NOUN
ejpam-5493	187	37	a.	a.	NOUN
ejpam-5493	187	38	z.	z.	PROPN
ejpam-5493	187	39	ansari	ansari	PROPN
ejpam-5493	187	40	et	et	PROPN
ejpam-5493	187	41	al	al	PROPN
ejpam-5493	187	42	.	.	PUNCT
ejpam-5493	187	43	/	/	SYM
ejpam-5493	187	44	eur	eur	PROPN
ejpam-5493	187	45	.	.	PUNCT
ejpam-5493	188	1	j.	j.	PROPN
ejpam-5493	188	2	pure	pure	PROPN
ejpam-5493	188	3	appl	appl	PROPN
ejpam-5493	188	4	.	.	PROPN
ejpam-5493	188	5	math	math	PROPN
ejpam-5493	188	6	,	,	PUNCT
ejpam-5493	188	7	18	18	NUM
ejpam-5493	188	8	(	(	PUNCT
ejpam-5493	188	9	1	1	NUM
ejpam-5493	188	10	)	)	PUNCT
ejpam-5493	188	11	(	(	PUNCT
ejpam-5493	188	12	2025	2025	NUM
ejpam-5493	188	13	)	)	PUNCT
ejpam-5493	188	14	,	,	PUNCT
ejpam-5493	188	15	5493	5493	NUM
ejpam-5493	188	16	8	8	NUM
ejpam-5493	188	17	of	of	ADP
ejpam-5493	188	18	10	10	NUM
ejpam-5493	188	19	h	h	NOUN
ejpam-5493	188	20	:	:	PUNCT
ejpam-5493	188	21	r	r	NOUN
ejpam-5493	188	22	→	→	SYM
ejpam-5493	188	23	r	r	NOUN
ejpam-5493	188	24	is	be	AUX
ejpam-5493	188	25	known	know	VERB
ejpam-5493	188	26	as	as	ADP
ejpam-5493	188	27	a	a	DET
ejpam-5493	188	28	right	right	NOUN
ejpam-5493	188	29	(	(	PUNCT
ejpam-5493	188	30	resp	resp	NOUN
ejpam-5493	188	31	.	.	PUNCT
ejpam-5493	189	1	left	leave	VERB
ejpam-5493	189	2	)	)	PUNCT
ejpam-5493	189	3	φ	φ	PROPN
ejpam-5493	189	4	-	-	PUNCT
ejpam-5493	189	5	iv	iv	ADP
ejpam-5493	189	6	-	-	PUNCT
ejpam-5493	189	7	centralizer	centralizer	NOUN
ejpam-5493	189	8	if	if	SCONJ
ejpam-5493	189	9	h(rt	h(rt	NOUN
ejpam-5493	189	10	)	)	PUNCT
ejpam-5493	189	11	=	=	SYM
ejpam-5493	189	12	φ(iv(r))h(t	φ(iv(r))h(t	NOUN
ejpam-5493	189	13	)	)	PUNCT
ejpam-5493	189	14	(	(	PUNCT
ejpam-5493	190	1	resp	resp	NOUN
ejpam-5493	190	2	.	.	PUNCT
ejpam-5493	191	1	h(rt	h(rt	NOUN
ejpam-5493	191	2	)	)	PUNCT
ejpam-5493	191	3	=	=	SYM
ejpam-5493	191	4	h(r)φ(iv(t	h(r)φ(iv(t	NOUN
ejpam-5493	191	5	)	)	PUNCT
ejpam-5493	191	6	)	)	PUNCT
ejpam-5493	191	7	)	)	PUNCT
ejpam-5493	191	8	holds	hold	VERB
ejpam-5493	191	9	for	for	ADP
ejpam-5493	191	10	all	all	DET
ejpam-5493	191	11	r	r	NOUN
ejpam-5493	191	12	,	,	PUNCT
ejpam-5493	191	13	t	t	PROPN
ejpam-5493	191	14	∈	∈	PROPN
ejpam-5493	191	15	r	r	NOUN
ejpam-5493	192	1	and	and	CCONJ
ejpam-5493	192	2	it	it	PRON
ejpam-5493	192	3	is	be	AUX
ejpam-5493	192	4	φ	φ	NUM
ejpam-5493	192	5	-	-	PUNCT
ejpam-5493	192	6	iv	iv	ADP
ejpam-5493	192	7	-	-	PUNCT
ejpam-5493	192	8	centralizer	centralizer	NOUN
ejpam-5493	192	9	if	if	SCONJ
ejpam-5493	192	10	it	it	PRON
ejpam-5493	192	11	left	leave	VERB
ejpam-5493	192	12	as	as	ADV
ejpam-5493	192	13	well	well	ADV
ejpam-5493	192	14	right	right	ADJ
ejpam-5493	192	15	φ	φ	NUM
ejpam-5493	192	16	-	-	PUNCT
ejpam-5493	192	17	iv	iv	ADP
ejpam-5493	192	18	-	-	PUNCT
ejpam-5493	192	19	centralizer	centralizer	NOUN
ejpam-5493	192	20	.	.	PUNCT
ejpam-5493	193	1	an	an	DET
ejpam-5493	193	2	additive	additive	ADJ
ejpam-5493	193	3	mapping	mapping	NOUN
ejpam-5493	193	4	h	h	NOUN
ejpam-5493	193	5	is	be	AUX
ejpam-5493	193	6	a	a	DET
ejpam-5493	193	7	right	right	ADJ
ejpam-5493	193	8	(	(	PUNCT
ejpam-5493	193	9	resp	resp	NOUN
ejpam-5493	193	10	.	.	PUNCT
ejpam-5493	194	1	left	left	PROPN
ejpam-5493	194	2	)	)	PUNCT
ejpam-5493	195	1	jordan	jordan	PROPN
ejpam-5493	195	2	φ	φ	PROPN
ejpam-5493	195	3	-	-	PUNCT
ejpam-5493	195	4	iv	iv	ADP
ejpam-5493	195	5	-	-	PUNCT
ejpam-5493	195	6	centralizer	centralizer	NOUN
ejpam-5493	195	7	if	if	SCONJ
ejpam-5493	195	8	for	for	ADP
ejpam-5493	195	9	all	all	DET
ejpam-5493	195	10	r	r	NOUN
ejpam-5493	195	11	∈	∈	NOUN
ejpam-5493	195	12	r	r	NOUN
ejpam-5493	195	13	,	,	PUNCT
ejpam-5493	195	14	h(r2	h(r2	NOUN
ejpam-5493	195	15	)	)	PUNCT
ejpam-5493	195	16	=	=	SYM
ejpam-5493	195	17	φ(iv(r))h(r	φ(iv(r))h(r	NOUN
ejpam-5493	195	18	)	)	PUNCT
ejpam-5493	195	19	(	(	PUNCT
ejpam-5493	195	20	resp	resp	NOUN
ejpam-5493	195	21	.	.	PUNCT
ejpam-5493	196	1	h(r2	h(r2	PROPN
ejpam-5493	196	2	)	)	PUNCT
ejpam-5493	196	3	=	=	SYM
ejpam-5493	196	4	h(r)φ(iv(r	h(r)φ(iv(r	ADJ
ejpam-5493	196	5	)	)	PUNCT
ejpam-5493	196	6	)	)	PUNCT
ejpam-5493	196	7	)	)	PUNCT
ejpam-5493	196	8	.	.	PUNCT
ejpam-5493	197	1	if	if	SCONJ
ejpam-5493	197	2	it	it	PRON
ejpam-5493	197	3	is	be	AUX
ejpam-5493	197	4	both	both	PRON
ejpam-5493	197	5	,	,	PUNCT
ejpam-5493	197	6	then	then	ADV
ejpam-5493	197	7	it	it	PRON
ejpam-5493	197	8	is	be	AUX
ejpam-5493	197	9	jordan	jordan	PROPN
ejpam-5493	197	10	φ	φ	PROPN
ejpam-5493	197	11	-	-	PUNCT
ejpam-5493	197	12	iv	iv	ADP
ejpam-5493	197	13	-	-	PUNCT
ejpam-5493	197	14	centralizer	centralizer	NOUN
ejpam-5493	197	15	of	of	ADP
ejpam-5493	197	16	r.	r.	PROPN
ejpam-5493	197	17	we	we	PRON
ejpam-5493	197	18	investigate	investigate	VERB
ejpam-5493	197	19	about	about	ADP
ejpam-5493	197	20	the	the	DET
ejpam-5493	197	21	interesting	interesting	ADJ
ejpam-5493	197	22	extension	extension	NOUN
ejpam-5493	197	23	of	of	ADP
ejpam-5493	197	24	the	the	DET
ejpam-5493	197	25	results	result	NOUN
ejpam-5493	197	26	presented	present	VERB
ejpam-5493	197	27	in	in	ADP
ejpam-5493	197	28	the	the	DET
ejpam-5493	197	29	last	last	ADJ
ejpam-5493	197	30	section	section	NOUN
ejpam-5493	197	31	in	in	ADP
ejpam-5493	197	32	context	context	NOUN
ejpam-5493	197	33	of	of	ADP
ejpam-5493	197	34	involution	involution	NOUN
ejpam-5493	197	35	ring	ring	NOUN
ejpam-5493	197	36	.	.	PUNCT
ejpam-5493	198	1	the	the	DET
ejpam-5493	198	2	study	study	NOUN
ejpam-5493	198	3	of	of	ADP
ejpam-5493	198	4	some	some	DET
ejpam-5493	198	5	identities	identity	NOUN
ejpam-5493	198	6	on	on	ADP
ejpam-5493	198	7	involution	involution	NOUN
ejpam-5493	198	8	ring	ring	NOUN
ejpam-5493	198	9	is	be	AUX
ejpam-5493	198	10	the	the	DET
ejpam-5493	198	11	main	main	ADJ
ejpam-5493	198	12	focus	focus	NOUN
ejpam-5493	198	13	of	of	ADP
ejpam-5493	198	14	this	this	DET
ejpam-5493	198	15	section	section	NOUN
ejpam-5493	198	16	.	.	PUNCT
ejpam-5493	199	1	however	however	ADV
ejpam-5493	199	2	,	,	PUNCT
ejpam-5493	199	3	evidence	evidence	NOUN
ejpam-5493	199	4	suggests	suggest	VERB
ejpam-5493	199	5	that	that	SCONJ
ejpam-5493	199	6	an	an	DET
ejpam-5493	199	7	additive	additive	ADJ
