id	sid	tid	token	lemma	pos
ejpam-4344	1	1	european	european	PROPN
ejpam-4344	1	2	journal	journal	PROPN
ejpam-4344	1	3	of	of	ADP
ejpam-4344	1	4	pure	pure	ADJ
ejpam-4344	1	5	and	and	CCONJ
ejpam-4344	1	6	applied	apply	VERB
ejpam-4344	1	7	mathematics	mathematic	NOUN
ejpam-4344	1	8	vol	vol	NOUN
ejpam-4344	1	9	.	.	PROPN
ejpam-4344	2	1	15	15	NUM
ejpam-4344	2	2	,	,	PUNCT
ejpam-4344	2	3	no	no	INTJ
ejpam-4344	2	4	.	.	NOUN
ejpam-4344	2	5	2	2	NUM
ejpam-4344	2	6	,	,	PUNCT
ejpam-4344	2	7	2022	2022	NUM
ejpam-4344	2	8	,	,	PUNCT
ejpam-4344	2	9	454	454	NUM
ejpam-4344	2	10	-	-	SYM
ejpam-4344	2	11	466	466	NUM
ejpam-4344	2	12	issn	issn	PROPN
ejpam-4344	2	13	1307	1307	NUM
ejpam-4344	2	14	-	-	SYM
ejpam-4344	2	15	5543	5543	NUM
ejpam-4344	2	16	–	–	PUNCT
ejpam-4344	2	17	ejpam.com	ejpam.com	X
ejpam-4344	2	18	published	publish	VERB
ejpam-4344	2	19	by	by	ADP
ejpam-4344	2	20	new	new	PROPN
ejpam-4344	2	21	york	york	PROPN
ejpam-4344	2	22	business	business	PROPN
ejpam-4344	2	23	global	global	ADJ
ejpam-4344	2	24	derivations	derivation	NOUN
ejpam-4344	2	25	in	in	ADP
ejpam-4344	2	26	differentially	differentially	ADV
ejpam-4344	2	27	δ	δ	NOUN
ejpam-4344	2	28	-	-	ADJ
ejpam-4344	2	29	prime	prime	PROPN
ejpam-4344	2	30	rings	ring	NOUN
ejpam-4344	2	31	iman	iman	NOUN
ejpam-4344	2	32	taha1,∗	taha1,∗	NOUN
ejpam-4344	2	33	,	,	PUNCT
ejpam-4344	2	34	rohaidah	rohaidah	NOUN
ejpam-4344	2	35	masri1	masri1	NOUN
ejpam-4344	2	36	,	,	PUNCT
ejpam-4344	2	37	ahmad	ahmad	PROPN
ejpam-4344	2	38	al	al	PROPN
ejpam-4344	2	39	khalaf2	khalaf2	PROPN
ejpam-4344	2	40	,	,	PUNCT
ejpam-4344	2	41	rawdah	rawdah	NOUN
ejpam-4344	2	42	tarmizi1	tarmizi1	NOUN
ejpam-4344	2	43	1	1	NUM
ejpam-4344	2	44	department	department	NOUN
ejpam-4344	2	45	of	of	ADP
ejpam-4344	2	46	mathematics	mathematic	NOUN
ejpam-4344	2	47	,	,	PUNCT
ejpam-4344	2	48	faculty	faculty	NOUN
ejpam-4344	2	49	of	of	ADP
ejpam-4344	2	50	sciences	science	NOUN
ejpam-4344	2	51	and	and	CCONJ
ejpam-4344	2	52	mathematics	mathematic	NOUN
ejpam-4344	2	53	,	,	PUNCT
ejpam-4344	2	54	sultan	sultan	PROPN
ejpam-4344	2	55	idris	idris	PROPN
ejpam-4344	2	56	education	education	PROPN
ejpam-4344	2	57	university	university	PROPN
ejpam-4344	2	58	,	,	PUNCT
ejpam-4344	2	59	tanjong	tanjong	PROPN
ejpam-4344	2	60	malim	malim	PROPN
ejpam-4344	2	61	,	,	PUNCT
ejpam-4344	2	62	perak	perak	PROPN
ejpam-4344	2	63	,	,	PUNCT
ejpam-4344	2	64	malaysia	malaysia	PROPN
ejpam-4344	2	65	2	2	NUM
ejpam-4344	2	66	department	department	NOUN
ejpam-4344	2	67	of	of	ADP
ejpam-4344	2	68	mathematics	mathematic	NOUN
ejpam-4344	2	69	and	and	CCONJ
ejpam-4344	2	70	statistic	statistic	NOUN
ejpam-4344	2	71	,	,	PUNCT
ejpam-4344	2	72	faculty	faculty	NOUN
ejpam-4344	2	73	of	of	ADP
ejpam-4344	2	74	sciences	science	NOUN
ejpam-4344	2	75	,	,	PUNCT
ejpam-4344	2	76	imam	imam	PROPN
ejpam-4344	2	77	mohammad	mohammad	PROPN
ejpam-4344	2	78	ibn	ibn	PROPN
ejpam-4344	2	79	saud	saud	PROPN
ejpam-4344	2	80	islamic	islamic	PROPN
ejpam-4344	2	81	university	university	PROPN
ejpam-4344	2	82	,	,	PUNCT
ejpam-4344	2	83	riyadh	riyadh	PROPN
ejpam-4344	2	84	,	,	PUNCT
ejpam-4344	2	85	saudi	saudi	PROPN
ejpam-4344	2	86	arabia	arabia	PROPN
ejpam-4344	2	87	abstract	abstract	NOUN
ejpam-4344	2	88	.	.	PUNCT
ejpam-4344	3	1	let	let	VERB
ejpam-4344	3	2	r	r	PRON
ejpam-4344	3	3	be	be	AUX
ejpam-4344	3	4	an	an	DET
ejpam-4344	3	5	associative	associative	ADJ
ejpam-4344	3	6	ring	ring	NOUN
ejpam-4344	3	7	with	with	ADP
ejpam-4344	3	8	identity	identity	NOUN
ejpam-4344	3	9	.	.	PUNCT
ejpam-4344	4	1	in	in	ADP
ejpam-4344	4	2	this	this	DET
ejpam-4344	4	3	paper	paper	NOUN
ejpam-4344	4	4	we	we	PRON
ejpam-4344	4	5	extend	extend	VERB
ejpam-4344	4	6	the	the	DET
ejpam-4344	4	7	j.h	j.h	PROPN
ejpam-4344	4	8	.	.	PROPN
ejpam-4344	4	9	maynes	mayne	NOUN
ejpam-4344	4	10	results	result	NOUN
ejpam-4344	4	11	,	,	PUNCT
ejpam-4344	4	12	which	which	PRON
ejpam-4344	4	13	he	he	PRON
ejpam-4344	4	14	treatised	treatise	VERB
ejpam-4344	4	15	in	in	ADP
ejpam-4344	4	16	[	[	X
ejpam-4344	4	17	27	27	NUM
ejpam-4344	4	18	]	]	PUNCT
ejpam-4344	4	19	.	.	PUNCT
ejpam-4344	5	1	in	in	ADP
ejpam-4344	5	2	particular	particular	ADJ
ejpam-4344	5	3	,	,	PUNCT
ejpam-4344	5	4	we	we	PRON
ejpam-4344	5	5	prove	prove	VERB
ejpam-4344	5	6	that	that	SCONJ
ejpam-4344	5	7	if	if	SCONJ
ejpam-4344	5	8	r	r	NOUN
ejpam-4344	5	9	is	be	AUX
ejpam-4344	5	10	a	a	DET
ejpam-4344	5	11	δ	δ	NOUN
ejpam-4344	5	12	-	-	ADJ
ejpam-4344	5	13	prime	prime	ADJ
ejpam-4344	5	14	ring	ring	NOUN
ejpam-4344	5	15	with	with	ADP
ejpam-4344	5	16	charr	charr	NOUN
ejpam-4344	5	17	6=	6=	ADP
ejpam-4344	5	18	2	2	NUM
ejpam-4344	5	19	and	and	CCONJ
ejpam-4344	5	20	i	i	PRON
ejpam-4344	5	21	is	be	AUX
ejpam-4344	5	22	a	a	DET
ejpam-4344	5	23	nonzero	nonzero	ADJ
ejpam-4344	5	24	δ	δ	NOUN
ejpam-4344	5	25	-	-	PUNCT
ejpam-4344	5	26	ideal	ideal	NOUN
ejpam-4344	5	27	of	of	ADP
ejpam-4344	5	28	r	r	NOUN
ejpam-4344	5	29	,	,	PUNCT
ejpam-4344	5	30	where	where	SCONJ
ejpam-4344	5	31	0	0	NUM
ejpam-4344	5	32	6=	6=	NUM
ejpam-4344	5	33	δ	δ	PROPN
ejpam-4344	5	34	∈	∈	PROPN
ejpam-4344	5	35	d	d	PROPN
ejpam-4344	5	36	,	,	PUNCT
ejpam-4344	5	37	c	c	PROPN
ejpam-4344	5	38	∈	∈	PROPN
ejpam-4344	5	39	r	r	NOUN
ejpam-4344	5	40	and	and	CCONJ
ejpam-4344	5	41	[	[	X
ejpam-4344	5	42	c	c	X
ejpam-4344	5	43	,	,	PUNCT
ejpam-4344	5	44	δ(c	δ(c	PROPN
ejpam-4344	5	45	)	)	PUNCT
ejpam-4344	5	46	]	]	PUNCT
ejpam-4344	5	47	in	in	ADP
ejpam-4344	5	48	the	the	DET
ejpam-4344	5	49	center	center	NOUN
ejpam-4344	5	50	of	of	ADP
ejpam-4344	5	51	r	r	NOUN
ejpam-4344	5	52	,	,	PUNCT
ejpam-4344	5	53	then	then	ADV
ejpam-4344	5	54	r	r	NOUN
ejpam-4344	5	55	is	be	AUX
ejpam-4344	5	56	commutative	commutative	ADJ
ejpam-4344	5	57	.	.	PUNCT
ejpam-4344	6	1	2020	2020	NUM
ejpam-4344	6	2	mathematics	mathematic	NOUN
ejpam-4344	6	3	subject	subject	NOUN
ejpam-4344	6	4	classifications	classification	NOUN
ejpam-4344	6	5	:	:	PUNCT
ejpam-4344	6	6	16n60	16n60	NUM
ejpam-4344	6	7	,	,	PUNCT
ejpam-4344	6	8	16w25	16w25	NUM
ejpam-4344	6	9	key	key	ADJ
ejpam-4344	6	10	words	word	NOUN
ejpam-4344	6	11	and	and	CCONJ
ejpam-4344	6	12	phrases	phrase	NOUN
ejpam-4344	6	13	:	:	PUNCT
ejpam-4344	6	14	derivation	derivation	NOUN
ejpam-4344	6	15	,	,	PUNCT
ejpam-4344	6	16	prime	prime	ADJ
ejpam-4344	6	17	ring	ring	NOUN
ejpam-4344	6	18	,	,	PUNCT
ejpam-4344	6	19	δ	δ	PROPN
ejpam-4344	6	20	-	-	PUNCT
ejpam-4344	6	21	prime	prime	ADJ
ejpam-4344	6	22	ring	ring	NOUN
ejpam-4344	6	23	,	,	PUNCT
ejpam-4344	6	24	δ	δ	PROPN
ejpam-4344	6	25	-	-	PUNCT
ejpam-4344	6	26	ideal	ideal	ADJ
ejpam-4344	6	27	.	.	PUNCT
ejpam-4344	7	1	1	1	X
ejpam-4344	7	2	.	.	X
ejpam-4344	7	3	introduction	introduction	NOUN
ejpam-4344	7	4	it	it	PRON
ejpam-4344	7	5	shall	shall	AUX
ejpam-4344	7	6	be	be	AUX
ejpam-4344	7	7	assumed	assume	VERB
ejpam-4344	7	8	throughout	throughout	ADP
ejpam-4344	7	9	here	here	ADV
ejpam-4344	7	10	,	,	PUNCT
ejpam-4344	7	11	that	that	SCONJ
ejpam-4344	7	12	r	r	NOUN
ejpam-4344	7	13	is	be	AUX
ejpam-4344	7	14	an	an	DET
ejpam-4344	7	15	associative	associative	ADJ
ejpam-4344	7	16	ring	ring	NOUN
ejpam-4344	7	17	with	with	ADP
ejpam-4344	7	18	respect	respect	NOUN
ejpam-4344	7	19	to	to	ADP
ejpam-4344	7	20	the	the	DET
ejpam-4344	7	21	addition	addition	NOUN
ejpam-4344	7	22	(	(	PUNCT
ejpam-4344	7	23	+	+	NOUN
ejpam-4344	7	24	)	)	PUNCT
ejpam-4344	7	25	and	and	CCONJ
ejpam-4344	7	26	the	the	DET
ejpam-4344	7	27	multiplication	multiplication	NOUN
ejpam-4344	7	28	(	(	PUNCT
ejpam-4344	7	29	·	·	PUNCT
ejpam-4344	7	30	)	)	PUNCT
ejpam-4344	7	31	with	with	ADP
ejpam-4344	7	32	an	an	DET
ejpam-4344	7	33	identity	identity	NOUN
ejpam-4344	7	34	,	,	PUNCT
ejpam-4344	7	35	d	d	PRON
ejpam-4344	7	36	is	be	AUX
ejpam-4344	7	37	the	the	DET
ejpam-4344	7	38	set	set	NOUN
ejpam-4344	7	39	of	of	ADP
ejpam-4344	7	40	all	all	DET
ejpam-4344	7	41	derivations	derivation	NOUN
ejpam-4344	7	42	in	in	ADP
ejpam-4344	7	43	r.	r.	PROPN
ejpam-4344	7	44	consider	consider	VERB
ejpam-4344	7	45	lie	lie	NOUN
ejpam-4344	7	46	multiplication	multiplication	NOUN
ejpam-4344	7	47	“	"	PUNCT
ejpam-4344	7	48	[	[	X
ejpam-4344	7	49	−,−	−,−	X
ejpam-4344	7	50	]	]	X
ejpam-4344	7	51	”	"	PUNCT
ejpam-4344	7	52	on	on	ADP
ejpam-4344	7	53	r	r	NOUN
ejpam-4344	7	54	,	,	PUNCT
ejpam-4344	7	55	which	which	PRON
ejpam-4344	7	56	is	be	AUX
ejpam-4344	7	57	defined	define	VERB
ejpam-4344	7	58	by	by	ADP
ejpam-4344	7	59	[	[	X
ejpam-4344	7	60	c	c	X
ejpam-4344	7	61	,	,	PUNCT
ejpam-4344	7	62	d	d	X