ejpam-5493	199	8	mappings	mapping	NOUN
ejpam-5493	199	9	h	h	NOUN
ejpam-5493	199	10	on	on	ADP
ejpam-5493	199	11	a	a	DET
ejpam-5493	199	12	suitable	suitable	ADJ
ejpam-5493	199	13	torsion	torsion	NOUN
ejpam-5493	199	14	free	free	ADJ
ejpam-5493	199	15	restricted	restrict	VERB
ejpam-5493	199	16	semiprime	semiprime	NOUN
ejpam-5493	199	17	ring	ring	NOUN
ejpam-5493	199	18	r	r	NOUN
ejpam-5493	199	19	satisfying	satisfy	VERB
ejpam-5493	199	20	2h(r2p	2h(r2p	NUM
ejpam-5493	199	21	)	)	PUNCT
ejpam-5493	199	22	=	=	SYM
ejpam-5493	199	23	h(rp)φ(iv(r	h(rp)φ(iv(r	NOUN
ejpam-5493	199	24	)	)	PUNCT
ejpam-5493	199	25	)	)	PUNCT
ejpam-5493	200	1	p	p	NOUN
ejpam-5493	200	2	+	+	NUM
ejpam-5493	200	3	φ(iv(r	φ(iv(r	PROPN
ejpam-5493	200	4	)	)	PUNCT
ejpam-5493	200	5	)	)	PUNCT
ejpam-5493	201	1	ph(rp	ph(rp	PROPN
ejpam-5493	201	2	)	)	PUNCT
ejpam-5493	201	3	,	,	PUNCT
ejpam-5493	201	4	3h(r3p	3h(r3p	NUM
ejpam-5493	201	5	)	)	PUNCT
ejpam-5493	201	6	=	=	SYM
ejpam-5493	201	7	h(rp)φ(iv(r	h(rp)φ(iv(r	NOUN
ejpam-5493	201	8	)	)	PUNCT
ejpam-5493	201	9	)	)	PUNCT
ejpam-5493	202	1	2p	2p	NOUN
ejpam-5493	202	2	+	+	CCONJ
ejpam-5493	202	3	φ(iv(r	φ(iv(r	ADJ
ejpam-5493	202	4	)	)	PUNCT
ejpam-5493	202	5	)	)	PUNCT
ejpam-5493	202	6	ph(rp)φ(iv(r	ph(rp)φ(iv(r	NOUN
ejpam-5493	202	7	)	)	PUNCT
ejpam-5493	202	8	)	)	PUNCT
ejpam-5493	203	1	p	p	NOUN
ejpam-5493	203	2	+	+	NUM
ejpam-5493	203	3	φ(iv(r	φ(iv(r	PROPN
ejpam-5493	203	4	)	)	PUNCT
ejpam-5493	203	5	)	)	PUNCT
ejpam-5493	203	6	2ph(rp	2ph(rp	NUM
ejpam-5493	203	7	)	)	PUNCT
ejpam-5493	203	8	and	and	CCONJ
ejpam-5493	203	9	h(r3p	h(r3p	NOUN
ejpam-5493	203	10	)	)	PUNCT
ejpam-5493	203	11	=	=	SYM
ejpam-5493	203	12	φ(iv(r	φ(iv(r	PROPN
ejpam-5493	203	13	)	)	PUNCT
ejpam-5493	203	14	)	)	PUNCT
ejpam-5493	203	15	ph(rp)φ(iv(r	ph(rp)φ(iv(r	NOUN
ejpam-5493	203	16	)	)	PUNCT
ejpam-5493	203	17	)	)	PUNCT
ejpam-5493	204	1	p	p	NOUN
ejpam-5493	204	2	for	for	ADP
ejpam-5493	204	3	all	all	DET
ejpam-5493	204	4	r	r	NOUN
ejpam-5493	204	5	∈	∈	NOUN
ejpam-5493	204	6	r	r	NOUN
ejpam-5493	204	7	,	,	PUNCT
ejpam-5493	204	8	will	will	AUX
ejpam-5493	204	9	be	be	AUX
ejpam-5493	204	10	a	a	DET
ejpam-5493	204	11	φ	φ	PROPN
ejpam-5493	204	12	-	-	PUNCT
ejpam-5493	204	13	iv	iv	NOUN
ejpam-5493	204	14	-	-	PUNCT
ejpam-5493	204	15	centralizer	centralizer	NOUN
ejpam-5493	204	16	of	of	ADP
ejpam-5493	204	17	r.	r.	PROPN
ejpam-5493	204	18	we	we	PRON
ejpam-5493	204	19	require	require	VERB
ejpam-5493	204	20	the	the	DET
ejpam-5493	204	21	following	follow	VERB
ejpam-5493	204	22	lemma	lemma	PROPN
ejpam-5493	204	23	that	that	PRON
ejpam-5493	204	24	supports	support	VERB
ejpam-5493	204	25	our	our	PRON
ejpam-5493	204	26	primary	primary	ADJ
ejpam-5493	204	27	findings	finding	NOUN
ejpam-5493	204	28	.	.	PUNCT
ejpam-5493	205	1	lemma	lemma	PROPN
ejpam-5493	205	2	2	2	NUM
ejpam-5493	205	3	(	(	PUNCT
ejpam-5493	205	4	[	[	X
ejpam-5493	205	5	3	3	NUM
ejpam-5493	205	6	,	,	PUNCT
ejpam-5493	205	7	corollary	corollary	ADJ
ejpam-5493	205	8	2.1	2.1	NUM
ejpam-5493	205	9	]	]	PUNCT
ejpam-5493	205	10	)	)	PUNCT
ejpam-5493	205	11	.	.	PUNCT
ejpam-5493	206	1	if	if	SCONJ
ejpam-5493	206	2	φ	φ	PROPN
ejpam-5493	206	3	is	be	AUX
ejpam-5493	206	4	a	a	DET
ejpam-5493	206	5	surjective	surjective	ADJ
ejpam-5493	206	6	endomorphism	endomorphism	NOUN
ejpam-5493	206	7	on	on	ADP
ejpam-5493	206	8	a	a	DET
ejpam-5493	206	9	2	2	NUM
ejpam-5493	206	10	torsion	torsion	NOUN
ejpam-5493	206	11	free	free	ADJ
ejpam-5493	206	12	semiprime	semiprime	NOUN
ejpam-5493	206	13	ring	ring	NOUN
ejpam-5493	206	14	r	r	NOUN
ejpam-5493	206	15	with	with	ADP
ejpam-5493	206	16	involution	involution	NOUN
ejpam-5493	206	17	iv	iv	ADP
ejpam-5493	206	18	and	and	CCONJ
ejpam-5493	206	19	h	h	NOUN
ejpam-5493	206	20	:	:	PUNCT
ejpam-5493	206	21	r	r	NOUN
ejpam-5493	206	22	→	→	SYM
ejpam-5493	206	23	r	r	NOUN
ejpam-5493	206	24	is	be	AUX
ejpam-5493	206	25	an	an	DET
ejpam-5493	206	26	additive	additive	ADJ
ejpam-5493	206	27	mapping	mapping	NOUN
ejpam-5493	206	28	that	that	PRON
ejpam-5493	206	29	satisfies	satisfy	VERB
ejpam-5493	206	30	2h(r2	2h(r2	NUM
ejpam-5493	206	31	)	)	PUNCT
ejpam-5493	206	32	=	=	SYM
ejpam-5493	206	33	h(r)φ(iv(r	h(r)φ(iv(r	ADJ
ejpam-5493	206	34	)	)	PUNCT
ejpam-5493	206	35	)	)	PUNCT
ejpam-5493	207	1	+	+	CCONJ
ejpam-5493	207	2	φ(iv(r))h(r	φ(iv(r))h(r	NOUN
ejpam-5493	207	3	)	)	PUNCT
ejpam-5493	207	4	for	for	ADP
ejpam-5493	207	5	all	all	DET
ejpam-5493	207	6	r	r	NOUN
ejpam-5493	207	7	∈	∈	NOUN
ejpam-5493	207	8	r	r	NOUN
ejpam-5493	207	9	,	,	PUNCT
ejpam-5493	207	10	then	then	ADV
ejpam-5493	207	11	h	h	PROPN
ejpam-5493	207	12	is	be	AUX
ejpam-5493	207	13	a	a	DET
ejpam-5493	207	14	φ	φ	PROPN
ejpam-5493	207	15	-	-	PUNCT
ejpam-5493	207	16	iv	iv	NOUN
ejpam-5493	207	17	-	-	PUNCT
ejpam-5493	207	18	centralizer	centralizer	NOUN
ejpam-5493	207	19	on	on	ADP
ejpam-5493	207	20	r.	r.	PROPN
ejpam-5493	207	21	next	next	ADV
ejpam-5493	207	22	,	,	PUNCT
ejpam-5493	207	23	start	start	VERB
ejpam-5493	207	24	main	main	ADJ
ejpam-5493	207	25	result	result	NOUN
ejpam-5493	207	26	of	of	ADP
ejpam-5493	207	27	this	this	DET
ejpam-5493	207	28	part	part	NOUN
ejpam-5493	207	29	.	.	PUNCT
ejpam-5493	208	1	theorem	theorem	VERB
ejpam-5493	208	2	4	4	NUM
ejpam-5493	208	3	.	.	PUNCT
ejpam-5493	209	1	if	if	SCONJ
ejpam-5493	209	2	φ	φ	PROPN
ejpam-5493	209	3	is	be	AUX
ejpam-5493	209	4	a	a	DET
ejpam-5493	209	5	surjective	surjective	ADJ
ejpam-5493	209	6	endomorphism	endomorphism	NOUN
ejpam-5493	209	7	on	on	ADP
ejpam-5493	209	8	a	a	DET
ejpam-5493	209	9	(	(	PUNCT
ejpam-5493	209	10	3p−1	3p−1	NUM
ejpam-5493	209	11	)	)	PUNCT
ejpam-5493	209	12	!	!	PUNCT
ejpam-5493	210	1	torsion	torsion	NOUN
ejpam-5493	210	2	free	free	ADJ
ejpam-5493	210	3	semiprime	semiprime	NOUN
ejpam-5493	210	4	ring	ring	NOUN
ejpam-5493	210	5	r	r	NOUN
ejpam-5493	210	6	with	with	ADP
ejpam-5493	210	7	involution	involution	NOUN
ejpam-5493	210	8	iv	iv	ADP
ejpam-5493	210	9	and	and	CCONJ
ejpam-5493	210	10	h	h	NOUN
ejpam-5493	210	11	:	:	PUNCT
ejpam-5493	210	12	r	r	NOUN
ejpam-5493	210	13	→	→	SYM
ejpam-5493	210	14	r	r	NOUN
ejpam-5493	210	15	is	be	AUX
ejpam-5493	210	16	an	an	DET
ejpam-5493	210	17	additive	additive	ADJ
ejpam-5493	210	18	mapping	mapping	NOUN
ejpam-5493	210	19	that	that	PRON
ejpam-5493	210	20	satisfies	satisfy	VERB
ejpam-5493	210	21	any	any	DET
ejpam-5493	210	22	one	one	NUM
ejpam-5493	210	23	of	of	ADP
ejpam-5493	210	24	the	the	DET
ejpam-5493	210	25	following	follow	VERB
ejpam-5493	210	26	algebraic	algebraic	ADJ
ejpam-5493	210	27	identities	identity	NOUN
ejpam-5493	210	28	:	:	PUNCT
ejpam-5493	210	29	(	(	PUNCT
ejpam-5493	210	30	i	i	NOUN
ejpam-5493	210	31	)	)	PUNCT
ejpam-5493	210	32	3h(r3p	3h(r3p	NUM
ejpam-5493	210	33	)	)	PUNCT
ejpam-5493	210	34	=	=	SYM
ejpam-5493	210	35	h(rp)φ(iv(r	h(rp)φ(iv(r	NOUN
ejpam-5493	210	36	)	)	PUNCT
ejpam-5493	210	37	)	)	PUNCT
ejpam-5493	210	38	2p	2p	NOUN
ejpam-5493	210	39	+	+	CCONJ
ejpam-5493	210	40	φ(iv(r	φ(iv(r	ADJ
ejpam-5493	210	41	)	)	PUNCT
ejpam-5493	210	42	)	)	PUNCT
ejpam-5493	210	43	ph(rp)φ(iv(r	ph(rp)φ(iv(r	NOUN
ejpam-5493	210	44	)	)	PUNCT
ejpam-5493	210	45	)	)	PUNCT
ejpam-5493	211	1	p	p	NOUN
ejpam-5493	211	2	+	+	NUM
ejpam-5493	211	3	φ(iv(r	φ(iv(r	PROPN
ejpam-5493	211	4	)	)	PUNCT
ejpam-5493	211	5	)	)	PUNCT
ejpam-5493	211	6	2ph(rp	2ph(rp	NUM
ejpam-5493	211	7	)	)	PUNCT
ejpam-5493	211	8	(	(	PUNCT
ejpam-5493	211	9	ii	ii	NOUN
ejpam-5493	211	10	)	)	PUNCT
ejpam-5493	211	11	2h(r2p	2h(r2p	NUM
ejpam-5493	211	12	)	)	PUNCT
ejpam-5493	211	13	=	=	SYM
ejpam-5493	211	14	h(rp)φ(iv(r	h(rp)φ(iv(r	NOUN
ejpam-5493	211	15	)	)	PUNCT
ejpam-5493	211	16	)	)	PUNCT
ejpam-5493	212	1	p	p	NOUN
ejpam-5493	212	2	+	+	NUM
ejpam-5493	212	3	φ(iv(r	φ(iv(r	ADJ
ejpam-5493	212	4	)	)	PUNCT
ejpam-5493	212	5	)	)	PUNCT
ejpam-5493	213	1	ph(rp	ph(rp	PROPN
ejpam-5493	213	2	)	)	PUNCT
ejpam-5493	213	3	(	(	PUNCT
ejpam-5493	213	4	iii	iii	NOUN
ejpam-5493	213	5	)	)	PUNCT
ejpam-5493	213	6	h(r3p	h(r3p	NOUN
ejpam-5493	213	7	)	)	PUNCT
ejpam-5493	213	8	=	=	SYM
ejpam-5493	213	9	φ(iv(r	φ(iv(r	PROPN
ejpam-5493	213	10	)	)	PUNCT
ejpam-5493	213	11	)	)	PUNCT
ejpam-5493	213	12	ph(rp)φ(iv(r	ph(rp)φ(iv(r	NOUN
ejpam-5493	213	13	)	)	PUNCT
ejpam-5493	213	14	)	)	PUNCT
ejpam-5493	214	1	p	p	NOUN
ejpam-5493	214	2	for	for	ADP
ejpam-5493	214	3	all	all	DET
ejpam-5493	214	4	r	r	NOUN
ejpam-5493	214	5	∈	∈	NOUN
ejpam-5493	214	6	r	r	NOUN
ejpam-5493	214	7	,	,	PUNCT
ejpam-5493	214	8	then	then	ADV
ejpam-5493	214	9	,	,	PUNCT
ejpam-5493	214	10	h	h	NOUN
ejpam-5493	214	11	is	be	AUX
ejpam-5493	214	12	a	a	DET
ejpam-5493	214	13	φ	φ	PROPN
ejpam-5493	214	14	-	-	PUNCT
ejpam-5493	214	15	iv	iv	NOUN
ejpam-5493	214	16	-	-	PUNCT
ejpam-5493	214	17	centralizer	centralizer	NOUN
ejpam-5493	214	18	on	on	ADP
ejpam-5493	214	19	r	r	NOUN
ejpam-5493	214	20	,	,	PUNCT
ejpam-5493	214	21	where	where	SCONJ
ejpam-5493	214	22	p	p	NOUN
ejpam-5493	214	23	is	be	AUX
ejpam-5493	214	24	a	a	DET
ejpam-5493	214	25	fixed	fix	VERB
ejpam-5493	214	26	integer	integer	NOUN
ejpam-5493	214	27	greater	great	ADJ
ejpam-5493	214	28	than	than	ADP
ejpam-5493	214	29	or	or	CCONJ
ejpam-5493	214	30	equal	equal	ADJ
ejpam-5493	214	31	to	to	ADP
ejpam-5493	214	32	1	1	NUM
ejpam-5493	214	33	.	.	PUNCT
ejpam-5493	215	1	proof	proof	NOUN
ejpam-5493	215	2	.	.	PUNCT
ejpam-5493	216	1	(	(	PUNCT
ejpam-5493	216	2	i	i	NOUN
ejpam-5493	216	3	)	)	PUNCT
ejpam-5493	216	4	define	define	VERB
ejpam-5493	216	5	a	a	DET
ejpam-5493	216	6	mapping	mapping	NOUN
ejpam-5493	216	7	t	t	NOUN
ejpam-5493	216	8	:	:	PUNCT
ejpam-5493	216	9	r	r	NOUN
ejpam-5493	216	10	→	→	SYM
ejpam-5493	216	11	r	r	NOUN
ejpam-5493	216	12	such	such	ADJ
ejpam-5493	216	13	that	that	DET
ejpam-5493	216	14	t	t	PROPN
ejpam-5493	216	15	(	(	PUNCT
ejpam-5493	216	16	r	r	NOUN
ejpam-5493	216	17	)	)	PUNCT
ejpam-5493	216	18	=	=	SYM
ejpam-5493	216	19	h(iv(r	h(iv(r	PROPN
ejpam-5493	216	20	)	)	PUNCT
ejpam-5493	216	21	)	)	PUNCT
ejpam-5493	216	22	for	for	ADP
ejpam-5493	216	23	all	all	DET
ejpam-5493	216	24	r	r	PROPN
ejpam-5493	216	25	∈	∈	PROPN
ejpam-5493	216	26	r.	r.	NOUN
ejpam-5493	216	27	then	then	ADV
ejpam-5493	216	28	,	,	PUNCT
ejpam-5493	216	29	t	t	PROPN
ejpam-5493	216	30	(	(	PUNCT
ejpam-5493	216	31	r	r	NOUN
ejpam-5493	216	32	+	+	NUM
ejpam-5493	216	33	s	s	X
ejpam-5493	216	34	)	)	PUNCT
ejpam-5493	216	35	=	=	PUNCT
ejpam-5493	217	1	h(iv(r	h(iv(r	PROPN
ejpam-5493	217	2	+	+	NUM
ejpam-5493	217	3	s	s	NOUN
ejpam-5493	217	4	)	)	PUNCT
ejpam-5493	217	5	)	)	PUNCT
ejpam-5493	218	1	=	=	SYM
ejpam-5493	218	2	h(iv(r	h(iv(r	PROPN
ejpam-5493	218	3	)	)	PUNCT
ejpam-5493	218	4	+	+	NUM
ejpam-5493	218	5	iv(s	iv(s	NUM
ejpam-5493	218	6	)	)	PUNCT
ejpam-5493	218	7	)	)	PUNCT
ejpam-5493	219	1	=	=	PUNCT
ejpam-5493	219	2	h(iv(r	h(iv(r	NOUN
ejpam-5493	219	3	)	)	PUNCT
ejpam-5493	219	4	)	)	PUNCT
ejpam-5493	220	1	+	+	PROPN
ejpam-5493	220	2	h(iv(s	h(iv(s	NOUN
ejpam-5493	220	3	)	)	PUNCT
ejpam-5493	220	4	)	)	PUNCT
ejpam-5493	221	1	=	=	SYM
ejpam-5493	221	2	t	t	PROPN
ejpam-5493	221	3	(	(	PUNCT
ejpam-5493	221	4	r	r	NOUN
ejpam-5493	221	5	)	)	PUNCT
ejpam-5493	221	6	+	+	NOUN
ejpam-5493	221	7	t	t	PROPN
ejpam-5493	221	8	(	(	PUNCT
ejpam-5493	221	9	s	s	NOUN
ejpam-5493	221	10	)	)	PUNCT
ejpam-5493	221	11	for	for	ADP
ejpam-5493	221	12	every	every	DET
ejpam-5493	221	13	r	r	NOUN
ejpam-5493	221	14	,	,	PUNCT
ejpam-5493	221	15	s	s	PROPN
ejpam-5493	221	16	∈	∈	PROPN
ejpam-5493	221	17	r.	r.	PROPN
ejpam-5493	221	18	therefore	therefore	ADV
ejpam-5493	221	19	,	,	PUNCT
ejpam-5493	221	20	t	t	PROPN
ejpam-5493	221	21	is	be	AUX
ejpam-5493	221	22	an	an	DET
ejpam-5493	221	23	additive	additive	ADJ
ejpam-5493	221	24	mapping	mapping	NOUN
ejpam-5493	221	25	on	on	ADP
ejpam-5493	221	26	r.	r.	PROPN
ejpam-5493	221	27	now	now	ADV
ejpam-5493	221	28	,	,	PUNCT
ejpam-5493	221	29	consider	consider	VERB
ejpam-5493	221	30	3	3	NUM
ejpam-5493	221	31	t	t	NOUN
ejpam-5493	221	32	(	(	PUNCT
ejpam-5493	221	33	r3p	r3p	NOUN
ejpam-5493	221	34	)	)	PUNCT
ejpam-5493	221	35	=	=	SYM
ejpam-5493	221	36	3h(iv((r	3h(iv((r	NUM
ejpam-5493	221	37	3p	3p	NUM
ejpam-5493	221	38	)	)	PUNCT
ejpam-5493	221	39	)	)	PUNCT
ejpam-5493	222	1	=	=	SYM
ejpam-5493	222	2	h((iv(r	h((iv(r	NOUN
ejpam-5493	222	3	)	)	PUNCT