ejpam-4344	7	63	]	]	X
ejpam-4344	7	64	=	=	SYM
ejpam-4344	7	65	cd	cd	PROPN
ejpam-4344	7	66	−	−	PROPN
ejpam-4344	7	67	dc	dc	PROPN
ejpam-4344	7	68	,	,	PUNCT
ejpam-4344	7	69	where	where	SCONJ
ejpam-4344	7	70	[	[	X
ejpam-4344	7	71	c	c	X
ejpam-4344	7	72	,	,	PUNCT
ejpam-4344	7	73	d	d	X
ejpam-4344	7	74	]	]	X
ejpam-4344	7	75	is	be	AUX
ejpam-4344	7	76	called	call	VERB
ejpam-4344	7	77	a	a	DET
ejpam-4344	7	78	lie	lie	NOUN
ejpam-4344	7	79	commutator	commutator	NOUN
ejpam-4344	7	80	of	of	ADP
ejpam-4344	7	81	elements	element	NOUN
ejpam-4344	7	82	c	c	X
ejpam-4344	7	83	,	,	PUNCT
ejpam-4344	7	84	d	d	PROPN
ejpam-4344	7	85	of	of	ADP
ejpam-4344	7	86	r.	r.	PROPN
ejpam-4344	7	87	the	the	DET
ejpam-4344	7	88	set	set	NOUN
ejpam-4344	7	89	[	[	X
ejpam-4344	7	90	c	c	X
ejpam-4344	7	91	,	,	PUNCT
ejpam-4344	7	92	d	d	X
ejpam-4344	7	93	]	]	PUNCT
ejpam-4344	7	94	of	of	ADP
ejpam-4344	7	95	the	the	DET
ejpam-4344	7	96	additive	additive	ADJ
ejpam-4344	7	97	group	group	NOUN
ejpam-4344	7	98	r+	r+	NOUN
ejpam-4344	7	99	of	of	ADP
ejpam-4344	7	100	a	a	DET
ejpam-4344	7	101	ring	ring	NOUN
ejpam-4344	7	102	r	r	NOUN
ejpam-4344	7	103	is	be	AUX
ejpam-4344	7	104	the	the	DET
ejpam-4344	7	105	lie	lie	NOUN
ejpam-4344	7	106	commutator	commutator	NOUN
ejpam-4344	7	107	subgroup	subgroup	PROPN
ejpam-4344	7	108	generated	generate	VERB
ejpam-4344	7	109	by	by	ADP
ejpam-4344	7	110	all	all	PRON
ejpam-4344	7	111	[	[	X
ejpam-4344	7	112	c	c	X
ejpam-4344	7	113	,	,	PUNCT
ejpam-4344	7	114	d	d	X
ejpam-4344	7	115	]	]	X
ejpam-4344	7	116	such	such	ADJ
ejpam-4344	7	117	that	that	SCONJ
ejpam-4344	7	118	c	c	PROPN
ejpam-4344	7	119	∈	∈	PROPN
ejpam-4344	7	120	c	c	PROPN
ejpam-4344	7	121	and	and	CCONJ
ejpam-4344	7	122	d	d	PROPN
ejpam-4344	7	123	∈	∈	PROPN
ejpam-4344	7	124	d.	d.	PROPN
ejpam-4344	7	125	obsreve	obsreve	VERB
ejpam-4344	7	126	that	that	SCONJ
ejpam-4344	7	127	z(r	z(r	NOUN
ejpam-4344	7	128	)	)	PUNCT
ejpam-4344	7	129	is	be	AUX
ejpam-4344	7	130	the	the	DET
ejpam-4344	7	131	center	center	NOUN
ejpam-4344	7	132	of	of	ADP
ejpam-4344	7	133	r	r	PROPN
ejpam-4344	7	134	,	,	PUNCT
ejpam-4344	7	135	c(r	c(r	NOUN
ejpam-4344	7	136	)	)	PUNCT
ejpam-4344	7	137	is	be	AUX
ejpam-4344	7	138	the	the	DET
ejpam-4344	7	139	commutator	commutator	NOUN
ejpam-4344	7	140	ideal	ideal	NOUN
ejpam-4344	7	141	generated	generate	VERB
ejpam-4344	7	142	by	by	ADP
ejpam-4344	7	143	the	the	DET
ejpam-4344	7	144	set	set	NOUN
ejpam-4344	7	145	{	{	PUNCT
ejpam-4344	7	146	[	[	X
ejpam-4344	7	147	c	c	X
ejpam-4344	7	148	,	,	PUNCT
ejpam-4344	7	149	d	d	X
ejpam-4344	7	150	]	]	X
ejpam-4344	7	151	:	:	PUNCT
ejpam-4344	7	152	c	c	X
ejpam-4344	7	153	,	,	PUNCT
ejpam-4344	7	154	d	d	PROPN
ejpam-4344	7	155	∈	∈	PROPN
ejpam-4344	7	156	r	r	NOUN
ejpam-4344	7	157	}	}	PUNCT
ejpam-4344	7	158	,	,	PUNCT
ejpam-4344	7	159	annt	annt	NOUN
ejpam-4344	7	160	=	=	PUNCT
ejpam-4344	7	161	{	{	PUNCT
ejpam-4344	7	162	r	r	NOUN
ejpam-4344	7	163	∈	∈	NOUN
ejpam-4344	7	164	r	r	NOUN
ejpam-4344	7	165	:	:	PUNCT
ejpam-4344	7	166	rt	rt	PROPN
ejpam-4344	7	167	=	=	SYM
ejpam-4344	7	168	0	0	PUNCT
ejpam-4344	7	169	=	=	PUNCT
ejpam-4344	7	170	tr	tr	VERB
ejpam-4344	7	171	}	}	PUNCT
ejpam-4344	7	172	the	the	DET
ejpam-4344	7	173	annihilator	annihilator	NOUN
ejpam-4344	7	174	of	of	ADP
ejpam-4344	7	175	t	t	PROPN
ejpam-4344	7	176	⊆	⊆	PROPN
ejpam-4344	7	177	r.	r.	NOUN
ejpam-4344	7	178	an	an	DET
ejpam-4344	7	179	additive	additive	ADJ
ejpam-4344	7	180	subgroup	subgroup	NOUN
ejpam-4344	7	181	t	t	PROPN
ejpam-4344	7	182	of	of	ADP
ejpam-4344	7	183	r	r	NOUN
ejpam-4344	7	184	is	be	AUX
ejpam-4344	7	185	called	call	VERB
ejpam-4344	7	186	a	a	DET
ejpam-4344	7	187	lie	lie	NOUN
ejpam-4344	7	188	ideal	ideal	NOUN
ejpam-4344	7	189	of	of	ADP
ejpam-4344	7	190	r	r	NOUN
ejpam-4344	7	191	if	if	SCONJ
ejpam-4344	7	192	[	[	X
ejpam-4344	7	193	c	c	X
ejpam-4344	7	194	,	,	PUNCT
ejpam-4344	7	195	d	d	X
ejpam-4344	7	196	]	]	X
ejpam-4344	7	197	∈	∈	PROPN
ejpam-4344	7	198	t	t	PROPN
ejpam-4344	7	199	,	,	PUNCT
ejpam-4344	7	200	for	for	ADP
ejpam-4344	7	201	all	all	DET
ejpam-4344	7	202	c	c	NOUN
ejpam-4344	7	203	∈	∈	PROPN
ejpam-4344	7	204	t	t	PROPN
ejpam-4344	7	205	and	and	CCONJ
ejpam-4344	7	206	d	d	PROPN
ejpam-4344	7	207	∈	∈	PROPN
ejpam-4344	7	208	r.	r.	PROPN
ejpam-4344	7	209	an	an	DET
ejpam-4344	7	210	aditive	aditive	ADJ
ejpam-4344	7	211	map	map	NOUN
ejpam-4344	7	212	δ	δ	NOUN
ejpam-4344	7	213	:	:	PUNCT
ejpam-4344	7	214	r	r	NOUN
ejpam-4344	7	215	→	→	SYM
ejpam-4344	7	216	r	r	NOUN
ejpam-4344	7	217	is	be	AUX
ejpam-4344	7	218	called	call	VERB
ejpam-4344	7	219	a	a	DET
ejpam-4344	7	220	derivation	derivation	NOUN
ejpam-4344	7	221	on	on	ADP
ejpam-4344	7	222	r	r	NOUN
ejpam-4344	7	223	if	if	SCONJ
ejpam-4344	7	224	δ(cd	δ(cd	NOUN
ejpam-4344	7	225	)	)	PUNCT
ejpam-4344	7	226	=	=	PRON
ejpam-4344	7	227	δ(c)d+	δ(c)d+	NOUN
ejpam-4344	7	228	cδ(d	cδ(d	VERB
ejpam-4344	7	229	)	)	PUNCT
ejpam-4344	7	230	for	for	ADP
ejpam-4344	7	231	all	all	DET
ejpam-4344	7	232	c	c	NOUN
ejpam-4344	7	233	,	,	PUNCT
ejpam-4344	7	234	d	d	PROPN
ejpam-4344	7	235	∈	∈	PROPN
ejpam-4344	7	236	r.	r.	PROPN
ejpam-4344	7	237	furthermore	furthermore	ADV
ejpam-4344	7	238	,	,	PUNCT
ejpam-4344	7	239	the	the	DET
ejpam-4344	7	240	map	map	NOUN
ejpam-4344	8	1	∂a	∂a	NOUN
ejpam-4344	8	2	:	:	PUNCT
ejpam-4344	8	3	r	r	NOUN
ejpam-4344	8	4	→	→	SYM
ejpam-4344	8	5	r	r	NOUN
ejpam-4344	8	6	defined	define	VERB
ejpam-4344	8	7	by	by	ADP
ejpam-4344	8	8	,	,	PUNCT
ejpam-4344	8	9	∂a(c	∂a(c	NOUN
ejpam-4344	8	10	)	)	PUNCT
ejpam-4344	8	11	=	=	SYM
ejpam-4344	8	12	ac−	ac−	PROPN
ejpam-4344	8	13	ca	ca	NOUN
ejpam-4344	8	14	,	,	PUNCT
ejpam-4344	8	15	where	where	SCONJ
ejpam-4344	8	16	c	c	X
ejpam-4344	8	17	∈	∈	PROPN
ejpam-4344	8	18	r	r	NOUN
ejpam-4344	8	19	is	be	AUX
ejpam-4344	8	20	a	a	DET
ejpam-4344	8	21	partial	partial	ADJ
ejpam-4344	8	22	derivation	derivation	NOUN
ejpam-4344	8	23	generated	generate	VERB
ejpam-4344	8	24	by	by	ADP
ejpam-4344	8	25	a	a	DET
ejpam-4344	8	26	∈	∈	PROPN
ejpam-4344	8	27	r	r	NOUN
ejpam-4344	8	28	i.e.	i.e.	X
ejpam-4344	8	29	,	,	PUNCT
ejpam-4344	8	30	∂a(i	∂a(i	NOUN
ejpam-4344	8	31	)	)	PUNCT
ejpam-4344	9	1	=	=	PUNCT
ejpam-4344	10	1	[	[	X
ejpam-4344	10	2	a	a	X
ejpam-4344	10	3	,	,	PUNCT
ejpam-4344	10	4	i	i	PRON
ejpam-4344	10	5	]	]	X
ejpam-4344	10	6	=	=	PUNCT
ejpam-4344	10	7	{	{	PUNCT
ejpam-4344	10	8	[	[	X
ejpam-4344	10	9	a	a	X
ejpam-4344	10	10	,	,	PUNCT
ejpam-4344	10	11	i	i	PRON
ejpam-4344	10	12	]	]	X
ejpam-4344	10	13	:	:	PUNCT
ejpam-4344	11	1	i	i	PRON
ejpam-4344	11	2	∈	∈	VERB
ejpam-4344	11	3	i	i	PRON
ejpam-4344	11	4	}	}	PUNCT
ejpam-4344	11	5	.	.	PUNCT
ejpam-4344	12	1	∗corresponding	∗corresponde	VERB
ejpam-4344	12	2	author	author	NOUN
ejpam-4344	12	3	.	.	PUNCT
ejpam-4344	13	1	doi	doi	NOUN
ejpam-4344	13	2	:	:	PUNCT
ejpam-4344	13	3	https://doi.org/10.29020/nybg.ejpam.v15i2.4344	https://doi.org/10.29020/nybg.ejpam.v15i2.4344	NOUN
ejpam-4344	13	4	email	email	NOUN
ejpam-4344	13	5	addresses	address	NOUN
ejpam-4344	13	6	:	:	PUNCT
ejpam-4344	13	7	tfaith80gmail.com	tfaith80gmail.com	X
ejpam-4344	13	8	(	(	PUNCT
ejpam-4344	13	9	i.	i.	PROPN
ejpam-4344	13	10	taha	taha	PROPN
ejpam-4344	13	11	)	)	PUNCT
ejpam-4344	13	12	,	,	PUNCT
ejpam-4344	13	13	ajalkalaf@imamu.edu.sa	ajalkalaf@imamu.edu.sa	NOUN
ejpam-4344	13	14	(	(	PUNCT
ejpam-4344	13	15	a.	a.	PROPN
ejpam-4344	13	16	al	al	PROPN
ejpam-4344	13	17	khalaf	khalaf	PROPN
ejpam-4344	13	18	)	)	PUNCT
ejpam-4344	13	19	,	,	PUNCT
ejpam-4344	13	20	rohaidah@fsmt.upsi.edu.my	rohaidah@fsmt.upsi.edu.my	PROPN
ejpam-4344	13	21	(	(	PUNCT
ejpam-4344	13	22	r.	r.	PROPN
ejpam-4344	13	23	masri	masri	PROPN
ejpam-4344	13	24	)	)	PUNCT
ejpam-4344	13	25	,	,	PUNCT
ejpam-4344	13	26	rawdah@fsmt.upsi.edu.my	rawdah@fsmt.upsi.edu.my	NOUN
ejpam-4344	13	27	(	(	PUNCT
ejpam-4344	13	28	rawdah	rawdah	PROPN
ejpam-4344	13	29	tarmizi	tarmizi	PROPN
ejpam-4344	13	30	)	)	PUNCT
ejpam-4344	13	31	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4344	14	1	454	454	NUM
ejpam-4344	14	2	©	©	PROPN
ejpam-4344	14	3	2022	2022	NUM
ejpam-4344	14	4	ejpam	ejpam	VERB
ejpam-4344	14	5	all	all	DET
ejpam-4344	14	6	rights	right	NOUN
ejpam-4344	14	7	reserved	reserve	VERB
ejpam-4344	14	8	.	.	PUNCT
ejpam-4344	15	1	i.	i.	PROPN
ejpam-4344	15	2	taha	taha	PROPN
ejpam-4344	15	3	et	et	PROPN
ejpam-4344	15	4	al	al	PROPN
ejpam-4344	15	5	.	.	PUNCT
ejpam-4344	15	6	/	/	SYM
ejpam-4344	15	7	eur	eur	PROPN
ejpam-4344	15	8	.	.	PUNCT
ejpam-4344	16	1	j.	j.	PROPN