ejpam-5493	222	4	)	)	PUNCT
ejpam-5493	223	1	p)φ((r)2p	p)φ((r)2p	NOUN
ejpam-5493	223	2	)	)	PUNCT
ejpam-5493	224	1	+	+	CCONJ
ejpam-5493	224	2	φ((r)p)h((iv(r	φ((r)p)h((iv(r	ADJ
ejpam-5493	224	3	)	)	PUNCT
ejpam-5493	224	4	)	)	PUNCT
ejpam-5493	224	5	p)φ((r)p	p)φ((r)p	PROPN
ejpam-5493	224	6	)	)	PUNCT
ejpam-5493	224	7	+	+	CCONJ
ejpam-5493	224	8	φ((r)2p)h(iv(r	φ((r)2p)h(iv(r	NOUN
ejpam-5493	224	9	)	)	PUNCT
ejpam-5493	224	10	)	)	PUNCT
ejpam-5493	225	1	=	=	SYM
ejpam-5493	225	2	t	t	PROPN
ejpam-5493	225	3	(	(	PUNCT
ejpam-5493	225	4	rp)φ(r2p	rp)φ(r2p	PROPN
ejpam-5493	225	5	)	)	PUNCT
ejpam-5493	225	6	+	+	CCONJ
ejpam-5493	225	7	φ(rp)t	φ(rp)t	PROPN
ejpam-5493	225	8	(	(	PUNCT
ejpam-5493	225	9	rp)φ(rp	rp)φ(rp	PROPN
ejpam-5493	225	10	)	)	PUNCT
ejpam-5493	225	11	+	+	NUM
ejpam-5493	225	12	φ(r2p)t	φ(r2p)t	PROPN
ejpam-5493	225	13	(	(	PUNCT
ejpam-5493	225	14	rp	rp	NOUN
ejpam-5493	225	15	)	)	PUNCT
ejpam-5493	225	16	for	for	ADP
ejpam-5493	225	17	all	all	DET
ejpam-5493	225	18	r	r	NOUN
ejpam-5493	225	19	,	,	PUNCT
ejpam-5493	225	20	t	t	PROPN
ejpam-5493	225	21	∈	∈	PROPN
ejpam-5493	225	22	r.	r.	PROPN
ejpam-5493	225	23	a.	a.	PROPN
ejpam-5493	225	24	z.	z.	PROPN
ejpam-5493	225	25	ansari	ansari	PROPN
ejpam-5493	225	26	et	et	PROPN
ejpam-5493	225	27	al	al	PROPN
ejpam-5493	225	28	.	.	PUNCT
ejpam-5493	225	29	/	/	SYM
ejpam-5493	225	30	eur	eur	PROPN
ejpam-5493	225	31	.	.	PUNCT
ejpam-5493	226	1	j.	j.	PROPN
ejpam-5493	226	2	pure	pure	PROPN
ejpam-5493	226	3	appl	appl	PROPN
ejpam-5493	226	4	.	.	PROPN
ejpam-5493	226	5	math	math	PROPN
ejpam-5493	226	6	,	,	PUNCT
ejpam-5493	226	7	18	18	NUM
ejpam-5493	226	8	(	(	PUNCT
ejpam-5493	226	9	1	1	NUM
ejpam-5493	226	10	)	)	PUNCT
ejpam-5493	226	11	(	(	PUNCT
ejpam-5493	226	12	2025	2025	NUM
ejpam-5493	226	13	)	)	PUNCT
ejpam-5493	226	14	,	,	PUNCT
ejpam-5493	226	15	5493	5493	NUM
ejpam-5493	226	16	9	9	NUM
ejpam-5493	226	17	of	of	ADP
ejpam-5493	226	18	10	10	NUM
ejpam-5493	226	19	use	use	NOUN
ejpam-5493	226	20	first	first	ADJ
ejpam-5493	226	21	theorem	theorem	NOUN
ejpam-5493	226	22	of	of	ADP
ejpam-5493	226	23	the	the	DET
ejpam-5493	226	24	last	last	ADJ
ejpam-5493	226	25	section	section	NOUN
ejpam-5493	226	26	to	to	PART
ejpam-5493	226	27	find	find	VERB
ejpam-5493	226	28	that	that	SCONJ
ejpam-5493	226	29	t	t	PROPN
ejpam-5493	226	30	is	be	AUX
ejpam-5493	226	31	a	a	DET
ejpam-5493	226	32	φ	φ	NOUN
ejpam-5493	226	33	-	-	PUNCT
ejpam-5493	226	34	centralizer	centralizer	NOUN
ejpam-5493	226	35	on	on	ADP
ejpam-5493	226	36	r.	r.	PROPN
ejpam-5493	226	37	hence	hence	ADV
ejpam-5493	226	38	,	,	PUNCT
ejpam-5493	226	39	h(r2	h(r2	NOUN
ejpam-5493	226	40	)	)	PUNCT
ejpam-5493	226	41	=	=	X
ejpam-5493	226	42	h(iv(iv(r	h(iv(iv(r	ADJ
ejpam-5493	226	43	2	2	NUM
ejpam-5493	226	44	)	)	PUNCT
ejpam-5493	226	45	)	)	PUNCT
ejpam-5493	227	1	=	=	SYM
ejpam-5493	227	2	t	t	PROPN
ejpam-5493	227	3	(	(	PUNCT
ejpam-5493	227	4	iv(r	iv(r	NUM
ejpam-5493	227	5	2	2	X
ejpam-5493	227	6	)	)	PUNCT
ejpam-5493	227	7	=	=	SYM
ejpam-5493	227	8	t	t	PROPN
ejpam-5493	227	9	(	(	PUNCT
ejpam-5493	227	10	iv(r)iv(r	iv(r)iv(r	PROPN
ejpam-5493	227	11	)	)	PUNCT
ejpam-5493	227	12	)	)	PUNCT
ejpam-5493	228	1	=	=	SYM
ejpam-5493	228	2	t	t	PROPN
ejpam-5493	228	3	(	(	PUNCT
ejpam-5493	228	4	iv(r))φ(iv(r	iv(r))φ(iv(r	NOUN
ejpam-5493	228	5	)	)	PUNCT
ejpam-5493	228	6	)	)	PUNCT
ejpam-5493	228	7	,	,	PUNCT
ejpam-5493	228	8	as	as	SCONJ
ejpam-5493	228	9	t	t	PROPN
ejpam-5493	228	10	is	be	AUX
ejpam-5493	228	11	a	a	DET
ejpam-5493	228	12	φ	φ	NOUN
ejpam-5493	228	13	-	-	PUNCT
ejpam-5493	228	14	centralizer	centralizer	NOUN
ejpam-5493	228	15	on	on	ADP
ejpam-5493	228	16	r	r	NOUN
ejpam-5493	228	17	=	=	SYM
ejpam-5493	228	18	h(r)φ(iv(r	h(r)φ(iv(r	NOUN
ejpam-5493	228	19	)	)	PUNCT
ejpam-5493	228	20	)	)	PUNCT
ejpam-5493	229	1	this	this	PRON
ejpam-5493	229	2	implies	imply	VERB
ejpam-5493	229	3	that	that	SCONJ
ejpam-5493	229	4	h	h	NOUN
ejpam-5493	229	5	is	be	AUX
ejpam-5493	229	6	a	a	DET
ejpam-5493	229	7	jordan	jordan	PROPN
ejpam-5493	229	8	left	leave	VERB
ejpam-5493	229	9	φ	φ	PROPN
ejpam-5493	229	10	-	-	PUNCT
ejpam-5493	229	11	iv	iv	ADP
ejpam-5493	229	12	-	-	PUNCT
ejpam-5493	229	13	centralizer	centralizer	NOUN
ejpam-5493	229	14	on	on	ADP
ejpam-5493	229	15	r.	r.	PROPN
ejpam-5493	229	16	similarly	similarly	ADV
ejpam-5493	229	17	,	,	PUNCT
ejpam-5493	229	18	we	we	PRON
ejpam-5493	229	19	can	can	AUX
ejpam-5493	229	20	prove	prove	VERB
ejpam-5493	229	21	that	that	SCONJ
ejpam-5493	229	22	h	h	NOUN
ejpam-5493	229	23	is	be	AUX
ejpam-5493	229	24	a	a	DET
ejpam-5493	229	25	jordan	jordan	PROPN
ejpam-5493	229	26	right	right	PROPN
ejpam-5493	229	27	φ	φ	PROPN
ejpam-5493	229	28	-	-	PUNCT
ejpam-5493	229	29	iv	iv	ADP
ejpam-5493	229	30	-	-	PUNCT
ejpam-5493	229	31	centralizer	centralizer	NOUN
ejpam-5493	229	32	on	on	ADP
ejpam-5493	229	33	r.	r.	PROPN
ejpam-5493	229	34	now	now	ADV
ejpam-5493	229	35	,	,	PUNCT
ejpam-5493	229	36	combine	combine	VERB
ejpam-5493	229	37	and	and	CCONJ
ejpam-5493	229	38	use	use	VERB
ejpam-5493	229	39	lemma	lemma	PROPN
ejpam-5493	229	40	2	2	NUM
ejpam-5493	229	41	to	to	PART
ejpam-5493	229	42	obtain	obtain	VERB
ejpam-5493	229	43	the	the	DET
ejpam-5493	229	44	required	required	ADJ
ejpam-5493	229	45	conclusion	conclusion	NOUN
ejpam-5493	229	46	.	.	PUNCT
ejpam-5493	230	1	using	use	VERB
ejpam-5493	230	2	same	same	ADJ
ejpam-5493	230	3	technique	technique	NOUN
ejpam-5493	230	4	,	,	PUNCT
ejpam-5493	230	5	we	we	PRON
ejpam-5493	230	6	can	can	AUX
ejpam-5493	230	7	get	get	VERB
ejpam-5493	230	8	proof	proof	NOUN
ejpam-5493	230	9	of	of	ADP
ejpam-5493	230	10	(	(	PUNCT
ejpam-5493	230	11	ii	ii	NOUN
ejpam-5493	230	12	)	)	PUNCT
ejpam-5493	230	13	and	and	CCONJ
ejpam-5493	230	14	(	(	PUNCT
ejpam-5493	230	15	iii	iii	NOUN
ejpam-5493	230	16	)	)	PUNCT
ejpam-5493	230	17	part	part	NOUN
ejpam-5493	230	18	.	.	PUNCT
ejpam-5493	231	1	example	example	NOUN
ejpam-5493	232	1	2	2	NUM
ejpam-5493	232	2	.	.	PUNCT
ejpam-5493	232	3	let	let	VERB
ejpam-5493	232	4	r	r	NOUN
ejpam-5493	232	5	=	=	PRON
ejpam-5493	232	6	{	{	PUNCT
ejpam-5493	232	7	(	(	PUNCT
ejpam-5493	232	8	z1	z1	NOUN
ejpam-5493	232	9	0	0	NUM
ejpam-5493	232	10	0	0	NUM
ejpam-5493	232	11	z2	z2	PROPN
ejpam-5493	232	12	)	)	PUNCT
ejpam-5493	232	13	|	|	ADV
ejpam-5493	232	14	z1	z1	VERB
ejpam-5493	232	15	,	,	PUNCT
ejpam-5493	232	16	z2	z2	PROPN
ejpam-5493	232	17	∈	∈	PROPN
ejpam-5493	232	18	2z8	2z8	NUM
ejpam-5493	232	19	}	}	PUNCT
ejpam-5493	232	20	is	be	AUX
ejpam-5493	232	21	a	a	DET
ejpam-5493	232	22	ring	ring	NOUN
ejpam-5493	232	23	with	with	ADP
ejpam-5493	232	24	involution	involution	NOUN
ejpam-5493	232	25	iv	iv	ADP
ejpam-5493	232	26	:	:	PUNCT
ejpam-5493	232	27	r	r	NOUN
ejpam-5493	232	28	→	→	SYM
ejpam-5493	232	29	r	r	NOUN
ejpam-5493	232	30	by	by	ADP
ejpam-5493	232	31	iv(r	iv(r	NUM
ejpam-5493	232	32	)	)	PUNCT
ejpam-5493	232	33	=	=	PUNCT
ejpam-5493	232	34	(	(	PUNCT
ejpam-5493	232	35	z2	z2	NOUN
ejpam-5493	232	36	0	0	NUM
ejpam-5493	232	37	0	0	NUM
ejpam-5493	232	38	z1	z1	PROPN
ejpam-5493	232	39	)	)	PUNCT
ejpam-5493	232	40	,	,	PUNCT
ejpam-5493	232	41	where	where	SCONJ
ejpam-5493	232	42	z8	z8	NOUN
ejpam-5493	232	43	signifies	signify	VERB
ejpam-5493	232	44	what	what	PRON
ejpam-5493	232	45	it	it	PRON
ejpam-5493	232	46	normally	normally	ADV
ejpam-5493	232	47	does	do	VERB
ejpam-5493	232	48	.	.	PUNCT
ejpam-5493	233	1	define	define	VERB
ejpam-5493	233	2	mappings	mapping	NOUN
ejpam-5493	233	3	h	h	NOUN
ejpam-5493	233	4	,	,	PUNCT
ejpam-5493	233	5	φ	φ	X
ejpam-5493	233	6	:	:	PUNCT
ejpam-5493	233	7	r	r	NOUN
ejpam-5493	233	8	→	→	SYM
ejpam-5493	233	9	r	r	NOUN
ejpam-5493	233	10	by	by	ADP
ejpam-5493	233	11	h(r	h(r	NOUN
ejpam-5493	233	12	)	)	PUNCT
ejpam-5493	233	13	=	=	PUNCT
ejpam-5493	234	1	(	(	PUNCT
ejpam-5493	234	2	0	0	NUM
ejpam-5493	234	3	0	0	NUM
ejpam-5493	234	4	0	0	NUM
ejpam-5493	234	5	z2	z2	PROPN
ejpam-5493	234	6	)	)	PUNCT
ejpam-5493	234	7	and	and	CCONJ
ejpam-5493	234	8	ϕ(r	ϕ(r	PROPN
ejpam-5493	234	9	)	)	PUNCT
ejpam-5493	235	1	=	=	PRON
ejpam-5493	235	2	(	(	PUNCT
ejpam-5493	235	3	2z2	2z2	NUM
ejpam-5493	235	4	0	0	NUM
ejpam-5493	235	5	0	0	NUM
ejpam-5493	235	6	2z1	2z1	NUM
ejpam-5493	235	7	)	)	PUNCT
ejpam-5493	236	1	for	for	ADP
ejpam-5493	236	2	all	all	DET
ejpam-5493	236	3	r	r	PROPN
ejpam-5493	236	4	∈	∈	PROPN
ejpam-5493	236	5	r.	r.	NOUN
ejpam-5493	236	6	it	it	PRON
ejpam-5493	236	7	is	be	AUX
ejpam-5493	236	8	clear	clear	ADJ
ejpam-5493	236	9	that	that	SCONJ
ejpam-5493	236	10	h	h	NOUN
ejpam-5493	236	11	satisfy	satisfy	VERB
ejpam-5493	236	12	the	the	DET
ejpam-5493	236	13	identities	identity	NOUN
ejpam-5493	236	14	in	in	ADP
ejpam-5493	236	15	theorem	theorem	ADJ
ejpam-5493	236	16	4	4	NUM
ejpam-5493	236	17	(	(	PUNCT
ejpam-5493	236	18	(	(	PUNCT
ejpam-5493	236	19	ii	ii	NOUN
ejpam-5493	236	20	)	)	PUNCT
ejpam-5493	236	21	p	p	NOUN
ejpam-5493	236	22	>	>	X
ejpam-5493	236	23	1	1	NUM
ejpam-5493	236	24	)	)	PUNCT
ejpam-5493	236	25	and	and	CCONJ
ejpam-5493	236	26	r	r	NOUN
ejpam-5493	236	27	is	be	AUX
ejpam-5493	236	28	neither	neither	CCONJ
ejpam-5493	236	29	a	a	DET
ejpam-5493	236	30	2	2	NUM
ejpam-5493	236	31	-	-	PUNCT
ejpam-5493	236	32	torsion	torsion	NOUN
ejpam-5493	236	33	free	free	ADJ
ejpam-5493	236	34	semiprime	semiprime	NOUN
ejpam-5493	236	35	ring	ring	NOUN
ejpam-5493	236	36	nor	nor	CCONJ
ejpam-5493	236	37	h	h	NOUN
ejpam-5493	236	38	is	be	AUX
ejpam-5493	236	39	a	a	DET
ejpam-5493	236	40	φ	φ	PROPN
ejpam-5493	236	41	-	-	PUNCT
ejpam-5493	236	42	iv	iv	NOUN
ejpam-5493	236	43	-	-	PUNCT
ejpam-5493	236	44	centralizer	centralizer	NOUN
ejpam-5493	236	45	on	on	ADP
ejpam-5493	236	46	r	r	NOUN
ejpam-5493	236	47	,	,	PUNCT
ejpam-5493	236	48	hence	hence	ADV
ejpam-5493	236	49	semiprimeness	semiprimeness	NOUN
ejpam-5493	236	50	hypothesis	hypothesis	NOUN
ejpam-5493	236	51	is	be	AUX
ejpam-5493	236	52	crucial	crucial	ADJ
ejpam-5493	236	53	for	for	ADP
ejpam-5493	236	54	theorem	theorem	ADJ
ejpam-5493	236	55	4	4	NUM
ejpam-5493	236	56	.	.	NOUN
ejpam-5493	236	57	4	4	NUM
ejpam-5493	236	58	.	.	X
ejpam-5493	236	59	conclusion	conclusion	NOUN
ejpam-5493	236	60	we	we	PRON
ejpam-5493	236	61	explore	explore	VERB
ejpam-5493	236	62	φ	φ	NOUN
ejpam-5493	236	63	-	-	PUNCT
ejpam-5493	236	64	centralizer	centralizer	NOUN
ejpam-5493	236	65	on	on	ADP
ejpam-5493	236	66	rings	ring	NOUN
ejpam-5493	236	67	and	and	CCONJ
ejpam-5493	236	68	φ	φ	NUM
ejpam-5493	236	69	-	-	PUNCT
ejpam-5493	236	70	iv	iv	NOUN
ejpam-5493	236	71	-	-	PUNCT
ejpam-5493	236	72	centralizer	centralizer	NOUN
ejpam-5493	236	73	on	on	ADP
ejpam-5493	236	74	rings	ring	NOUN
ejpam-5493	236	75	with	with	ADP
ejpam-5493	236	76	involution	involution	NOUN
ejpam-5493	236	77	in	in	ADP
ejpam-5493	236	78	depth	depth	NOUN
ejpam-5493	236	79	,	,	PUNCT
ejpam-5493	236	80	which	which	PRON
ejpam-5493	236	81	is	be	AUX
ejpam-5493	236	82	an	an	DET
ejpam-5493	236	83	intriguing	intriguing	ADJ
ejpam-5493	236	84	topic	topic	NOUN
ejpam-5493	236	85	.	.	PUNCT
ejpam-5493	237	1	obtaining	obtain	VERB
ejpam-5493	237	2	continuity	continuity	NOUN
ejpam-5493	237	3	theorems	theorem	NOUN
ejpam-5493	237	4	on	on	ADP
ejpam-5493	237	5	other	other	ADJ
ejpam-5493	237	6	algebraic	algebraic	ADJ
ejpam-5493	237	7	structures	structure	NOUN
ejpam-5493	237	8	,	,	PUNCT
ejpam-5493	237	9	such	such	ADJ
ejpam-5493	237	10	as	as	ADP
ejpam-5493	237	11	banach	banach	NOUN
ejpam-5493	237	12	algebra	algebra	NOUN
ejpam-5493	237	13	,	,	PUNCT
ejpam-5493	237	14	semi	semi	ADJ
ejpam-5493	237	15	-	-	ADJ
ejpam-5493	237	16	simple	simple	ADJ
ejpam-5493	237	17	banach	banach	NOUN
ejpam-5493	237	18	algebra	algebra	NOUN
ejpam-5493	237	19	,	,	PUNCT
ejpam-5493	237	20	lie	lie	NOUN
ejpam-5493	237	21	algebra	algebra	NOUN
ejpam-5493	237	22	,	,	PUNCT
ejpam-5493	237	23	c∗	c∗	PROPN
ejpam-5493	237	24	algebra	algebra	PROPN
ejpam-5493	237	25	,	,	PUNCT
ejpam-5493	237	26	etc	etc	X
ejpam-5493	237	27	.	.	X
ejpam-5493	237	28	,	,	PUNCT
ejpam-5493	237	29	is	be	AUX
ejpam-5493	237	30	the	the	DET
ejpam-5493	237	31	area	area	NOUN
ejpam-5493	237	32	of	of	ADP
ejpam-5493	237	33	future	future	ADJ
ejpam-5493	237	34	study	study	NOUN
ejpam-5493	237	35	in	in	ADP
ejpam-5493	237	36	the	the	DET