ejpam-4344	16	2	pure	pure	PROPN
ejpam-4344	16	3	appl	appl	PROPN
ejpam-4344	16	4	.	.	PROPN
ejpam-4344	16	5	math	math	PROPN
ejpam-4344	16	6	,	,	PUNCT
ejpam-4344	16	7	15	15	NUM
ejpam-4344	16	8	(	(	PUNCT
ejpam-4344	16	9	2	2	NUM
ejpam-4344	16	10	)	)	PUNCT
ejpam-4344	16	11	(	(	PUNCT
ejpam-4344	16	12	2022	2022	NUM
ejpam-4344	16	13	)	)	PUNCT
ejpam-4344	16	14	,	,	PUNCT
ejpam-4344	16	15	454	454	NUM
ejpam-4344	16	16	-	-	SYM
ejpam-4344	16	17	466	466	NUM
ejpam-4344	16	18	455	455	NUM
ejpam-4344	16	19	in	in	ADP
ejpam-4344	16	20	addition	addition	NOUN
ejpam-4344	16	21	,	,	PUNCT
ejpam-4344	16	22	the	the	DET
ejpam-4344	16	23	map	map	NOUN
ejpam-4344	16	24	δ	δ	PROPN
ejpam-4344	16	25	is	be	AUX
ejpam-4344	16	26	called	call	VERB
ejpam-4344	16	27	centralizing	centralize	VERB
ejpam-4344	16	28	on	on	ADP
ejpam-4344	16	29	a	a	DET
ejpam-4344	16	30	subset	subset	NOUN
ejpam-4344	16	31	i	i	PRON
ejpam-4344	16	32	of	of	ADP
ejpam-4344	16	33	r	r	NOUN
ejpam-4344	16	34	if	if	SCONJ
ejpam-4344	16	35	[	[	X
ejpam-4344	16	36	c	c	X
ejpam-4344	16	37	,	,	PUNCT
ejpam-4344	16	38	δ(c	δ(c	PROPN
ejpam-4344	16	39	)	)	PUNCT
ejpam-4344	16	40	]	]	PUNCT
ejpam-4344	16	41	=	=	PUNCT
ejpam-4344	16	42	cδ(c)−	cδ(c)−	NOUN
ejpam-4344	16	43	δ(c)c	δ(c)c	PROPN
ejpam-4344	16	44	∈	∈	PROPN
ejpam-4344	16	45	z(r	z(r	PROPN
ejpam-4344	16	46	)	)	PUNCT
ejpam-4344	16	47	∀c	∀c	X
ejpam-4344	16	48	∈	∈	PROPN
ejpam-4344	16	49	i	i	PRON
ejpam-4344	16	50	.	.	PUNCT
ejpam-4344	17	1	assume	assume	VERB
ejpam-4344	17	2	that	that	SCONJ
ejpam-4344	17	3	∆	∆	PROPN
ejpam-4344	17	4	is	be	AUX
ejpam-4344	17	5	a	a	DET
ejpam-4344	17	6	non	non	ADJ
ejpam-4344	17	7	-	-	ADJ
ejpam-4344	17	8	empty	empty	ADJ
ejpam-4344	17	9	subset	subset	NOUN
ejpam-4344	17	10	of	of	ADP
ejpam-4344	17	11	d.	d.	PROPN
ejpam-4344	17	12	an	an	DET
ejpam-4344	17	13	ideal	ideal	NOUN
ejpam-4344	17	14	i	i	PRON
ejpam-4344	17	15	of	of	ADP
ejpam-4344	17	16	r	r	NOUN
ejpam-4344	17	17	,	,	PUNCT
ejpam-4344	17	18	where	where	SCONJ
ejpam-4344	17	19	δ(i	δ(i	NOUN
ejpam-4344	17	20	)	)	PUNCT
ejpam-4344	17	21	⊆	⊆	NUM
ejpam-4344	17	22	i	i	PRON
ejpam-4344	17	23	for	for	ADP
ejpam-4344	17	24	δ	δ	PROPN
ejpam-4344	17	25	∈	∈	PROPN
ejpam-4344	17	26	∆	∆	PROPN
ejpam-4344	17	27	is	be	AUX
ejpam-4344	17	28	called	call	VERB
ejpam-4344	17	29	a	a	DET
ejpam-4344	17	30	δ	δ	NOUN
ejpam-4344	17	31	-	-	PUNCT
ejpam-4344	17	32	ideal	ideal	NOUN
ejpam-4344	17	33	.	.	PUNCT
ejpam-4344	18	1	a	a	DET
ejpam-4344	18	2	ring	ring	NOUN
ejpam-4344	18	3	r	r	NOUN
ejpam-4344	18	4	is	be	AUX
ejpam-4344	18	5	called	call	VERB
ejpam-4344	18	6	δ	δ	NOUN
ejpam-4344	18	7	-	-	NOUN
ejpam-4344	18	8	prime	prime	NOUN
ejpam-4344	18	9	if	if	SCONJ
ejpam-4344	18	10	,	,	PUNCT
ejpam-4344	18	11	for	for	ADP
ejpam-4344	18	12	any	any	DET
ejpam-4344	18	13	two	two	NUM
ejpam-4344	18	14	δ	δ	NOUN
ejpam-4344	18	15	-	-	PUNCT
ejpam-4344	18	16	ideals	ideal	NOUN
ejpam-4344	18	17	i	i	PRON
ejpam-4344	18	18	,	,	PUNCT
ejpam-4344	18	19	j	j	PROPN
ejpam-4344	18	20	of	of	ADP
ejpam-4344	18	21	r	r	PROPN
ejpam-4344	18	22	,	,	PUNCT
ejpam-4344	18	23	the	the	DET
ejpam-4344	18	24	condition	condition	NOUN
ejpam-4344	18	25	ij	ij	NOUN
ejpam-4344	18	26	=	=	SYM
ejpam-4344	18	27	0	0	PROPN
ejpam-4344	18	28	implies	imply	VERB
ejpam-4344	18	29	that	that	SCONJ
ejpam-4344	18	30	i	i	PRON
ejpam-4344	18	31	=	=	PUNCT
ejpam-4344	18	32	0	0	NUM
ejpam-4344	18	33	or	or	CCONJ
ejpam-4344	18	34	j	j	PROPN
ejpam-4344	18	35	=	=	SYM
ejpam-4344	18	36	0	0	PROPN
ejpam-4344	18	37	.	.	PUNCT
ejpam-4344	19	1	the	the	DET
ejpam-4344	19	2	special	special	ADJ
ejpam-4344	19	3	case	case	NOUN
ejpam-4344	19	4	where	where	SCONJ
ejpam-4344	19	5	a	a	DET
ejpam-4344	19	6	centralizing	centralize	VERB
ejpam-4344	19	7	automorphism	automorphism	NOUN
ejpam-4344	19	8	is	be	AUX
ejpam-4344	19	9	a	a	DET
ejpam-4344	19	10	commuting	commuting	NOUN
ejpam-4344	19	11	automorphism	automorphism	NOUN
ejpam-4344	19	12	is	be	AUX
ejpam-4344	19	13	defined	define	VERB
ejpam-4344	19	14	by	by	ADP
ejpam-4344	19	15	cd(c	cd(c	NUM
ejpam-4344	19	16	)	)	PUNCT
ejpam-4344	20	1	=	=	SYM
ejpam-4344	20	2	d(c)c	d(c)c	PROPN
ejpam-4344	20	3	,	,	PUNCT
ejpam-4344	20	4	c	c	PROPN
ejpam-4344	20	5	∈	∈	PROPN
ejpam-4344	20	6	r.	r.	PROPN
ejpam-4344	20	7	likewise	likewise	ADV
ejpam-4344	20	8	,	,	PUNCT
ejpam-4344	20	9	d	d	PROPN
ejpam-4344	20	10	is	be	AUX
ejpam-4344	20	11	called	call	VERB
ejpam-4344	20	12	a	a	DET
ejpam-4344	20	13	semi	semi	ADJ
ejpam-4344	20	14	commuting	commute	VERB
ejpam-4344	20	15	automorphism	automorphism	NOUN
ejpam-4344	20	16	if	if	SCONJ
ejpam-4344	20	17	cd(c	cd(c	NUM
ejpam-4344	20	18	)	)	PUNCT
ejpam-4344	20	19	=	=	PUNCT
ejpam-4344	20	20	d(c)c	d(c)c	NOUN
ejpam-4344	20	21	or	or	CCONJ
ejpam-4344	20	22	cd(c	cd(c	NUM
ejpam-4344	20	23	)	)	PUNCT
ejpam-4344	21	1	=	=	PUNCT
ejpam-4344	22	1	−d(c)c	−d(c)c	PRON
ejpam-4344	22	2	holds	hold	VERB
ejpam-4344	22	3	for	for	ADP
ejpam-4344	22	4	any	any	DET
ejpam-4344	22	5	c	c	PROPN
ejpam-4344	22	6	∈	∈	PROPN
ejpam-4344	22	7	r.	r.	NOUN
ejpam-4344	22	8	all	all	DET
ejpam-4344	22	9	other	other	ADJ
ejpam-4344	22	10	definitions	definition	NOUN
ejpam-4344	22	11	and	and	CCONJ
ejpam-4344	22	12	facts	fact	NOUN
ejpam-4344	22	13	are	be	AUX
ejpam-4344	22	14	standard	standard	ADJ
ejpam-4344	22	15	and	and	CCONJ
ejpam-4344	22	16	they	they	PRON
ejpam-4344	22	17	can	can	AUX
ejpam-4344	22	18	be	be	AUX
ejpam-4344	22	19	found	find	VERB
ejpam-4344	22	20	in	in	ADP
ejpam-4344	22	21	[	[	X
ejpam-4344	22	22	17	17	NUM
ejpam-4344	22	23	]	]	PUNCT
ejpam-4344	22	24	,	,	PUNCT
ejpam-4344	23	1	[	[	X
ejpam-4344	23	2	18	18	NUM
ejpam-4344	23	3	]	]	PUNCT
ejpam-4344	23	4	,	,	PUNCT
ejpam-4344	23	5	[	[	X
ejpam-4344	23	6	19	19	NUM
ejpam-4344	23	7	]	]	PUNCT
ejpam-4344	23	8	and	and	CCONJ
ejpam-4344	23	9	[	[	X
ejpam-4344	23	10	23	23	NUM
ejpam-4344	23	11	]	]	PUNCT
ejpam-4344	23	12	.	.	PUNCT
ejpam-4344	24	1	recall	recall	VERB
ejpam-4344	24	2	that	that	PRON
ejpam-4344	24	3	,	,	PUNCT
ejpam-4344	24	4	the	the	DET
ejpam-4344	24	5	first	first	ADJ
ejpam-4344	24	6	theorem	theorem	NOUN
ejpam-4344	24	7	of	of	ADP
ejpam-4344	24	8	posner	posner	NOUN
ejpam-4344	24	9	informs	inform	VERB
ejpam-4344	24	10	us	we	PRON
ejpam-4344	24	11	that	that	SCONJ
ejpam-4344	24	12	if	if	SCONJ
ejpam-4344	24	13	r	r	NOUN
ejpam-4344	24	14	is	be	AUX
ejpam-4344	24	15	a	a	DET
ejpam-4344	24	16	prime	prime	ADJ
ejpam-4344	24	17	ring	ring	NOUN
ejpam-4344	24	18	with	with	ADP
ejpam-4344	24	19	charr	charr	NOUN
ejpam-4344	24	20	6=	6=	ADP
ejpam-4344	24	21	2	2	NUM
ejpam-4344	24	22	,	,	PUNCT
ejpam-4344	24	23	then	then	ADV
ejpam-4344	24	24	a	a	DET
ejpam-4344	24	25	composition	composition	NOUN
ejpam-4344	24	26	of	of	ADP
ejpam-4344	24	27	two	two	NUM
ejpam-4344	24	28	nonzero	nonzero	NOUN
ejpam-4344	24	29	derivations	derivation	NOUN
ejpam-4344	24	30	is	be	AUX
ejpam-4344	24	31	not	not	PART
ejpam-4344	24	32	a	a	DET
ejpam-4344	24	33	derivation	derivation	NOUN
ejpam-4344	24	34	.	.	PUNCT
ejpam-4344	25	1	many	many	ADJ
ejpam-4344	25	2	authors	author	NOUN
ejpam-4344	25	3	generalized	generalize	VERB
ejpam-4344	25	4	posner	posner	NOUN
ejpam-4344	25	5	’s	’s	PART
ejpam-4344	25	6	theorem	theorem	NOUN
ejpam-4344	25	7	in	in	ADP
ejpam-4344	25	8	various	various	ADJ
ejpam-4344	25	9	ways	way	NOUN
ejpam-4344	25	10	as	as	ADP
ejpam-4344	25	11	bergen	bergen	PROPN
ejpam-4344	26	1	[	[	X
ejpam-4344	26	2	6	6	NUM
ejpam-4344	26	3	]	]	PUNCT
ejpam-4344	26	4	,	,	PUNCT
ejpam-4344	26	5	chebotar	chebotar	VERB
ejpam-4344	26	6	[	[	X
ejpam-4344	26	7	11	11	NUM
ejpam-4344	26	8	]	]	PUNCT
ejpam-4344	26	9	,	,	PUNCT
ejpam-4344	26	10	chuang	chuang	PROPN
ejpam-4344	27	1	[	[	X
ejpam-4344	27	2	12	12	NUM
ejpam-4344	27	3	]	]	PUNCT
ejpam-4344	27	4	,	,	PUNCT
ejpam-4344	28	1	[	[	X
ejpam-4344	28	2	13	13	NUM
ejpam-4344	28	3	]	]	PUNCT
ejpam-4344	28	4	,	,	PUNCT
ejpam-4344	28	5	hirano	hirano	PROPN
ejpam-4344	29	1	[	[	X
ejpam-4344	29	2	21	21	NUM
ejpam-4344	29	3	]	]	PUNCT
ejpam-4344	29	4	,	,	PUNCT
ejpam-4344	29	5	lanski	lanski	NOUN
ejpam-4344	29	6	[	[	X
ejpam-4344	29	7	24	24	NUM
ejpam-4344	29	8	]	]	PUNCT
ejpam-4344	29	9	and	and	CCONJ
ejpam-4344	29	10	martindale	martindale	PROPN
ejpam-4344	30	1	[	[	X
ejpam-4344	30	2	25	25	NUM
ejpam-4344	30	3	]	]	PUNCT
ejpam-4344	30	4	.	.	PUNCT
ejpam-4344	31	1	furthermore	furthermore	ADV
ejpam-4344	31	2	,	,	PUNCT
ejpam-4344	31	3	creedon[15	creedon[15	PROPN
ejpam-4344	31	4	]	]	X
ejpam-4344	31	5	generalized	generalized	ADJ
ejpam-4344	31	6	posner	posner	NOUN
ejpam-4344	31	7	’s	’s	PART
ejpam-4344	31	8	first	first	ADJ
ejpam-4344	31	9	theorem	theorem	NOUN
ejpam-4344	31	10	to	to	ADP
ejpam-4344	31	11	semiprime	semiprime	PROPN
ejpam-4344	31	12	algebras	algebras	PROPN
ejpam-4344	31	13	,	,	PUNCT
ejpam-4344	31	14	i.e.	i.e.	X
ejpam-4344	31	15	he	he	PRON
ejpam-4344	31	16	showed	show	VERB
ejpam-4344	31	17	that	that	SCONJ
ejpam-4344	31	18	the	the	DET
ejpam-4344	31	19	composition	composition	NOUN
ejpam-4344	31	20	of	of	ADP
ejpam-4344	31	21	two	two	NUM
ejpam-4344	31	22	nonzero	nonzero	ADJ
ejpam-4344	31	23	derivations	derivation	NOUN
ejpam-4344	31	24	in	in	ADP
ejpam-4344	31	25	any	any	DET
ejpam-4344	31	26	algebra	algebra	NOUN
ejpam-4344	31	27	s	s	VERB
ejpam-4344	31	28	is	be	AUX
ejpam-4344	31	29	a	a	DET
ejpam-4344	31	30	derivation	derivation	NOUN
ejpam-4344	31	31	.	.	PUNCT
ejpam-4344	32	1	on	on	ADP
ejpam-4344	32	2	the	the	DET
ejpam-4344	32	3	other	other	ADJ
ejpam-4344	32	4	hand	hand	NOUN
ejpam-4344	32	5	,	,	PUNCT
ejpam-4344	32	6	from	from	ADP
ejpam-4344	32	7	the	the	DET
ejpam-4344	32	8	second	second	ADJ
ejpam-4344	32	9	posner	posner	NOUN
ejpam-4344	32	10	theorem	theorem	NOUN
ejpam-4344	32	11	which	which	PRON
ejpam-4344	32	12	states	state	VERB
ejpam-4344	32	13	:	:	PUNCT
ejpam-4344	32	14	if	if	SCONJ
ejpam-4344	32	15	r	r	NOUN
ejpam-4344	32	16	is	be	AUX
ejpam-4344	32	17	a	a	DET
ejpam-4344	32	18	prime	prime	ADJ
ejpam-4344	32	19	ring	ring	NOUN
ejpam-4344	32	20	with	with	ADP
ejpam-4344	32	21	centralizing	centralize	VERB
ejpam-4344	32	22	derivation	derivation	NOUN
ejpam-4344	32	23	d	d	NOUN
ejpam-4344	32	24	6=	6=	ADP
ejpam-4344	32	25	0	0	NUM
ejpam-4344	32	26	on	on	ADP
ejpam-4344	32	27	r	r	NOUN
ejpam-4344	32	28	,	,	PUNCT
ejpam-4344	32	29	then	then	ADV
ejpam-4344	32	30	r	r	NOUN
ejpam-4344	32	31	is	be	AUX
ejpam-4344	32	32	commutative	commutative	ADJ
ejpam-4344	32	33	.	.	PUNCT
ejpam-4344	33	1	in	in	ADP
ejpam-4344	33	2	fact	fact	NOUN
ejpam-4344	33	3	,	,	PUNCT
ejpam-4344	33	4	this	this	DET
ejpam-4344	33	5	theorem	theorem	NOUN
ejpam-4344	33	6	extremely	extremely	ADV
ejpam-4344	33	7	helped	help	VERB
ejpam-4344	33	8	some	some	DET
ejpam-4344	33	9	researches	research	NOUN
ejpam-4344	33	10	to	to	PART
ejpam-4344	33	11	study	study	VERB
ejpam-4344	33	12	the	the	DET
ejpam-4344	33	13	commuting	commuting	NOUN
ejpam-4344	33	14	derivations	derivation	NOUN
ejpam-4344	33	15	,	,	PUNCT
ejpam-4344	33	16	because	because	SCONJ
ejpam-4344	33	17	every	every	DET
ejpam-4344	33	18	centralizing	centralizing	NOUN
ejpam-4344	33	19	derivation	derivation	NOUN
ejpam-4344	33	20	is	be	AUX
ejpam-4344	33	21	a	a	DET
ejpam-4344	33	22	commuting	commute	VERB
ejpam-4344	33	23	derivation	derivation	NOUN
ejpam-4344	33	24	.	.	PUNCT
ejpam-4344	34	1	recall	recall	VERB
ejpam-4344	34	2	that	that	PRON
ejpam-4344	34	3	,	,	PUNCT
ejpam-4344	34	4	the	the	DET
ejpam-4344	34	5	assumption	assumption	NOUN
ejpam-4344	34	6	of	of	ADP
ejpam-4344	34	7	primeness	primeness	NOUN
ejpam-4344	34	8	in	in	ADP
ejpam-4344	34	9	the	the	DET
ejpam-4344	34	10	second	second	ADJ
ejpam-4344	34	11	posner	posner	NOUN
ejpam-4344	34	12	theorem	theorem	NOUN
ejpam-4344	34	13	is	be	AUX
ejpam-4344	34	14	necessarily	necessarily	ADV
ejpam-4344	34	15	,	,	PUNCT
ejpam-4344	34	16	since	since	SCONJ
ejpam-4344	34	17	if	if	SCONJ
ejpam-4344	34	18	we	we	PRON
ejpam-4344	34	19	take	take	VERB
ejpam-4344	34	20	for	for	ADP
ejpam-4344	34	21	example	example	NOUN
ejpam-4344	34	22	the	the	DET
ejpam-4344	34	23	ring	ring	NOUN
ejpam-4344	34	24	r	r	NOUN
ejpam-4344	34	25	=	=	PUNCT
ejpam-4344	34	26	s	s	PART
ejpam-4344	34	27	×	×	NOUN
ejpam-4344	34	28	t	t	NOUN
ejpam-4344	34	29	such	such	ADJ
ejpam-4344	35	1	that	that	PRON
ejpam-4344	35	2	s	s	VERB
ejpam-4344	35	3	is	be	AUX
ejpam-4344	35	4	a	a	DET
ejpam-4344	35	5	commutative	commutative	ADJ
ejpam-4344	35	6	ring	ring	NOUN
ejpam-4344	35	7	with	with	ADP
ejpam-4344	35	8	derivation	derivation	NOUN
ejpam-4344	35	9	d1	d1	PROPN
ejpam-4344	35	10	and	and	CCONJ
ejpam-4344	35	11	t	t	PROPN
ejpam-4344	35	12	is	be	AUX
ejpam-4344	35	13	a	a	DET
ejpam-4344	35	14	non	non	ADJ
ejpam-4344	35	15	-	-	ADJ
ejpam-4344	35	16	commutative	commutative	ADJ
ejpam-4344	35	17	ring	ring	NOUN
ejpam-4344	35	18	,	,	PUNCT
ejpam-4344	35	19	then	then	ADV
ejpam-4344	35	20	we	we	PRON
ejpam-4344	35	21	can	can	AUX
ejpam-4344	35	22	prove	prove	VERB
ejpam-4344	35	23	that	that	SCONJ
ejpam-4344	35	24	the	the	DET
ejpam-4344	35	25	derivation	derivation	NOUN
ejpam-4344	35	26	on	on	ADP
ejpam-4344	35	27	r	r	NOUN
ejpam-4344	35	28	given	give	VERB
ejpam-4344	35	29	by	by	ADP
ejpam-4344	35	30	d(s	d(s	PROPN
ejpam-4344	35	31	,	,	PUNCT
ejpam-4344	35	32	t	t	PROPN
ejpam-4344	35	33	)	)	PUNCT
ejpam-4344	35	34	=	=	PUNCT
ejpam-4344	35	35	(	(	PUNCT
ejpam-4344	35	36	d1(s	d1(s	PROPN
ejpam-4344	35	37	)	)	PUNCT
ejpam-4344	35	38	,	,	PUNCT
ejpam-4344	35	39	0	0	NUM
ejpam-4344	35	40	)	)	PUNCT
ejpam-4344	35	41	is	be	AUX
ejpam-4344	35	42	a	a	DET
ejpam-4344	35	43	non	non	ADJ
ejpam-4344	35	44	zero	zero	NUM
ejpam-4344	35	45	commuting	commute	VERB
ejpam-4344	35	46	derivation	derivation	NOUN
ejpam-4344	35	47	,	,	PUNCT
ejpam-4344	35	48	but	but	CCONJ
ejpam-4344	35	49	r	r	NOUN
ejpam-4344	35	50	is	be	AUX
ejpam-4344	35	51	not	not	PART
ejpam-4344	35	52	a	a	DET
ejpam-4344	35	53	commutative	commutative	ADJ
ejpam-4344	35	54	ring	ring	NOUN
ejpam-4344	35	55	.	.	PUNCT
ejpam-4344	36	1	in	in	ADP
ejpam-4344	36	2	the	the	DET
ejpam-4344	36	3	last	last	ADJ
ejpam-4344	36	4	fifty	fifty	NUM
ejpam-4344	36	5	years	year	NOUN
ejpam-4344	36	6	,	,	PUNCT
ejpam-4344	36	7	a	a	DET
ejpam-4344	36	8	lot	lot	NOUN
ejpam-4344	36	9	of	of	ADP
ejpam-4344	36	10	results	result	NOUN
ejpam-4344	36	11	have	have	AUX
ejpam-4344	36	12	been	be	AUX
ejpam-4344	36	13	obtained	obtain	VERB
ejpam-4344	36	14	about	about	ADP
ejpam-4344	36	15	commuting	commute	VERB
ejpam-4344	36	16	and	and	CCONJ
ejpam-4344	36	17	centralizing	centralize	VERB
ejpam-4344	36	18	derivations	derivation	NOUN
ejpam-4344	37	1	d	d	X
ejpam-4344	37	2	(	(	PUNCT
ejpam-4344	37	3	d	d	ADP
ejpam-4344	37	4	satisfies	satisfy	VERB
ejpam-4344	37	5	the	the	DET
ejpam-4344	37	6	condition	condition	NOUN
ejpam-4344	38	1	[	[	X
ejpam-4344	38	2	d(c	d(c	PROPN
ejpam-4344	38	3	)	)	PUNCT
ejpam-4344	38	4	,	,	PUNCT
ejpam-4344	38	5	c	c	X
ejpam-4344	38	6	]	]	X
ejpam-4344	38	7	∈	∈	PROPN
ejpam-4344	38	8	z(r	z(r	PROPN
ejpam-4344	38	9	)	)	PUNCT
ejpam-4344	38	10	for	for	ADP
ejpam-4344	38	11	all	all	DET
ejpam-4344	38	12	c	c	NOUN
ejpam-4344	38	13	∈	∈	NOUN
ejpam-4344	38	14	r	r	NOUN
ejpam-4344	38	15	)	)	PUNCT
ejpam-4344	38	16	.	.	PUNCT
ejpam-4344	39	1	however	however	ADV
ejpam-4344	39	2	,	,	PUNCT
ejpam-4344	39	3	many	many	ADJ
ejpam-4344	39	4	authors	author	NOUN
ejpam-4344	39	5	extended	extend	VERB
ejpam-4344	39	6	it	it	PRON
ejpam-4344	39	7	by	by	ADP
ejpam-4344	39	8	taking	take	VERB
ejpam-4344	39	9	a	a	DET
ejpam-4344	39	10	centralizing	centralizing	NOUN
ejpam-4344	39	11	map	map	NOUN
ejpam-4344	39	12	on	on	ADP
ejpam-4344	39	13	a	a	DET
ejpam-4344	39	14	ring	ring	NOUN
ejpam-4344	39	15	only	only	ADV
ejpam-4344	39	16	.	.	PUNCT
ejpam-4344	40	1	in	in	ADP
ejpam-4344	40	2	1973	1973	NUM
ejpam-4344	40	3	,	,	PUNCT
ejpam-4344	40	4	awtar	awtar	NOUN
ejpam-4344	40	5	[	[	X
ejpam-4344	40	6	4	4	NUM
ejpam-4344	40	7	]	]	PUNCT
ejpam-4344	40	8	studied	study	VERB
ejpam-4344	40	9	the	the	DET
ejpam-4344	40	10	centralizing	centralize	VERB
ejpam-4344	40	11	derivation	derivation	NOUN
ejpam-4344	40	12	on	on	ADP
ejpam-4344	40	13	lie	lie	NOUN
ejpam-4344	40	14	ideals	ideal	NOUN
ejpam-4344	40	15	and	and	CCONJ
ejpam-4344	40	16	jordan	jordan	PROPN
ejpam-4344	40	17	ideals	ideal	NOUN
ejpam-4344	40	18	.	.	PUNCT
ejpam-4344	41	1	in	in	ADP
ejpam-4344	41	2	particular	particular	ADJ
ejpam-4344	41	3	,	,	PUNCT
ejpam-4344	41	4	he	he	PRON
ejpam-4344	41	5	proved	prove	VERB
ejpam-4344	41	6	that	that	SCONJ
ejpam-4344	41	7	if	if	SCONJ
ejpam-4344	41	8	r	r	NOUN
ejpam-4344	41	9	is	be	AUX
ejpam-4344	41	10	a	a	DET
ejpam-4344	41	11	prime	prime	ADJ
ejpam-4344	41	12	ring	ring	NOUN
ejpam-4344	41	13	of	of	ADP
ejpam-4344	41	14	charr	charr	NOUN
ejpam-4344	41	15	6=	6=	ADP
ejpam-4344	41	16	2	2	NUM
ejpam-4344	41	17	and	and	CCONJ
ejpam-4344	41	18	t	t	PROPN
ejpam-4344	41	19	6=	6=	X
ejpam-4344	41	20	{	{	PUNCT
ejpam-4344	41	21	0	0	NUM
ejpam-4344	41	22	}	}	PUNCT
ejpam-4344	41	23	is	be	AUX
ejpam-4344	41	24	a	a	DET
ejpam-4344	41	25	lie	lie	NOUN