ejpam-5493	237	37	framework	framework	NOUN
ejpam-5493	237	38	of	of	ADP
ejpam-5493	237	39	the	the	DET
ejpam-5493	237	40	provided	provide	VERB
ejpam-5493	237	41	research	research	NOUN
ejpam-5493	237	42	.	.	PUNCT
ejpam-5493	238	1	it	it	PRON
ejpam-5493	238	2	would	would	AUX
ejpam-5493	238	3	be	be	AUX
ejpam-5493	238	4	fascinating	fascinating	ADJ
ejpam-5493	238	5	to	to	PART
ejpam-5493	238	6	view	view	VERB
ejpam-5493	238	7	our	our	PRON
ejpam-5493	238	8	concept	concept	NOUN
ejpam-5493	238	9	in	in	ADP
ejpam-5493	238	10	the	the	DET
ejpam-5493	238	11	context	context	NOUN
ejpam-5493	238	12	of	of	ADP
ejpam-5493	238	13	[	[	X
ejpam-5493	238	14	13	13	NUM
ejpam-5493	238	15	]	]	PUNCT
ejpam-5493	238	16	with	with	ADP
ejpam-5493	238	17	the	the	DET
ejpam-5493	238	18	aid	aid	NOUN
ejpam-5493	238	19	of	of	ADP
ejpam-5493	238	20	algebra	algebra	NOUN
ejpam-5493	238	21	of	of	ADP
ejpam-5493	238	22	linear	linear	PROPN
ejpam-5493	238	23	operators	operator	NOUN
ejpam-5493	238	24	(	(	PUNCT
ejpam-5493	238	25	transformations	transformation	NOUN
ejpam-5493	238	26	)	)	PUNCT
ejpam-5493	238	27	.	.	PUNCT
ejpam-5493	239	1	it	it	PRON
ejpam-5493	239	2	is	be	AUX
ejpam-5493	239	3	also	also	ADV
ejpam-5493	239	4	interesting	interesting	ADJ
ejpam-5493	239	5	that	that	SCONJ
ejpam-5493	239	6	the	the	DET
ejpam-5493	239	7	reader	reader	NOUN
ejpam-5493	239	8	can	can	AUX
ejpam-5493	239	9	consider	consider	VERB
ejpam-5493	239	10	various	various	ADJ
ejpam-5493	239	11	functional	functional	ADJ
ejpam-5493	239	12	identities	identity	NOUN
ejpam-5493	239	13	involving	involve	VERB
ejpam-5493	239	14	specific	specific	ADJ
ejpam-5493	239	15	sorts	sort	NOUN
ejpam-5493	239	16	of	of	ADP
ejpam-5493	239	17	derivations	derivation	NOUN
ejpam-5493	239	18	,	,	PUNCT
ejpam-5493	239	19	such	such	ADJ
ejpam-5493	239	20	as	as	ADP
ejpam-5493	239	21	generalized	generalized	ADJ
ejpam-5493	239	22	(	(	PUNCT
ejpam-5493	239	23	α	α	NOUN
ejpam-5493	239	24	,	,	PUNCT
ejpam-5493	239	25	β)-derivations	β)-derivations	PROPN
ejpam-5493	239	26	on	on	ADP
ejpam-5493	239	27	semiprime	semiprime	NOUN
ejpam-5493	239	28	rings	ring	NOUN
ejpam-5493	239	29	with	with	ADP
ejpam-5493	239	30	involution	involution	NOUN
ejpam-5493	239	31	and	and	CCONJ
ejpam-5493	239	32	generalized	generalize	VERB
ejpam-5493	239	33	(	(	PUNCT
ejpam-5493	239	34	α	α	NOUN
ejpam-5493	239	35	,	,	PUNCT
ejpam-5493	239	36	β)-higher	β)-higher	ADP
ejpam-5493	239	37	derivations	derivation	NOUN
ejpam-5493	239	38	.	.	PUNCT
ejpam-5493	240	1	the	the	DET
ejpam-5493	240	2	forms	form	NOUN
ejpam-5493	240	3	of	of	ADP
ejpam-5493	240	4	additive	additive	ADJ
ejpam-5493	240	5	maps	map	NOUN
ejpam-5493	240	6	applying	apply	VERB
ejpam-5493	240	7	to	to	ADP
ejpam-5493	240	8	rings	ring	NOUN
ejpam-5493	240	9	and	and	CCONJ
ejpam-5493	240	10	their	their	PRON
ejpam-5493	240	11	corresponding	correspond	VERB
ejpam-5493	240	12	subsets	subset	NOUN
ejpam-5493	240	13	have	have	AUX
ejpam-5493	240	14	been	be	AUX
ejpam-5493	240	15	described	describe	VERB
ejpam-5493	240	16	using	use	VERB
ejpam-5493	240	17	just	just	ADV
ejpam-5493	240	18	algebraic	algebraic	ADJ
ejpam-5493	240	19	techniques	technique	NOUN
ejpam-5493	240	20	.	.	PUNCT
ejpam-5493	241	1	competing	compete	VERB
ejpam-5493	241	2	interests	interest	NOUN
ejpam-5493	241	3	regarding	regard	VERB
ejpam-5493	241	4	the	the	DET
ejpam-5493	241	5	publication	publication	NOUN
ejpam-5493	241	6	of	of	ADP
ejpam-5493	241	7	this	this	DET
ejpam-5493	241	8	work	work	NOUN
ejpam-5493	241	9	,	,	PUNCT
ejpam-5493	241	10	the	the	DET
ejpam-5493	241	11	authors	author	NOUN
ejpam-5493	241	12	affirm	affirm	VERB
ejpam-5493	241	13	that	that	SCONJ
ejpam-5493	241	14	they	they	PRON
ejpam-5493	241	15	have	have	VERB
ejpam-5493	241	16	no	no	DET
ejpam-5493	241	17	conflicts	conflict	NOUN
ejpam-5493	241	18	of	of	ADP
ejpam-5493	241	19	interest	interest	NOUN
ejpam-5493	241	20	.	.	PUNCT
ejpam-5493	242	1	a.	a.	NOUN
ejpam-5493	242	2	z.	z.	PROPN
ejpam-5493	242	3	ansari	ansari	PROPN
ejpam-5493	242	4	et	et	PROPN
ejpam-5493	242	5	al	al	PROPN
ejpam-5493	242	6	.	.	PUNCT
ejpam-5493	242	7	/	/	SYM
ejpam-5493	242	8	eur	eur	PROPN
ejpam-5493	242	9	.	.	PUNCT
ejpam-5493	243	1	j.	j.	PROPN
ejpam-5493	243	2	pure	pure	PROPN
ejpam-5493	243	3	appl	appl	PROPN
ejpam-5493	243	4	.	.	PROPN
ejpam-5493	243	5	math	math	PROPN
ejpam-5493	243	6	,	,	PUNCT
ejpam-5493	243	7	18	18	NUM
ejpam-5493	243	8	(	(	PUNCT
ejpam-5493	243	9	1	1	NUM
ejpam-5493	243	10	)	)	PUNCT
ejpam-5493	243	11	(	(	PUNCT
ejpam-5493	243	12	2025	2025	NUM
ejpam-5493	243	13	)	)	PUNCT
ejpam-5493	243	14	,	,	PUNCT
ejpam-5493	243	15	5493	5493	NUM
ejpam-5493	243	16	10	10	NUM
ejpam-5493	243	17	of	of	ADP
ejpam-5493	243	18	10	10	NUM
ejpam-5493	243	19	acknowledgements	acknowledgement	NOUN
ejpam-5493	243	20	the	the	DET
ejpam-5493	243	21	authors	author	NOUN
ejpam-5493	243	22	are	be	AUX
ejpam-5493	243	23	extremely	extremely	ADV
ejpam-5493	243	24	grateful	grateful	ADJ
ejpam-5493	243	25	to	to	ADP
ejpam-5493	243	26	the	the	DET
ejpam-5493	243	27	reviewers	reviewer	NOUN
ejpam-5493	243	28	and	and	CCONJ
ejpam-5493	243	29	editor	editor	NOUN
ejpam-5493	243	30	for	for	ADP
ejpam-5493	243	31	their	their	PRON
ejpam-5493	243	32	generous	generous	ADJ
ejpam-5493	243	33	suggestions	suggestion	NOUN
ejpam-5493	243	34	,	,	PUNCT
ejpam-5493	243	35	insightful	insightful	ADJ
ejpam-5493	243	36	remarks	remark	NOUN
ejpam-5493	243	37	and	and	CCONJ
ejpam-5493	243	38	recommendations	recommendation	NOUN
ejpam-5493	243	39	to	to	PART
ejpam-5493	243	40	make	make	VERB
ejpam-5493	243	41	this	this	DET
ejpam-5493	243	42	manuscript	manuscript	NOUN
ejpam-5493	243	43	well	well	ADV
ejpam-5493	243	44	organized	organized	ADJ
ejpam-5493	243	45	.	.	PUNCT
ejpam-5493	244	1	authors	author	NOUN
ejpam-5493	244	2	extend	extend	VERB
ejpam-5493	244	3	their	their	PRON
ejpam-5493	244	4	gratitude	gratitude	NOUN
ejpam-5493	244	5	to	to	ADP
ejpam-5493	244	6	the	the	DET
ejpam-5493	244	7	deanship	deanship	NOUN
ejpam-5493	244	8	of	of	ADP
ejpam-5493	244	9	higher	high	ADJ