ejpam-4344	41	26	ideal	ideal	NOUN
ejpam-4344	41	27	or	or	CCONJ
ejpam-4344	41	28	jordan	jordan	PROPN
ejpam-4344	41	29	ideal	ideal	PROPN
ejpam-4344	41	30	and	and	CCONJ
ejpam-4344	41	31	subring	subre	VERB
ejpam-4344	41	32	in	in	ADP
ejpam-4344	41	33	r	r	NOUN
ejpam-4344	41	34	,	,	PUNCT
ejpam-4344	41	35	with	with	ADP
ejpam-4344	41	36	d	d	PROPN
ejpam-4344	41	37	6=	6=	ADP
ejpam-4344	41	38	0	0	NUM
ejpam-4344	41	39	being	be	AUX
ejpam-4344	41	40	a	a	DET
ejpam-4344	41	41	derivation	derivation	NOUN
ejpam-4344	41	42	on	on	ADP
ejpam-4344	41	43	r	r	NOUN
ejpam-4344	41	44	,	,	PUNCT
ejpam-4344	41	45	if	if	SCONJ
ejpam-4344	41	46	[	[	X
ejpam-4344	41	47	c	c	X
ejpam-4344	41	48	,	,	PUNCT
ejpam-4344	41	49	d(c	d(c	PROPN
ejpam-4344	41	50	)	)	PUNCT
ejpam-4344	41	51	]	]	PUNCT
ejpam-4344	42	1	∈	∈	PROPN
ejpam-4344	42	2	z(r	z(r	PROPN
ejpam-4344	42	3	)	)	PUNCT
ejpam-4344	42	4	,	,	PUNCT
ejpam-4344	42	5	for	for	ADP
ejpam-4344	42	6	all	all	DET
ejpam-4344	42	7	c	c	NOUN
ejpam-4344	42	8	∈	∈	PROPN
ejpam-4344	42	9	t	t	NOUN
ejpam-4344	42	10	then	then	ADV
ejpam-4344	42	11	r	r	NOUN
ejpam-4344	42	12	is	be	AUX
ejpam-4344	42	13	commutative	commutative	ADJ
ejpam-4344	42	14	.	.	PUNCT
ejpam-4344	43	1	in	in	ADP
ejpam-4344	43	2	addition	addition	NOUN
ejpam-4344	43	3	,	,	PUNCT
ejpam-4344	43	4	if	if	SCONJ
ejpam-4344	43	5	we	we	PRON
ejpam-4344	43	6	assume	assume	VERB
ejpam-4344	43	7	that	that	SCONJ
ejpam-4344	43	8	either	either	DET
ejpam-4344	43	9	t	t	PROPN
ejpam-4344	43	10	is	be	AUX
ejpam-4344	43	11	a	a	DET
ejpam-4344	43	12	lie	lie	NOUN
ejpam-4344	43	13	(	(	PUNCT
ejpam-4344	43	14	jordan	jordan	PROPN
ejpam-4344	43	15	)	)	PUNCT
ejpam-4344	43	16	ideal	ideal	NOUN
ejpam-4344	43	17	or	or	CCONJ
ejpam-4344	43	18	a	a	DET
ejpam-4344	43	19	subring	subring	NOUN
ejpam-4344	43	20	,	,	PUNCT
ejpam-4344	43	21	then	then	ADV
ejpam-4344	43	22	r	r	NOUN
ejpam-4344	43	23	is	be	AUX
ejpam-4344	43	24	not	not	PART
ejpam-4344	43	25	necessarily	necessarily	ADV
ejpam-4344	43	26	commutative	commutative	ADJ
ejpam-4344	43	27	.	.	PUNCT
ejpam-4344	44	1	that	that	PRON
ejpam-4344	44	2	can	can	AUX
ejpam-4344	44	3	be	be	AUX
ejpam-4344	44	4	shown	show	VERB
ejpam-4344	44	5	as	as	SCONJ
ejpam-4344	44	6	follows	follow	VERB
ejpam-4344	44	7	:	:	PUNCT
ejpam-4344	44	8	let	let	VERB
ejpam-4344	44	9	r	r	PRON
ejpam-4344	44	10	be	be	AUX
ejpam-4344	44	11	a	a	DET
ejpam-4344	44	12	prime	prime	ADJ
ejpam-4344	44	13	ring	ring	NOUN
ejpam-4344	44	14	with	with	ADP
ejpam-4344	44	15	charr	charr	NOUN
ejpam-4344	44	16	6=	6=	ADP
ejpam-4344	44	17	2	2	NUM
ejpam-4344	44	18	and	and	CCONJ
ejpam-4344	44	19	d	d	NOUN
ejpam-4344	44	20	6=	6=	ADP
ejpam-4344	44	21	0	0	NUM
ejpam-4344	44	22	is	be	AUX
ejpam-4344	44	23	a	a	DET
ejpam-4344	44	24	derivation	derivation	NOUN
ejpam-4344	44	25	of	of	ADP
ejpam-4344	44	26	r.	r.	PROPN
ejpam-4344	44	27	if	if	SCONJ
ejpam-4344	44	28	t	t	PROPN
ejpam-4344	44	29	is	be	AUX
ejpam-4344	44	30	a	a	DET
ejpam-4344	44	31	lie	lie	NOUN
ejpam-4344	44	32	or	or	CCONJ
ejpam-4344	44	33	jordan	jordan	PROPN
ejpam-4344	44	34	ideal	ideal	PROPN
ejpam-4344	44	35	and	and	CCONJ
ejpam-4344	44	36	a	a	DET
ejpam-4344	44	37	subring	subring	NOUN
ejpam-4344	44	38	of	of	ADP
ejpam-4344	44	39	r	r	NOUN
ejpam-4344	44	40	and	and	CCONJ
ejpam-4344	44	41	if	if	SCONJ
ejpam-4344	44	42	[	[	X
ejpam-4344	44	43	c	c	X
ejpam-4344	44	44	,	,	PUNCT
ejpam-4344	44	45	d(c	d(c	PROPN
ejpam-4344	44	46	)	)	PUNCT
ejpam-4344	44	47	]	]	PUNCT
ejpam-4344	45	1	∈	∈	PROPN
ejpam-4344	45	2	z(r	z(r	PROPN
ejpam-4344	45	3	)	)	PUNCT
ejpam-4344	45	4	,	,	PUNCT
ejpam-4344	45	5	for	for	ADP
ejpam-4344	45	6	all	all	DET
ejpam-4344	45	7	c	c	NOUN
ejpam-4344	45	8	∈	∈	PROPN
ejpam-4344	45	9	t	t	NOUN
ejpam-4344	45	10	,	,	PUNCT
ejpam-4344	45	11	then	then	ADV
ejpam-4344	45	12	the	the	DET
ejpam-4344	45	13	ring	ring	NOUN
ejpam-4344	45	14	r	r	NOUN
ejpam-4344	45	15	is	be	AUX
ejpam-4344	45	16	commutative	commutative	ADJ
ejpam-4344	45	17	.	.	PUNCT
ejpam-4344	46	1	mayne	mayne	PROPN
ejpam-4344	47	1	[	[	X
ejpam-4344	47	2	26	26	NUM
ejpam-4344	47	3	]	]	PUNCT
ejpam-4344	47	4	got	get	VERB
ejpam-4344	47	5	the	the	DET
ejpam-4344	47	6	same	same	ADJ
ejpam-4344	47	7	result	result	NOUN
ejpam-4344	47	8	,	,	PUNCT
ejpam-4344	47	9	i.e.	i.e.	X
ejpam-4344	47	10	if	if	SCONJ
ejpam-4344	47	11	r	r	NOUN
ejpam-4344	47	12	is	be	AUX
ejpam-4344	47	13	a	a	DET
ejpam-4344	47	14	prime	prime	ADJ
ejpam-4344	47	15	ring	ring	NOUN
ejpam-4344	47	16	and	and	CCONJ
ejpam-4344	47	17	d	d	NOUN
ejpam-4344	47	18	6=	6=	PROPN
ejpam-4344	47	19	0	0	NUM
ejpam-4344	47	20	is	be	AUX
ejpam-4344	47	21	a	a	DET
ejpam-4344	47	22	centralizing	centralize	VERB
ejpam-4344	47	23	automorphism	automorphism	NOUN
ejpam-4344	47	24	,	,	PUNCT
ejpam-4344	47	25	then	then	ADV
ejpam-4344	47	26	r	r	NOUN
ejpam-4344	47	27	is	be	AUX
ejpam-4344	47	28	an	an	DET
ejpam-4344	47	29	integral	integral	ADJ
ejpam-4344	47	30	domain	domain	NOUN
ejpam-4344	47	31	.	.	PUNCT
ejpam-4344	48	1	furthermore	furthermore	ADV
ejpam-4344	48	2	,	,	PUNCT
ejpam-4344	48	3	mayne	mayne	PROPN
ejpam-4344	48	4	[	[	X
ejpam-4344	48	5	27	27	NUM
ejpam-4344	48	6	]	]	PUNCT
ejpam-4344	48	7	generalized	generalize	VERB
ejpam-4344	48	8	the	the	DET
ejpam-4344	48	9	previous	previous	ADJ
ejpam-4344	48	10	results	result	NOUN
ejpam-4344	48	11	for	for	ADP
ejpam-4344	48	12	a	a	DET
ejpam-4344	48	13	derivation	derivation	NOUN
ejpam-4344	48	14	d	d	NOUN
ejpam-4344	48	15	or	or	CCONJ
ejpam-4344	48	16	an	an	DET
ejpam-4344	48	17	automorphism	automorphism	NOUN
ejpam-4344	48	18	,	,	PUNCT
ejpam-4344	48	19	moreover	moreover	ADV
ejpam-4344	48	20	,	,	PUNCT
ejpam-4344	48	21	mayne	mayne	PROPN
ejpam-4344	49	1	[	[	X
ejpam-4344	49	2	28	28	NUM
ejpam-4344	49	3	]	]	PUNCT
ejpam-4344	49	4	showed	show	VERB
ejpam-4344	49	5	that	that	SCONJ
ejpam-4344	49	6	if	if	SCONJ
ejpam-4344	49	7	there	there	PRON
ejpam-4344	49	8	exists	exist	VERB
ejpam-4344	49	9	a	a	DET
ejpam-4344	49	10	centralizing	centralize	VERB
ejpam-4344	49	11	derivation	derivation	NOUN
ejpam-4344	49	12	d	d	NOUN
ejpam-4344	49	13	6=	6=	X
ejpam-4344	49	14	{	{	PUNCT
ejpam-4344	49	15	0	0	NUM
ejpam-4344	49	16	}	}	PUNCT
ejpam-4344	49	17	or	or	CCONJ
ejpam-4344	49	18	a	a	DET
ejpam-4344	49	19	centralizing	centralize	VERB
ejpam-4344	49	20	automorphis	automorphis	PRON
ejpam-4344	49	21	on	on	ADP
ejpam-4344	49	22	an	an	DET
ejpam-4344	49	23	ideal	ideal	ADJ
ejpam-4344	49	24	t	t	PROPN
ejpam-4344	49	25	6=	6=	ADP
ejpam-4344	49	26	0	0	NUM
ejpam-4344	49	27	of	of	ADP
ejpam-4344	49	28	a	a	DET
ejpam-4344	49	29	prime	prime	ADJ
ejpam-4344	49	30	ring	ring	NOUN
ejpam-4344	49	31	r	r	NOUN
ejpam-4344	49	32	,	,	PUNCT
ejpam-4344	49	33	then	then	ADV
ejpam-4344	49	34	r	r	NOUN
ejpam-4344	49	35	is	be	AUX
ejpam-4344	49	36	commutative	commutative	ADJ
ejpam-4344	49	37	.	.	PUNCT
ejpam-4344	50	1	i.	i.	PROPN
ejpam-4344	50	2	taha	taha	PROPN
ejpam-4344	50	3	et	et	PROPN
ejpam-4344	50	4	al	al	PROPN
ejpam-4344	50	5	.	.	PUNCT
ejpam-4344	50	6	/	/	SYM
ejpam-4344	50	7	eur	eur	PROPN
ejpam-4344	50	8	.	.	PUNCT
ejpam-4344	51	1	j.	j.	PROPN
ejpam-4344	51	2	pure	pure	PROPN
ejpam-4344	51	3	appl	appl	PROPN
ejpam-4344	51	4	.	.	PROPN
ejpam-4344	51	5	math	math	PROPN
ejpam-4344	51	6	,	,	PUNCT
ejpam-4344	51	7	15	15	NUM
ejpam-4344	51	8	(	(	PUNCT
ejpam-4344	51	9	2	2	NUM
ejpam-4344	51	10	)	)	PUNCT
ejpam-4344	51	11	(	(	PUNCT
ejpam-4344	51	12	2022	2022	NUM
ejpam-4344	51	13	)	)	PUNCT
ejpam-4344	51	14	,	,	PUNCT
ejpam-4344	51	15	454	454	NUM
ejpam-4344	51	16	-	-	SYM
ejpam-4344	51	17	466	466	NUM
ejpam-4344	51	18	456	456	NUM
ejpam-4344	51	19	also	also	ADV
ejpam-4344	51	20	,	,	PUNCT
ejpam-4344	51	21	awtar	awtar	NOUN
ejpam-4344	51	22	[	[	X
ejpam-4344	51	23	4	4	NUM
ejpam-4344	51	24	]	]	PUNCT
ejpam-4344	51	25	extended	extend	VERB
ejpam-4344	51	26	the	the	DET
ejpam-4344	51	27	derivation	derivation	NOUN
ejpam-4344	51	28	case	case	NOUN
ejpam-4344	51	29	on	on	ADP
ejpam-4344	51	30	a	a	DET
ejpam-4344	51	31	prime	prime	ADJ
ejpam-4344	51	32	ring	ring	NOUN
ejpam-4344	51	33	with	with	ADP
ejpam-4344	51	34	any	any	DET
ejpam-4344	51	35	characteristic	characteristic	NOUN
ejpam-4344	51	36	.	.	PUNCT
ejpam-4344	52	1	whereas	whereas	SCONJ
ejpam-4344	52	2	,	,	PUNCT
ejpam-4344	52	3	mccrimmon	mccrimmon	ADJ
ejpam-4344	52	4	[	[	X
ejpam-4344	52	5	29	29	NUM
ejpam-4344	52	6	]	]	PUNCT
ejpam-4344	52	7	proved	prove	VERB
ejpam-4344	52	8	that	that	SCONJ
ejpam-4344	52	9	the	the	DET
ejpam-4344	52	10	automorphism	automorphism	NOUN
ejpam-4344	52	11	in	in	ADP
ejpam-4344	52	12	mayne	mayne	PROPN
ejpam-4344	52	13	’s	’s	PART
ejpam-4344	52	14	theorem	theorem	NOUN
ejpam-4344	52	15	did	do	AUX
ejpam-4344	52	16	not	not	PART
ejpam-4344	52	17	generalize	generalize	VERB
ejpam-4344	52	18	for	for	ADP
ejpam-4344	52	19	a	a	DET
ejpam-4344	52	20	semiprime	semiprime	NOUN
ejpam-4344	52	21	ring	ring	NOUN
ejpam-4344	52	22	.	.	PUNCT
ejpam-4344	53	1	likewise	likewise	ADV
ejpam-4344	53	2	,	,	PUNCT
ejpam-4344	53	3	vukman	vukman	NOUN
ejpam-4344	53	4	[	[	X
ejpam-4344	53	5	32	32	NUM
ejpam-4344	53	6	]	]	PUNCT
ejpam-4344	53	7	has	have	AUX
ejpam-4344	53	8	extended	extend	VERB
ejpam-4344	53	9	posner	posner	NOUN
ejpam-4344	53	10	’s	’s	PART
ejpam-4344	53	11	second	second	ADJ
ejpam-4344	53	12	theorem	theorem	NOUN
ejpam-4344	53	13	by	by	ADP
ejpam-4344	53	14	proving	prove	VERB
ejpam-4344	53	15	that	that	SCONJ
ejpam-4344	53	16	if	if	SCONJ
ejpam-4344	53	17	d	d	PROPN
ejpam-4344	53	18	6=	6=	ADP
ejpam-4344	53	19	0	0	NUM
ejpam-4344	53	20	is	be	AUX
ejpam-4344	53	21	a	a	DET
ejpam-4344	53	22	derivation	derivation	NOUN
ejpam-4344	53	23	on	on	ADP
ejpam-4344	53	24	prime	prime	ADJ
ejpam-4344	53	25	ring	ring	NOUN
ejpam-4344	53	26	with	with	ADP
ejpam-4344	53	27	charr	charr	NOUN
ejpam-4344	53	28	6=	6=	ADP
ejpam-4344	53	29	2	2	NUM
ejpam-4344	53	30	and	and	CCONJ
ejpam-4344	53	31	[	[	X
ejpam-4344	53	32	[	[	X
ejpam-4344	53	33	d(c	d(c	PROPN
ejpam-4344	53	34	)	)	PUNCT
ejpam-4344	53	35	,	,	PUNCT
ejpam-4344	54	1	c	c	X
ejpam-4344	54	2	]	]	X
ejpam-4344	54	3	,	,	PUNCT
ejpam-4344	54	4	c	c	X
ejpam-4344	54	5	]	]	X
ejpam-4344	54	6	=	=	SYM
ejpam-4344	54	7	0	0	NUM
ejpam-4344	54	8	,	,	PUNCT
ejpam-4344	54	9	for	for	ADP
ejpam-4344	54	10	all	all	PRON
ejpam-4344	54	11	c	c	NOUN
ejpam-4344	54	12	∈	∈	PROPN
ejpam-4344	54	13	r	r	NOUN
ejpam-4344	54	14	,	,	PUNCT
ejpam-4344	54	15	then	then	ADV
ejpam-4344	54	16	either	either	CCONJ
ejpam-4344	54	17	d	d	PROPN
ejpam-4344	54	18	=	=	SYM
ejpam-4344	54	19	0	0	NUM
ejpam-4344	54	20	or	or	CCONJ
ejpam-4344	54	21	r	r	NOUN
ejpam-4344	54	22	is	be	AUX
ejpam-4344	54	23	commutative	commutative	ADJ
ejpam-4344	54	24	.	.	PUNCT
ejpam-4344	55	1	in	in	ADP
ejpam-4344	55	2	fact	fact	NOUN
ejpam-4344	55	3	,	,	PUNCT
ejpam-4344	55	4	this	this	DET
ejpam-4344	55	5	theorem	theorem	NOUN
ejpam-4344	55	6	has	have	AUX
ejpam-4344	55	7	merely	merely	ADV
ejpam-4344	55	8	showed	show	VERB
ejpam-4344	55	9	that	that	SCONJ
ejpam-4344	55	10	d	d	NOUN
ejpam-4344	55	11	is	be	AUX
ejpam-4344	55	12	commuting	commute	VERB
ejpam-4344	55	13	.	.	PUNCT
ejpam-4344	56	1	in	in	ADP
ejpam-4344	56	2	addition	addition	NOUN
ejpam-4344	56	3	,	,	PUNCT
ejpam-4344	56	4	in	in	ADP
ejpam-4344	56	5	1992	1992	NUM
ejpam-4344	56	6	,	,	PUNCT
ejpam-4344	56	7	vukman	vukman	PROPN
ejpam-4344	56	8	extended	extend	VERB
ejpam-4344	56	9	the	the	DET
ejpam-4344	56	10	second	second	ADJ
ejpam-4344	56	11	posner	posner	NOUN
ejpam-4344	56	12	’s	’s	PART
ejpam-4344	56	13	result	result	NOUN
ejpam-4344	56	14	for	for	ADP
ejpam-4344	56	15	an	an	DET
ejpam-4344	56	16	automorphism	automorphism	NOUN
ejpam-4344	56	17	or	or	CCONJ
ejpam-4344	56	18	a	a	DET
ejpam-4344	56	19	centralizing	centralize	VERB
ejpam-4344	56	20	derivation	derivation	NOUN
ejpam-4344	56	21	on	on	ADP
ejpam-4344	56	22	a	a	DET
ejpam-4344	56	23	lie	lie	NOUN
ejpam-4344	56	24	ideal	ideal	NOUN
ejpam-4344	56	25	t	t	PROPN
ejpam-4344	56	26	6=	6=	PROPN
ejpam-4344	56	27	{	{	PUNCT
ejpam-4344	56	28	0	0	NUM
ejpam-4344	56	29	}	}	PUNCT
ejpam-4344	56	30	.	.	PUNCT
ejpam-4344	57	1	whereas	whereas	SCONJ
ejpam-4344	57	2	,	,	PUNCT
ejpam-4344	57	3	in	in	ADP
ejpam-4344	57	4	1993	1993	NUM
ejpam-4344	57	5	bresar	bresar	VERB
ejpam-4344	57	6	[	[	X
ejpam-4344	57	7	8	8	NUM
ejpam-4344	57	8	]	]	PUNCT
ejpam-4344	57	9	showed	show	VERB
ejpam-4344	57	10	that	that	SCONJ
ejpam-4344	57	11	an	an	DET
ejpam-4344	57	12	additive	additive	ADJ
ejpam-4344	57	13	map	map	NOUN
ejpam-4344	57	14	is	be	AUX
ejpam-4344	57	15	not	not	PART
ejpam-4344	57	16	centralizing	centralize	VERB
ejpam-4344	57	17	on	on	ADP
ejpam-4344	57	18	determined	determined	ADJ
ejpam-4344	57	19	subsets	subset	NOUN
ejpam-4344	57	20	of	of	ADP
ejpam-4344	57	21	prime	prime	ADJ
ejpam-4344	57	22	and	and	CCONJ
ejpam-4344	57	23	non	non	ADJ
ejpam-4344	57	24	-	-	ADJ
ejpam-4344	57	25	commutative	commutative	ADJ
ejpam-4344	57	26	ring	ring	NOUN
ejpam-4344	57	27	.	.	PUNCT
ejpam-4344	58	1	futhermore	futhermore	NOUN
ejpam-4344	58	2	,	,	PUNCT
ejpam-4344	58	3	some	some	DET
ejpam-4344	58	4	generalizations	generalization	NOUN
ejpam-4344	58	5	of	of	ADP
ejpam-4344	58	6	these	these	DET
ejpam-4344	58	7	results	result	NOUN
ejpam-4344	58	8	for	for	ADP
ejpam-4344	58	9	a	a	DET
ejpam-4344	58	10	prime	prime	ADJ
ejpam-4344	58	11	ring	ring	NOUN
ejpam-4344	58	12	are	be	AUX
ejpam-4344	58	13	contained	contain	VERB
ejpam-4344	58	14	in	in	ADP
ejpam-4344	58	15	[	[	X
ejpam-4344	58	16	20–22	20–22	NOUN
ejpam-4344	58	17	]	]	X
ejpam-4344	58	18	.	.	PUNCT
ejpam-4344	59	1	as	as	ADP
ejpam-4344	59	2	for	for	ADP
ejpam-4344	59	3	a	a	DET
ejpam-4344	59	4	semiprime	semiprime	NOUN
ejpam-4344	59	5	ring	ring	NOUN
ejpam-4344	59	6	we	we	PRON
ejpam-4344	59	7	refer	refer	VERB
ejpam-4344	59	8	the	the	DET
ejpam-4344	59	9	reader	reader	NOUN
ejpam-4344	59	10	to	to	ADP
ejpam-4344	59	11	[	[	X
ejpam-4344	59	12	10	10	NUM
ejpam-4344	59	13	]	]	PUNCT
ejpam-4344	59	14	,	,	PUNCT
ejpam-4344	59	15	[	[	X
ejpam-4344	59	16	7	7	NUM
ejpam-4344	59	17	]	]	PUNCT
ejpam-4344	59	18	,	,	PUNCT
ejpam-4344	59	19	[	[	X
ejpam-4344	59	20	9	9	NUM
ejpam-4344	59	21	]	]	PUNCT
ejpam-4344	59	22	,	,	PUNCT
ejpam-4344	59	23	[	[	X
ejpam-4344	59	24	32	32	NUM
ejpam-4344	59	25	]	]	PUNCT
ejpam-4344	59	26	and	and	CCONJ
ejpam-4344	59	27	[	[	X
ejpam-4344	59	28	33	33	NUM
ejpam-4344	59	29	]	]	PUNCT
ejpam-4344	59	30	.	.	PUNCT
ejpam-4344	60	1	in	in	ADP
ejpam-4344	60	2	our	our	PRON
ejpam-4344	60	3	current	current	ADJ
ejpam-4344	60	4	research	research	NOUN
ejpam-4344	60	5	we	we	PRON
ejpam-4344	60	6	shall	shall	AUX
ejpam-4344	60	7	generalize	generalize	VERB
ejpam-4344	60	8	the	the	DET
ejpam-4344	60	9	theorem	theorem	NOUN
ejpam-4344	60	10	of	of	ADP
ejpam-4344	60	11	mayne	mayne	NOUN
ejpam-4344	60	12	[	[	X
ejpam-4344	60	13	27	27	NUM
ejpam-4344	60	14	]	]	PUNCT
ejpam-4344	60	15	and	and	CCONJ
ejpam-4344	60	16	theorem	theorem	NOUN
ejpam-4344	60	17	of	of	ADP
ejpam-4344	60	18	hirano	hirano	PROPN
ejpam-4344	60	19	and	and	CCONJ
ejpam-4344	60	20	tominaga	tominaga	NOUN
ejpam-4344	60	21	[	[	X
ejpam-4344	60	22	21	21	NUM
ejpam-4344	60	23	]	]	PUNCT
ejpam-4344	60	24	,	,	PUNCT
ejpam-4344	60	25	so	so	SCONJ
ejpam-4344	60	26	this	this	DET
ejpam-4344	60	27	generalization	generalization	NOUN
ejpam-4344	60	28	of	of	ADP
ejpam-4344	60	29	the	the	DET
ejpam-4344	60	30	two	two	NUM
ejpam-4344	60	31	theorems	theorem	NOUN
ejpam-4344	60	32	give	give	VERB
ejpam-4344	60	33	us	we	PRON
ejpam-4344	60	34	a	a	DET
ejpam-4344	60	35	new	new	ADJ
ejpam-4344	60	36	wider	wide	ADJ
ejpam-4344	60	37	class	class	NOUN
ejpam-4344	60	38	of	of	ADP
ejpam-4344	60	39	δ	δ	PROPN
ejpam-4344	60	40	-	-	PUNCT
ejpam-4344	60	41	prime	prime	NOUN
ejpam-4344	60	42	rings	ring	NOUN
ejpam-4344	60	43	and	and	CCONJ
ejpam-4344	60	44	we	we	PRON
ejpam-4344	60	45	prove	prove	VERB
ejpam-4344	60	46	the	the	DET
ejpam-4344	60	47	following	follow	VERB
ejpam-4344	60	48	theorem	theorem	NOUN
ejpam-4344	60	49	1	1	X
ejpam-4344	60	50	.	.	PUNCT
ejpam-4344	61	1	let	let	VERB
ejpam-4344	61	2	r	r	PRON
ejpam-4344	61	3	be	be	AUX
ejpam-4344	61	4	a	a	DET
ejpam-4344	61	5	δ	δ	NOUN
ejpam-4344	61	6	-	-	ADJ
ejpam-4344	61	7	prime	prime	ADJ
ejpam-4344	61	8	ring	ring	NOUN
ejpam-4344	61	9	of	of	ADP
ejpam-4344	61	10	charastristic	charastristic	ADJ
ejpam-4344	61	11	6=	6=	NUM
ejpam-4344	61	12	2	2	NUM
ejpam-4344	62	1	and	and	CCONJ
ejpam-4344	62	2	i	i	PRON
ejpam-4344	62	3	be	be	VERB
ejpam-4344	62	4	a	a	DET
ejpam-4344	62	5	nonzero	nonzero	ADJ
ejpam-4344	62	6	δ	δ	NOUN
ejpam-4344	62	7	-	-	PUNCT
ejpam-4344	62	8	ideal	ideal	NOUN
ejpam-4344	62	9	of	of	ADP
ejpam-4344	62	10	r	r	NOUN
ejpam-4344	62	11	,	,	PUNCT
ejpam-4344	62	12	where	where	SCONJ
ejpam-4344	62	13	0	0	NUM
ejpam-4344	62	14	6=	6=	NUM
ejpam-4344	62	15	δ	δ	PROPN
ejpam-4344	62	16	∈	∈	PROPN
ejpam-4344	62	17	d.	d.	NOUN
ejpam-4344	63	1	if	if	SCONJ
ejpam-4344	63	2	[	[	X
ejpam-4344	63	3	c	c	X
ejpam-4344	63	4	,	,	PUNCT
ejpam-4344	63	5	δ(c	δ(c	PROPN
ejpam-4344	63	6	)	)	PUNCT