ejpam-5493	244	10	education	education	NOUN
ejpam-5493	244	11	and	and	CCONJ
ejpam-5493	244	12	scientific	scientific	ADJ
ejpam-5493	244	13	research	research	NOUN
ejpam-5493	244	14	at	at	ADP
ejpam-5493	244	15	the	the	DET
ejpam-5493	244	16	islamic	islamic	PROPN
ejpam-5493	244	17	university	university	PROPN
ejpam-5493	244	18	of	of	ADP
ejpam-5493	244	19	madinah	madinah	PROPN
ejpam-5493	244	20	for	for	ADP
ejpam-5493	244	21	the	the	DET
ejpam-5493	244	22	support	support	NOUN
ejpam-5493	244	23	provided	provide	VERB
ejpam-5493	244	24	to	to	ADP
ejpam-5493	244	25	the	the	DET
ejpam-5493	244	26	postpublishing	postpublishe	VERB
ejpam-5493	244	27	program	program	NOUN
ejpam-5493	244	28	.	.	PUNCT
ejpam-5493	245	1	references	reference	NOUN
ejpam-5493	245	2	[	[	X
ejpam-5493	245	3	1	1	NUM
ejpam-5493	245	4	]	]	PUNCT
ejpam-5493	245	5	e	e	X
ejpam-5493	245	6	albas	albas	PROPN
ejpam-5493	245	7	.	.	PUNCT
ejpam-5493	246	1	on	on	ADP
ejpam-5493	246	2	ϕ-centralizers	ϕ-centralizer	NOUN
ejpam-5493	246	3	of	of	ADP
ejpam-5493	246	4	semiprime	semiprime	NOUN
ejpam-5493	246	5	rings	ring	NOUN
ejpam-5493	246	6	.	.	PUNCT
ejpam-5493	247	1	siberian	siberian	ADJ
ejpam-5493	247	2	math	math	PROPN
ejpam-5493	247	3	.	.	PUNCT
ejpam-5493	248	1	j.	j.	PROPN
ejpam-5493	248	2	,	,	PUNCT
ejpam-5493	248	3	48(2):191–196	48(2):191–196	PROPN
ejpam-5493	248	4	,	,	PUNCT
ejpam-5493	248	5	2007	2007	NUM
ejpam-5493	248	6	.	.	PUNCT
ejpam-5493	249	1	[	[	X
ejpam-5493	249	2	2	2	X
ejpam-5493	249	3	]	]	PUNCT
ejpam-5493	249	4	a	a	DET
ejpam-5493	249	5	z	z	NOUN
ejpam-5493	249	6	ansari	ansari	NOUN
ejpam-5493	249	7	and	and	CCONJ
ejpam-5493	249	8	f	f	PROPN
ejpam-5493	249	9	shujat	shujat	PROPN
ejpam-5493	249	10	.	.	PUNCT
ejpam-5493	250	1	jordan	jordan	PROPN
ejpam-5493	250	2	∗-derivations	∗-derivations	PROPN
ejpam-5493	250	3	on	on	ADP
ejpam-5493	250	4	standard	standard	ADJ
ejpam-5493	250	5	operator	operator	NOUN
ejpam-5493	250	6	algebras	algebra	NOUN
ejpam-5493	250	7	.	.	PUNCT
ejpam-5493	251	1	filomat	filomat	PROPN
ejpam-5493	251	2	,	,	PUNCT
ejpam-5493	251	3	37(1):37–41	37(1):37–41	NUM
ejpam-5493	251	4	,	,	PUNCT
ejpam-5493	251	5	2023	2023	NUM
ejpam-5493	251	6	.	.	PUNCT
ejpam-5493	252	1	[	[	X
ejpam-5493	252	2	3	3	X
ejpam-5493	252	3	]	]	PUNCT
ejpam-5493	252	4	m	m	NOUN
ejpam-5493	252	5	ashraf	ashraf	NOUN
ejpam-5493	252	6	and	and	CCONJ
ejpam-5493	252	7	m	m	VERB
ejpam-5493	252	8	r	r	NOUN
ejpam-5493	252	9	mozumder	mozumder	NOUN
ejpam-5493	252	10	.	.	PUNCT
ejpam-5493	253	1	on	on	ADP
ejpam-5493	253	2	jordan	jordan	PROPN
ejpam-5493	253	3	α-∗-centralizers	α-∗-centralizers	PROPN
ejpam-5493	253	4	in	in	ADP
ejpam-5493	253	5	semiprime	semiprime	NOUN
ejpam-5493	253	6	rings	ring	NOUN
ejpam-5493	253	7	with	with	ADP
ejpam-5493	253	8	involution	involution	NOUN
ejpam-5493	253	9	.	.	PUNCT
ejpam-5493	254	1	int	int	NOUN
ejpam-5493	254	2	.	.	PUNCT
ejpam-5493	255	1	j.	j.	PROPN
ejpam-5493	255	2	contemp	contemp	PROPN
ejpam-5493	255	3	.	.	PUNCT
ejpam-5493	256	1	math	math	NOUN
ejpam-5493	256	2	.	.	PUNCT
ejpam-5493	257	1	sciences	science	NOUN
ejpam-5493	257	2	,	,	PUNCT
ejpam-5493	257	3	7(23):1103–111	7(23):1103–111	NOUN
ejpam-5493	257	4	,	,	PUNCT
ejpam-5493	257	5	2012	2012	NUM
ejpam-5493	257	6	.	.	PUNCT
ejpam-5493	258	1	[	[	X
ejpam-5493	258	2	4	4	NUM
ejpam-5493	258	3	]	]	X
ejpam-5493	258	4	m	m	VERB
ejpam-5493	258	5	n	n	ADV
ejpam-5493	258	6	daif	daif	NOUN
ejpam-5493	258	7	and	and	CCONJ
ejpam-5493	258	8	m	m	PROPN
ejpam-5493	258	9	s	s	NOUN
ejpam-5493	258	10	tammam	tammam	NOUN
ejpam-5493	258	11	el	el	PROPN
ejpam-5493	258	12	-	-	PUNCT
ejpam-5493	258	13	sayiad	sayiad	NOUN
ejpam-5493	258	14	.	.	PUNCT
ejpam-5493	259	1	on	on	ADP
ejpam-5493	259	2	θ	θ	NOUN
ejpam-5493	259	3	-	-	PUNCT
ejpam-5493	259	4	centralizers	centralizer	NOUN
ejpam-5493	259	5	of	of	ADP
ejpam-5493	259	6	semiprime	semiprime	NOUN
ejpam-5493	259	7	rings	ring	NOUN
ejpam-5493	259	8	(	(	PUNCT
ejpam-5493	259	9	ii	ii	NOUN
ejpam-5493	259	10	)	)	PUNCT
ejpam-5493	259	11	.	.	PUNCT
ejpam-5493	260	1	st	st	PROPN
ejpam-5493	260	2	.	.	PROPN
ejpam-5493	260	3	petersburg	petersburg	PROPN
ejpam-5493	260	4	math	math	PROPN
ejpam-5493	260	5	.	.	PUNCT
ejpam-5493	261	1	j.	j.	PROPN
ejpam-5493	261	2	,	,	PUNCT
ejpam-5493	261	3	21(1):43–52	21(1):43–52	NUM
ejpam-5493	261	4	,	,	PUNCT
ejpam-5493	261	5	2010	2010	NUM
ejpam-5493	261	6	.	.	PUNCT
ejpam-5493	262	1	[	[	X
ejpam-5493	262	2	5	5	NUM
ejpam-5493	262	3	]	]	PUNCT
ejpam-5493	262	4	s	s	VERB
ejpam-5493	262	5	helgosen	helgosen	NOUN
ejpam-5493	262	6	.	.	PUNCT
ejpam-5493	263	1	multipliers	multiplier	NOUN
ejpam-5493	263	2	of	of	ADP
ejpam-5493	263	3	banach	banach	NOUN
ejpam-5493	263	4	algebras	algebra	NOUN
ejpam-5493	263	5	.	.	PUNCT
ejpam-5493	264	1	ann	ann	PROPN
ejpam-5493	264	2	.	.	PROPN
ejpam-5493	264	3	of	of	ADP
ejpam-5493	264	4	math	math	NOUN
ejpam-5493	264	5	.	.	PUNCT
ejpam-5493	264	6	,	,	PUNCT
ejpam-5493	265	1	64:240–254	64:240–254	PROPN
ejpam-5493	265	2	,	,	PUNCT
ejpam-5493	265	3	1956	1956	NUM
ejpam-5493	265	4	.	.	PUNCT
ejpam-5493	266	1	[	[	X
ejpam-5493	266	2	6	6	NUM
ejpam-5493	266	3	]	]	PUNCT
ejpam-5493	266	4	t	t	PROPN
ejpam-5493	266	5	husain	husain	PROPN
ejpam-5493	266	6	.	.	PUNCT
ejpam-5493	267	1	multipliers	multiplier	NOUN
ejpam-5493	267	2	of	of	ADP
ejpam-5493	267	3	topological	topological	ADJ
ejpam-5493	267	4	algebras	algebra	NOUN
ejpam-5493	267	5	.	.	PUNCT
ejpam-5493	268	1	dessertation	dessertation	NOUN
ejpam-5493	268	2	math	math	NOUN
ejpam-5493	268	3	.	.	PUNCT
ejpam-5493	269	1	(	(	PUNCT
ejpam-5493	269	2	rozprawy	rozprawy	PROPN
ejpam-5493	269	3	mat	mat	NOUN
ejpam-5493	269	4	.	.	PUNCT
ejpam-5493	269	5	)	)	PUNCT
ejpam-5493	269	6	,	,	PUNCT
ejpam-5493	269	7	284:44	284:44	NUM
ejpam-5493	269	8	,	,	PUNCT
ejpam-5493	269	9	1989	1989	NUM
ejpam-5493	269	10	.	.	PUNCT
ejpam-5493	270	1	[	[	X
ejpam-5493	270	2	7	7	NUM
ejpam-5493	270	3	]	]	SYM
ejpam-5493	270	4	b	b	PROPN
ejpam-5493	270	5	e	e	PROPN
ejpam-5493	270	6	johnson	johnson	PROPN
ejpam-5493	270	7	.	.	PUNCT
ejpam-5493	271	1	centralizers	centralizer	NOUN