ejpam-4344	63	7	]	]	PUNCT
ejpam-4344	63	8	∈	∈	PROPN
ejpam-4344	63	9	z(r	z(r	PROPN
ejpam-4344	63	10	)	)	PUNCT
ejpam-4344	63	11	∀c	∀c	X
ejpam-4344	63	12	∈	∈	PROPN
ejpam-4344	63	13	i.	i.	NOUN
ejpam-4344	63	14	then	then	ADV
ejpam-4344	63	15	r	r	NOUN
ejpam-4344	63	16	is	be	AUX
ejpam-4344	63	17	commutative	commutative	ADJ
ejpam-4344	63	18	.	.	PUNCT
ejpam-4344	64	1	2	2	X
ejpam-4344	64	2	.	.	X
ejpam-4344	64	3	preliminaries	preliminary	NOUN
ejpam-4344	64	4	many	many	ADJ
ejpam-4344	64	5	authors	author	NOUN
ejpam-4344	64	6	have	have	AUX
ejpam-4344	64	7	been	be	AUX
ejpam-4344	64	8	studying	study	VERB
ejpam-4344	64	9	the	the	DET
ejpam-4344	64	10	centralizing	centralize	VERB
ejpam-4344	64	11	automorphisms	automorphism	NOUN
ejpam-4344	64	12	and	and	CCONJ
ejpam-4344	64	13	derivation	derivation	NOUN
ejpam-4344	64	14	on	on	ADP
ejpam-4344	64	15	ring	ring	PROPN
ejpam-4344	64	16	r.	r.	PROPN
ejpam-4344	64	17	c.	c.	PROPN
ejpam-4344	64	18	r.	r.	PROPN
ejpam-4344	64	19	miers	miers	PROPN
ejpam-4344	65	1	[	[	X
ejpam-4344	65	2	30	30	NUM
ejpam-4344	65	3	]	]	PUNCT
ejpam-4344	65	4	has	have	AUX
ejpam-4344	65	5	considered	consider	VERB
ejpam-4344	65	6	the	the	DET
ejpam-4344	65	7	map	map	NOUN
ejpam-4344	65	8	defined	define	VERB
ejpam-4344	65	9	on	on	ADP
ejpam-4344	65	10	c∗	c∗	PROPN
ejpam-4344	65	11	algebra	algebra	NOUN
ejpam-4344	65	12	.	.	PUNCT
ejpam-4344	66	1	moreover	moreover	ADV
ejpam-4344	66	2	,	,	PUNCT
ejpam-4344	66	3	in	in	ADP
ejpam-4344	66	4	[	[	PUNCT
ejpam-4344	66	5	4	4	NUM
ejpam-4344	66	6	]	]	X
ejpam-4344	66	7	r.a	r.a	PROPN
ejpam-4344	66	8	.	.	PROPN
ejpam-4344	66	9	awtar	awtar	PROPN
ejpam-4344	66	10	showed	show	VERB
ejpam-4344	66	11	if	if	SCONJ
ejpam-4344	66	12	existence	existence	NOUN
ejpam-4344	66	13	a	a	DET
ejpam-4344	66	14	nonzero	nonzero	NOUN
ejpam-4344	66	15	centerlizing	centerlize	VERB
ejpam-4344	66	16	derivation	derivation	NOUN
ejpam-4344	66	17	on	on	ADP
ejpam-4344	66	18	a	a	DET
ejpam-4344	66	19	prime	prime	ADJ
ejpam-4344	66	20	ring	ring	NOUN
ejpam-4344	66	21	,	,	PUNCT
ejpam-4344	66	22	then	then	ADV
ejpam-4344	66	23	r	r	NOUN
ejpam-4344	66	24	is	be	AUX
ejpam-4344	66	25	commutative	commutative	ADJ
ejpam-4344	66	26	,	,	PUNCT
ejpam-4344	66	27	so	so	SCONJ
ejpam-4344	66	28	he	he	PRON
ejpam-4344	66	29	gives	give	VERB
ejpam-4344	66	30	a	a	DET
ejpam-4344	66	31	shorter	short	ADJ
ejpam-4344	66	32	proof	proof	NOUN
ejpam-4344	66	33	of	of	ADP
ejpam-4344	66	34	posner	posner	NOUN
ejpam-4344	66	35	’s	’s	PART
ejpam-4344	66	36	theorem	theorem	NOUN
ejpam-4344	66	37	[	[	X
ejpam-4344	66	38	31	31	NUM
ejpam-4344	66	39	]	]	PUNCT
ejpam-4344	66	40	.	.	PUNCT
ejpam-4344	67	1	awtar	awtar	NOUN
ejpam-4344	67	2	in	in	ADP
ejpam-4344	67	3	[	[	X
ejpam-4344	67	4	4	4	NUM
ejpam-4344	67	5	]	]	PUNCT
ejpam-4344	67	6	proved	prove	VERB
ejpam-4344	67	7	that	that	SCONJ
ejpam-4344	67	8	if	if	SCONJ
ejpam-4344	67	9	r	r	NOUN
ejpam-4344	67	10	is	be	AUX
ejpam-4344	67	11	a	a	DET
ejpam-4344	67	12	prime	prime	ADJ
ejpam-4344	67	13	ring	ring	NOUN
ejpam-4344	67	14	with	with	ADP
ejpam-4344	67	15	charr	charr	NOUN
ejpam-4344	67	16	6=	6=	ADP
ejpam-4344	67	17	2	2	NUM
ejpam-4344	67	18	havig	havig	VERB
ejpam-4344	67	19	a	a	DET
ejpam-4344	67	20	derivation	derivation	NOUN
ejpam-4344	67	21	d	d	NOUN
ejpam-4344	67	22	on	on	ADP
ejpam-4344	67	23	a	a	DET
ejpam-4344	67	24	jordan	jordan	PROPN
ejpam-4344	67	25	ideal	ideal	PROPN
ejpam-4344	67	26	j	j	PROPN
ejpam-4344	67	27	6=	6=	PRON
ejpam-4344	67	28	{	{	PUNCT
ejpam-4344	67	29	0	0	NUM
ejpam-4344	67	30	}	}	PUNCT
ejpam-4344	67	31	,	,	PUNCT
ejpam-4344	67	32	where	where	SCONJ
ejpam-4344	67	33	the	the	DET
ejpam-4344	67	34	derivation	derivation	NOUN
ejpam-4344	67	35	is	be	AUX
ejpam-4344	67	36	centralizing	centralize	VERB
ejpam-4344	67	37	on	on	ADP
ejpam-4344	67	38	j	j	PROPN
ejpam-4344	67	39	,	,	PUNCT
ejpam-4344	67	40	implies	imply	VERB
ejpam-4344	67	41	j	j	PROPN
ejpam-4344	67	42	⊆	⊆	NUM
ejpam-4344	67	43	z(r	z(r	NUM
ejpam-4344	67	44	)	)	PUNCT
ejpam-4344	67	45	.	.	PUNCT
ejpam-4344	68	1	in	in	ADP
ejpam-4344	68	2	[	[	X
ejpam-4344	68	3	14	14	NUM
ejpam-4344	68	4	]	]	X
ejpam-4344	68	5	l.o	l.o	PROPN
ejpam-4344	68	6	.	.	PROPN
ejpam-4344	68	7	chung	chung	PROPN
ejpam-4344	68	8	and	and	CCONJ
ejpam-4344	68	9	j.luh	j.luh	PROPN
ejpam-4344	68	10	showed	show	VERB
ejpam-4344	68	11	the	the	DET
ejpam-4344	68	12	equivalence	equivalence	NOUN
ejpam-4344	68	13	between	between	ADP
ejpam-4344	68	14	semi	semi	ADJ
ejpam-4344	68	15	-	-	ADJ
ejpam-4344	68	16	commuting	commuting	ADJ
ejpam-4344	68	17	automorphism	automorphism	NOUN
ejpam-4344	68	18	and	and	CCONJ
ejpam-4344	68	19	commuting	commute	VERB
ejpam-4344	68	20	automorphism	automorphism	NOUN
ejpam-4344	68	21	on	on	ADP
ejpam-4344	68	22	a	a	DET
ejpam-4344	68	23	prime	prime	ADJ
ejpam-4344	68	24	ring	ring	NOUN
ejpam-4344	68	25	.	.	PUNCT
ejpam-4344	69	1	if	if	SCONJ
ejpam-4344	69	2	the	the	DET
ejpam-4344	69	3	prime	prime	ADJ
ejpam-4344	69	4	ring	ring	NOUN
ejpam-4344	69	5	r	r	NOUN
ejpam-4344	69	6	has	have	VERB
ejpam-4344	69	7	a	a	DET
ejpam-4344	69	8	nontrivial	nontrivial	ADJ
ejpam-4344	69	9	semicommuting	semicommute	VERB
ejpam-4344	69	10	automorphism	automorphism	NOUN
ejpam-4344	69	11	and	and	CCONJ
ejpam-4344	69	12	r	r	NOUN
ejpam-4344	69	13	with	with	ADP
ejpam-4344	69	14	charr	charr	NOUN
ejpam-4344	69	15	6=	6=	ADP
ejpam-4344	69	16	2	2	NUM
ejpam-4344	69	17	or	or	CCONJ
ejpam-4344	69	18	z(r	z(r	NOUN
ejpam-4344	69	19	)	)	PUNCT
ejpam-4344	69	20	6=	6=	ADP
ejpam-4344	69	21	{	{	PUNCT
ejpam-4344	69	22	0	0	NUM
ejpam-4344	69	23	}	}	PUNCT
ejpam-4344	69	24	,	,	PUNCT
ejpam-4344	69	25	this	this	PRON
ejpam-4344	69	26	implies	imply	VERB
ejpam-4344	69	27	the	the	DET
ejpam-4344	69	28	commutativity	commutativity	NOUN
ejpam-4344	69	29	of	of	ADP
ejpam-4344	69	30	the	the	DET
ejpam-4344	69	31	ring	ring	NOUN
ejpam-4344	69	32	r.	r.	PROPN
ejpam-4344	69	33	in	in	ADP
ejpam-4344	69	34	[	[	X
ejpam-4344	69	35	16	16	NUM
ejpam-4344	69	36	]	]	X
ejpam-4344	69	37	n.	n.	PROPN
ejpam-4344	69	38	divinsky	divinsky	PROPN
ejpam-4344	69	39	proved	prove	VERB
ejpam-4344	69	40	that	that	SCONJ
ejpam-4344	69	41	if	if	SCONJ
ejpam-4344	69	42	the	the	DET
ejpam-4344	69	43	simple	simple	ADJ
ejpam-4344	69	44	artinian	artinian	ADJ
ejpam-4344	69	45	ring	ring	NOUN
ejpam-4344	69	46	has	have	VERB
ejpam-4344	69	47	a	a	DET
ejpam-4344	69	48	nontrivial	nontrivial	ADJ
ejpam-4344	69	49	centralizing	centralize	VERB
ejpam-4344	69	50	automorphism	automorphism	NOUN
ejpam-4344	69	51	,	,	PUNCT
ejpam-4344	69	52	then	then	ADV
ejpam-4344	69	53	r	r	NOUN
ejpam-4344	69	54	is	be	AUX
ejpam-4344	69	55	a	a	DET
ejpam-4344	69	56	field	field	NOUN
ejpam-4344	69	57	.	.	PUNCT
ejpam-4344	70	1	on	on	ADP
ejpam-4344	70	2	the	the	DET
ejpam-4344	70	3	other	other	ADJ
ejpam-4344	70	4	hand	hand	NOUN
ejpam-4344	70	5	in	in	ADP
ejpam-4344	70	6	[	[	X
ejpam-4344	70	7	21	21	NUM
ejpam-4344	70	8	]	]	X
ejpam-4344	70	9	it	it	PRON
ejpam-4344	70	10	has	have	AUX
ejpam-4344	70	11	been	be	AUX
ejpam-4344	70	12	proved	prove	VERB
ejpam-4344	70	13	that	that	SCONJ
ejpam-4344	70	14	if	if	SCONJ
ejpam-4344	70	15	r	r	NOUN
ejpam-4344	70	16	has	have	VERB
ejpam-4344	70	17	a	a	DET
ejpam-4344	70	18	nontrivial	nontrivial	ADJ
ejpam-4344	70	19	automorphism	automorphism	NOUN
ejpam-4344	70	20	,	,	PUNCT
ejpam-4344	70	21	then	then	ADV
ejpam-4344	70	22	r	r	NOUN
ejpam-4344	70	23	is	be	AUX
ejpam-4344	70	24	a	a	DET
ejpam-4344	70	25	field	field	NOUN
ejpam-4344	70	26	.	.	PUNCT
ejpam-4344	71	1	in	in	ADP
ejpam-4344	71	2	[	[	X
ejpam-4344	71	3	1	1	NUM
ejpam-4344	71	4	,	,	PUNCT
ejpam-4344	71	5	2	2	NUM
ejpam-4344	71	6	]	]	PUNCT
ejpam-4344	71	7	it	it	PRON
ejpam-4344	71	8	has	have	AUX
ejpam-4344	71	9	been	be	AUX
ejpam-4344	71	10	proved	prove	VERB
ejpam-4344	71	11	the	the	DET
ejpam-4344	71	12	commutativity	commutativity	NOUN
ejpam-4344	71	13	of	of	ADP
ejpam-4344	71	14	a	a	DET
ejpam-4344	71	15	prime	prime	ADJ
ejpam-4344	71	16	and	and	CCONJ
ejpam-4344	71	17	semiprime	semiprime	NOUN
ejpam-4344	71	18	rings	ring	NOUN
ejpam-4344	71	19	.	.	PUNCT
ejpam-4344	72	1	now	now	ADV
ejpam-4344	72	2	willing	willing	ADJ
ejpam-4344	72	3	to	to	PART
ejpam-4344	72	4	prove	prove	VERB
ejpam-4344	72	5	our	our	PRON
ejpam-4344	72	6	theorem	theorem	NOUN
ejpam-4344	72	7	,	,	PUNCT
ejpam-4344	72	8	we	we	PRON
ejpam-4344	72	9	will	will	AUX
ejpam-4344	72	10	need	need	VERB
ejpam-4344	72	11	to	to	PART
ejpam-4344	72	12	state	state	VERB