ejpam-5493	271	2	on	on	ADP
ejpam-5493	271	3	certain	certain	ADJ
ejpam-5493	271	4	topological	topological	ADJ
ejpam-5493	271	5	algebras	algebra	NOUN
ejpam-5493	271	6	.	.	PUNCT
ejpam-5493	272	1	j.	j.	PROPN
ejpam-5493	272	2	london	london	PROPN
ejpam-5493	272	3	math	math	PROPN
ejpam-5493	272	4	.	.	PUNCT
ejpam-5493	273	1	soc	soc	PROPN
ejpam-5493	273	2	.	.	PUNCT
ejpam-5493	273	3	,	,	PUNCT
ejpam-5493	273	4	39:603–614	39:603–614	NUM
ejpam-5493	273	5	,	,	PUNCT
ejpam-5493	273	6	1964	1964	NUM
ejpam-5493	273	7	.	.	PUNCT
ejpam-5493	274	1	[	[	X
ejpam-5493	274	2	8	8	NUM
ejpam-5493	274	3	]	]	SYM
ejpam-5493	274	4	b	b	PROPN
ejpam-5493	274	5	e	e	PROPN
ejpam-5493	274	6	johnson	johnson	PROPN
ejpam-5493	274	7	.	.	PUNCT
ejpam-5493	275	1	continuity	continuity	NOUN
ejpam-5493	275	2	of	of	ADP
ejpam-5493	275	3	centralizers	centralizer	NOUN
ejpam-5493	275	4	on	on	ADP
ejpam-5493	275	5	banach	banach	NOUN
ejpam-5493	275	6	algebras	algebras	PROPN
ejpam-5493	275	7	.	.	PUNCT
ejpam-5493	276	1	j.	j.	PROPN
ejpam-5493	276	2	london	london	PROPN
ejpam-5493	276	3	math	math	PROPN
ejpam-5493	276	4	.	.	PUNCT
ejpam-5493	277	1	soc	soc	PROPN
ejpam-5493	277	2	.	.	PUNCT
ejpam-5493	277	3	,	,	PUNCT
ejpam-5493	278	1	41:639–640	41:639–640	NUM
ejpam-5493	278	2	,	,	PUNCT
ejpam-5493	278	3	1964	1964	NUM
ejpam-5493	278	4	.	.	PUNCT
ejpam-5493	279	1	[	[	X
ejpam-5493	279	2	9	9	NUM
ejpam-5493	279	3	]	]	SYM
ejpam-5493	279	4	b	b	PROPN
ejpam-5493	279	5	e	e	X
ejpam-5493	279	6	johnson	johnson	PROPN
ejpam-5493	279	7	.	.	PUNCT
ejpam-5493	280	1	an	an	DET
ejpam-5493	280	2	introduction	introduction	NOUN
ejpam-5493	280	3	to	to	ADP
ejpam-5493	280	4	the	the	DET
ejpam-5493	280	5	theory	theory	NOUN
ejpam-5493	280	6	of	of	ADP
ejpam-5493	280	7	centralizers	centralizers	PROPN
ejpam-5493	280	8	.	.	PUNCT
ejpam-5493	281	1	proc	proc	PROPN
ejpam-5493	281	2	.	.	PUNCT
ejpam-5493	282	1	london	london	PROPN
ejpam-5493	282	2	math	math	PROPN
ejpam-5493	282	3	.	.	PUNCT
ejpam-5493	283	1	soc	soc	PROPN
ejpam-5493	283	2	.	.	PROPN
ejpam-5493	283	3	,	,	PUNCT
ejpam-5493	283	4	14:299–320	14:299–320	PROPN
ejpam-5493	283	5	,	,	PUNCT
ejpam-5493	283	6	1964	1964	NUM
ejpam-5493	283	7	.	.	PUNCT
ejpam-5493	284	1	[	[	X
ejpam-5493	284	2	10	10	NUM
ejpam-5493	284	3	]	]	X
ejpam-5493	284	4	l	l	NOUN
ejpam-5493	284	5	a	a	DET
ejpam-5493	284	6	khan	khan	PROPN
ejpam-5493	284	7	,	,	PUNCT
ejpam-5493	284	8	n	n	X
ejpam-5493	284	9	mohammad	mohammad	NOUN
ejpam-5493	284	10	,	,	PUNCT
ejpam-5493	284	11	and	and	CCONJ
ejpam-5493	284	12	a	a	DET
ejpam-5493	284	13	b	b	NOUN
ejpam-5493	284	14	thaheem	thaheem	NOUN
ejpam-5493	284	15	.	.	PUNCT
ejpam-5493	285	1	double	double	ADJ
ejpam-5493	285	2	multipliers	multiplier	NOUN
ejpam-5493	285	3	on	on	ADP
ejpam-5493	285	4	topological	topological	ADJ
ejpam-5493	285	5	algebras	algebra	NOUN
ejpam-5493	285	6	.	.	PUNCT
ejpam-5493	286	1	internat	internat	PROPN
ejpam-5493	286	2	.	.	PUNCT
ejpam-5493	287	1	j.	j.	PROPN
ejpam-5493	287	2	math	math	PROPN
ejpam-5493	287	3	.	.	PUNCT
ejpam-5493	288	1	math	math	NOUN
ejpam-5493	288	2	.	.	PUNCT
ejpam-5493	289	1	sci	sci	PROPN
ejpam-5493	289	2	.	.	PROPN
ejpam-5493	289	3	,	,	PUNCT
ejpam-5493	289	4	22:629–636	22:629–636	NUM
ejpam-5493	289	5	,	,	PUNCT
ejpam-5493	289	6	1999	1999	NUM
ejpam-5493	289	7	.	.	PUNCT
ejpam-5493	290	1	[	[	X
ejpam-5493	290	2	11	11	NUM
ejpam-5493	290	3	]	]	X
ejpam-5493	290	4	r	r	NOUN
ejpam-5493	290	5	larsen	larsen	PROPN
ejpam-5493	290	6	.	.	PUNCT
ejpam-5493	291	1	an	an	DET
ejpam-5493	291	2	introduction	introduction	NOUN
ejpam-5493	291	3	to	to	ADP
ejpam-5493	291	4	the	the	DET
ejpam-5493	291	5	theory	theory	NOUN
ejpam-5493	291	6	of	of	ADP
ejpam-5493	291	7	multipliers	multiplier	NOUN
ejpam-5493	291	8	.	.	PUNCT
ejpam-5493	292	1	1971	1971	NUM
ejpam-5493	292	2	.	.	PUNCT
ejpam-5493	293	1	[	[	X
ejpam-5493	293	2	12	12	NUM
ejpam-5493	293	3	]	]	PUNCT
ejpam-5493	293	4	n	n	CCONJ
ejpam-5493	293	5	mohammad	mohammad	NOUN
ejpam-5493	293	6	,	,	PUNCT
ejpam-5493	293	7	l	l	PROPN
ejpam-5493	293	8	a	a	DET
ejpam-5493	293	9	khan	khan	PROPN
ejpam-5493	293	10	,	,	PUNCT
ejpam-5493	293	11	and	and	CCONJ
ejpam-5493	293	12	a	a	DET
ejpam-5493	293	13	b	b	NOUN
ejpam-5493	293	14	thaheem	thaheem	NOUN
ejpam-5493	293	15	.	.	PUNCT
ejpam-5493	294	1	on	on	ADP
ejpam-5493	294	2	closed	closed	ADJ
ejpam-5493	294	3	range	range	NOUN
ejpam-5493	294	4	multipliers	multiplier	NOUN
ejpam-5493	294	5	on	on	ADP
ejpam-5493	294	6	topological	topological	ADJ
ejpam-5493	294	7	algebras	algebra	NOUN
ejpam-5493	294	8	.	.	PUNCT
ejpam-5493	295	1	scientiae	scientiae	PROPN
ejpam-5493	295	2	math	math	PROPN
ejpam-5493	295	3	.	.	PUNCT
ejpam-5493	296	1	japonica	japonica	PROPN
ejpam-5493	296	2	,	,	PUNCT
ejpam-5493	296	3	53:89–96	53:89–96	NUM
ejpam-5493	296	4	,	,	PUNCT
ejpam-5493	296	5	2001	2001	NUM
ejpam-5493	296	6	.	.	PUNCT
ejpam-5493	297	1	[	[	X
ejpam-5493	297	2	13	13	NUM
ejpam-5493	297	3	]	]	SYM
ejpam-5493	297	4	g	g	PROPN
ejpam-5493	297	5	j	j	PROPN
ejpam-5493	297	6	murphy	murphy	PROPN
ejpam-5493	297	7	.	.	PUNCT
ejpam-5493	298	1	c∗algebras	c∗algebra	NOUN
ejpam-5493	298	2	and	and	CCONJ
ejpam-5493	298	3	operator	operator	NOUN
ejpam-5493	298	4	theory	theory	NOUN
ejpam-5493	298	5	.	.	PUNCT
ejpam-5493	299	1	1999	1999	NUM
ejpam-5493	299	2	.	.	PUNCT
ejpam-5493	300	1	[	[	X
ejpam-5493	300	2	14	14	NUM
ejpam-5493	300	3	]	]	X
ejpam-5493	300	4	j	j	PROPN
ejpam-5493	300	5	k	k	PROPN
ejpam-5493	300	6	wang	wang	PROPN
ejpam-5493	300	7	.	.	PUNCT
ejpam-5493	301	1	multipliers	multiplier	NOUN
ejpam-5493	301	2	of	of	ADP
ejpam-5493	301	3	commutative	commutative	ADJ
ejpam-5493	301	4	banach	banach	NOUN
ejpam-5493	301	5	algebras	algebra	NOUN
ejpam-5493	301	6	.	.	PUNCT
ejpam-5493	302	1	pacific	pacific	PROPN
ejpam-5493	302	2	.	.	PUNCT
ejpam-5493	303	1	j.	j.	PROPN
ejpam-5493	303	2	math	math	PROPN
ejpam-5493	303	3	.	.	PUNCT
ejpam-5493	303	4	,	,	PUNCT
ejpam-5493	303	5	11:1131	11:1131	NUM
ejpam-5493	303	6	–	–	PUNCT
ejpam-5493	303	7	1149	1149	NUM
ejpam-5493	303	8	,	,	PUNCT
ejpam-5493	303	9	1961	1961	NUM
ejpam-5493	303	10	.	.	PUNCT