ejpam-4344	72	13	some	some	DET
ejpam-4344	72	14	lemmas	lemma	NOUN
ejpam-4344	72	15	:	:	PUNCT
ejpam-4344	72	16	lemma	lemma	PROPN
ejpam-4344	72	17	1	1	X
ejpam-4344	72	18	.	.	PUNCT
ejpam-4344	73	1	let	let	VERB
ejpam-4344	73	2	i	i	PRON
ejpam-4344	73	3	6=	6=	PRON
ejpam-4344	73	4	{	{	PUNCT
ejpam-4344	73	5	0	0	NUM
ejpam-4344	73	6	}	}	PUNCT
ejpam-4344	73	7	be	be	AUX
ejpam-4344	73	8	δ	δ	NOUN
ejpam-4344	73	9	-	-	NOUN
ejpam-4344	73	10	ideal	ideal	NOUN
ejpam-4344	73	11	of	of	ADP
ejpam-4344	73	12	a	a	DET
ejpam-4344	73	13	δ	δ	NOUN
ejpam-4344	73	14	-	-	ADJ
ejpam-4344	73	15	prime	prime	PROPN
ejpam-4344	73	16	ring	ring	NOUN
ejpam-4344	73	17	r.	r.	PROPN
ejpam-4344	73	18	if	if	SCONJ
ejpam-4344	73	19	δ(i	δ(i	PROPN
ejpam-4344	73	20	)	)	PUNCT
ejpam-4344	73	21	=	=	SYM
ejpam-4344	73	22	0	0	NUM
ejpam-4344	73	23	,	,	PUNCT
ejpam-4344	73	24	then	then	ADV
ejpam-4344	73	25	δ(r	δ(r	NOUN
ejpam-4344	73	26	)	)	PUNCT
ejpam-4344	74	1	=	=	SYM
ejpam-4344	74	2	0	0	X
ejpam-4344	74	3	.	.	PUNCT
ejpam-4344	74	4	i.	i.	PROPN
ejpam-4344	74	5	taha	taha	PROPN
ejpam-4344	74	6	et	et	PROPN
ejpam-4344	74	7	al	al	PROPN
ejpam-4344	74	8	.	.	PUNCT
ejpam-4344	74	9	/	/	SYM
ejpam-4344	74	10	eur	eur	PROPN
ejpam-4344	74	11	.	.	PUNCT
ejpam-4344	75	1	j.	j.	PROPN
ejpam-4344	75	2	pure	pure	PROPN
ejpam-4344	75	3	appl	appl	PROPN
ejpam-4344	75	4	.	.	PROPN
ejpam-4344	75	5	math	math	PROPN
ejpam-4344	75	6	,	,	PUNCT
ejpam-4344	75	7	15	15	NUM
ejpam-4344	75	8	(	(	PUNCT
ejpam-4344	75	9	2	2	NUM
ejpam-4344	75	10	)	)	PUNCT
ejpam-4344	75	11	(	(	PUNCT
ejpam-4344	75	12	2022	2022	NUM
ejpam-4344	75	13	)	)	PUNCT
ejpam-4344	75	14	,	,	PUNCT
ejpam-4344	75	15	454	454	NUM
ejpam-4344	75	16	-	-	SYM
ejpam-4344	75	17	466	466	NUM
ejpam-4344	75	18	457	457	NUM
ejpam-4344	75	19	proof	proof	NOUN
ejpam-4344	75	20	.	.	PUNCT
ejpam-4344	76	1	since	since	SCONJ
ejpam-4344	76	2	ri	ri	PROPN
ejpam-4344	76	3	⊆	⊆	NUM
ejpam-4344	76	4	i	i	PROPN
ejpam-4344	76	5	and	and	CCONJ
ejpam-4344	76	6	ir	ir	PROPN
ejpam-4344	76	7	⊆	⊆	NUM
ejpam-4344	76	8	i.	i.	NOUN
ejpam-4344	76	9	then	then	ADV
ejpam-4344	76	10	δ(ri	δ(ri	X
ejpam-4344	76	11	)	)	PUNCT
ejpam-4344	77	1	=	=	SYM
ejpam-4344	77	2	δ(r)i	δ(r)i	NOUN
ejpam-4344	77	3	=	=	SYM
ejpam-4344	77	4	0	0	NUM
ejpam-4344	77	5	=	=	SYM
ejpam-4344	77	6	δ(ir	δ(ir	NUM
ejpam-4344	77	7	)	)	PUNCT
ejpam-4344	77	8	=	=	SYM
ejpam-4344	77	9	iδ(r	iδ(r	X
ejpam-4344	77	10	)	)	PUNCT
ejpam-4344	77	11	.	.	PUNCT
ejpam-4344	78	1	thus	thus	ADV
ejpam-4344	78	2	we	we	PRON
ejpam-4344	78	3	deduce	deduce	VERB
ejpam-4344	78	4	that	that	SCONJ
ejpam-4344	78	5	δ(r	δ(r	NOUN
ejpam-4344	78	6	)	)	PUNCT
ejpam-4344	78	7	⊆	⊆	NUM
ejpam-4344	78	8	anni	anni	NOUN
ejpam-4344	78	9	,	,	PUNCT
ejpam-4344	78	10	but	but	CCONJ
ejpam-4344	78	11	i	i	PRON
ejpam-4344	78	12	is	be	AUX
ejpam-4344	78	13	a	a	DET
ejpam-4344	78	14	δ	δ	NOUN
ejpam-4344	78	15	-	-	PUNCT
ejpam-4344	78	16	ideal	ideal	ADJ
ejpam-4344	78	17	and	and	CCONJ
ejpam-4344	78	18	so	so	ADV
ejpam-4344	78	19	δ(r	δ(r	PROPN
ejpam-4344	78	20	)	)	PUNCT
ejpam-4344	78	21	=	=	SYM
ejpam-4344	79	1	0	0	X
ejpam-4344	79	2	.	.	PUNCT
ejpam-4344	80	1	lemma	lemma	PROPN
ejpam-4344	80	2	2	2	X
ejpam-4344	80	3	.	.	PUNCT
ejpam-4344	80	4	let	let	VERB
ejpam-4344	80	5	δ	δ	PROPN
ejpam-4344	80	6	6=	6=	ADP
ejpam-4344	80	7	0	0	NUM
ejpam-4344	80	8	be	be	AUX
ejpam-4344	80	9	a	a	DET
ejpam-4344	80	10	derivation	derivation	NOUN
ejpam-4344	80	11	on	on	ADP
ejpam-4344	80	12	a	a	DET
ejpam-4344	80	13	ring	ring	NOUN
ejpam-4344	80	14	r	r	NOUN
ejpam-4344	80	15	and	and	CCONJ
ejpam-4344	80	16	i	i	PRON
ejpam-4344	80	17	6=	6=	PROPN
ejpam-4344	80	18	{	{	PUNCT
ejpam-4344	80	19	0	0	NUM
ejpam-4344	80	20	}	}	PUNCT
ejpam-4344	80	21	be	be	AUX
ejpam-4344	80	22	δ	δ	NOUN
ejpam-4344	80	23	-	-	PUNCT
ejpam-4344	80	24	ideal	ideal	NOUN
ejpam-4344	80	25	of	of	ADP
ejpam-4344	80	26	r.	r.	PROPN
ejpam-4344	80	27	if	if	SCONJ
ejpam-4344	80	28	r	r	NOUN
ejpam-4344	80	29	is	be	AUX
ejpam-4344	80	30	δ	δ	NOUN
ejpam-4344	80	31	-	-	NOUN
ejpam-4344	80	32	prime	prime	NOUN
ejpam-4344	81	1	such	such	ADJ
ejpam-4344	81	2	that	that	SCONJ
ejpam-4344	81	3	[	[	X
ejpam-4344	81	4	δ(a	δ(a	PROPN
ejpam-4344	81	5	)	)	PUNCT
ejpam-4344	81	6	,	,	PUNCT
ejpam-4344	81	7	a	a	DET
ejpam-4344	81	8	]	]	X
ejpam-4344	81	9	=	=	SYM
ejpam-4344	81	10	0	0	NUM
ejpam-4344	81	11	∀a	∀a	NOUN
ejpam-4344	81	12	∈	∈	PROPN
ejpam-4344	81	13	i.	i.	NOUN
ejpam-4344	81	14	(	(	PUNCT
ejpam-4344	81	15	2−	2−	NUM
ejpam-4344	81	16	1	1	NUM
ejpam-4344	81	17	)	)	PUNCT
ejpam-4344	81	18	then	then	ADV
ejpam-4344	81	19	r	r	NOUN
ejpam-4344	81	20	is	be	AUX
ejpam-4344	81	21	commutative	commutative	ADJ
ejpam-4344	81	22	.	.	PUNCT
ejpam-4344	82	1	proof	proof	NOUN
ejpam-4344	82	2	.	.	PUNCT
ejpam-4344	83	1	linearizing	linearize	VERB
ejpam-4344	83	2	the	the	DET
ejpam-4344	83	3	equation	equation	NOUN
ejpam-4344	83	4	(	(	PUNCT
ejpam-4344	83	5	2	2	NUM
ejpam-4344	83	6	-	-	SYM
ejpam-4344	83	7	1	1	NUM
ejpam-4344	83	8	)	)	PUNCT
ejpam-4344	83	9	on	on	ADP
ejpam-4344	83	10	i	i	PRON
ejpam-4344	83	11	,	,	PUNCT
ejpam-4344	83	12	then	then	ADV
ejpam-4344	83	13	we	we	PRON
ejpam-4344	83	14	have	have	VERB
ejpam-4344	83	15	for	for	ADP
ejpam-4344	83	16	all	all	DET
ejpam-4344	83	17	a	a	DET
ejpam-4344	83	18	,	,	PUNCT
ejpam-4344	83	19	b	b	NOUN
ejpam-4344	83	20	,	,	PUNCT
ejpam-4344	83	21	c	c	PROPN
ejpam-4344	83	22	∈	∈	PROPN
ejpam-4344	84	1	i	i	PRON
ejpam-4344	84	2	0	0	PUNCT
ejpam-4344	85	1	=	=	PUNCT
ejpam-4344	86	1	[	[	X
ejpam-4344	86	2	δ(a+	δ(a+	NOUN
ejpam-4344	86	3	b	b	NOUN
ejpam-4344	86	4	)	)	PUNCT
ejpam-4344	86	5	,	,	PUNCT
ejpam-4344	86	6	a+	a+	PUNCT
ejpam-4344	87	1	b	b	X
ejpam-4344	87	2	]	]	X
ejpam-4344	87	3	=	=	PUNCT
ejpam-4344	88	1	[	[	X
ejpam-4344	88	2	δ(a	δ(a	PROPN
ejpam-4344	88	3	)	)	PUNCT
ejpam-4344	88	4	,	,	PUNCT
ejpam-4344	88	5	a	a	X
ejpam-4344	88	6	]	]	X
ejpam-4344	88	7	+	+	CCONJ
ejpam-4344	88	8	[	[	X
ejpam-4344	88	9	δ(a	δ(a	NOUN
ejpam-4344	88	10	)	)	PUNCT
ejpam-4344	88	11	,	,	PUNCT
ejpam-4344	88	12	b]+	b]+	PROPN
ejpam-4344	88	13	[	[	X
ejpam-4344	88	14	δ(b	δ(b	NOUN
ejpam-4344	88	15	)	)	PUNCT
ejpam-4344	88	16	,	,	PUNCT
ejpam-4344	88	17	a	a	X
ejpam-4344	88	18	]	]	X
ejpam-4344	88	19	+	+	PROPN
ejpam-4344	88	20	[	[	X
ejpam-4344	88	21	δ(b	δ(b	NOUN
ejpam-4344	88	22	)	)	PUNCT
ejpam-4344	88	23	,	,	PUNCT
ejpam-4344	88	24	b	b	X
ejpam-4344	88	25	]	]	X
ejpam-4344	88	26	=	=	PUNCT
ejpam-4344	88	27	[	[	X
ejpam-4344	88	28	δ(a	δ(a	PROPN
ejpam-4344	88	29	)	)	PUNCT
ejpam-4344	88	30	,	,	PUNCT
ejpam-4344	88	31	b	b	X
ejpam-4344	88	32	]	]	X
ejpam-4344	88	33	+	+	CCONJ
ejpam-4344	88	34	[	[	X
ejpam-4344	88	35	δ(b	δ(b	NOUN
ejpam-4344	88	36	)	)	PUNCT
ejpam-4344	88	37	,	,	PUNCT
ejpam-4344	88	38	a	a	DET
ejpam-4344	88	39	]	]	X
ejpam-4344	88	40	.	.	PUNCT
ejpam-4344	89	1	thus	thus	ADV
ejpam-4344	89	2	we	we	PRON
ejpam-4344	89	3	conclude	conclude	VERB
ejpam-4344	89	4	that	that	SCONJ
ejpam-4344	90	1	[	[	X
ejpam-4344	90	2	δ(a	δ(a	PROPN
ejpam-4344	90	3	)	)	PUNCT
ejpam-4344	90	4	,	,	PUNCT
ejpam-4344	90	5	b	b	X
ejpam-4344	90	6	]	]	X
ejpam-4344	90	7	=	=	PUNCT
ejpam-4344	91	1	[	[	X
ejpam-4344	91	2	a	a	PRON
ejpam-4344	91	3	,	,	PUNCT
ejpam-4344	91	4	δ(b	δ(b	PROPN
ejpam-4344	91	5	)	)	PUNCT
ejpam-4344	91	6	]	]	PUNCT
ejpam-4344	91	7	.	.	PUNCT
ejpam-4344	92	1	(	(	PUNCT
ejpam-4344	92	2	2−	2−	NUM
ejpam-4344	92	3	2	2	NUM
ejpam-4344	92	4	)	)	PUNCT
ejpam-4344	92	5	now	now	ADV
ejpam-4344	92	6	replacing	replace	VERB
ejpam-4344	92	7	the	the	DET
ejpam-4344	92	8	right	right	ADJ
ejpam-4344	92	9	side	side	NOUN
ejpam-4344	92	10	in	in	ADP
ejpam-4344	92	11	(	(	PUNCT
ejpam-4344	92	12	2	2	NUM
ejpam-4344	92	13	-	-	SYM
ejpam-4344	92	14	2	2	NUM
ejpam-4344	92	15	)	)	PUNCT
ejpam-4344	92	16	δ(b	δ(b	PROPN
ejpam-4344	92	17	)	)	PUNCT
ejpam-4344	92	18	by	by	ADP
ejpam-4344	92	19	aδ(b	aδ(b	NOUN
ejpam-4344	92	20	)	)	PUNCT
ejpam-4344	92	21	we	we	PRON
ejpam-4344	92	22	have	have	VERB
ejpam-4344	92	23	[	[	X
ejpam-4344	92	24	a	a	PRON
ejpam-4344	92	25	,	,	PUNCT
ejpam-4344	92	26	aδ(b	aδ(b	NUM
ejpam-4344	92	27	)	)	PUNCT
ejpam-4344	92	28	]	]	PUNCT
ejpam-4344	93	1	=	=	SYM
ejpam-4344	93	2	a[a	a[a	NOUN
ejpam-4344	93	3	,	,	PUNCT
ejpam-4344	93	4	δ(b	δ(b	PROPN
ejpam-4344	93	5	)	)	PUNCT
ejpam-4344	93	6	]	]	PUNCT
ejpam-4344	93	7	=	=	SYM
ejpam-4344	93	8	a[δ(a	a[δ(a	PROPN
ejpam-4344	93	9	)	)	PUNCT
ejpam-4344	93	10	,	,	PUNCT
ejpam-4344	93	11	b	b	X
ejpam-4344	93	12	]	]	X
ejpam-4344	93	13	=	=	PUNCT
ejpam-4344	93	14	aδ(a)b−	aδ(a)b−	PROPN
ejpam-4344	93	15	abδ(a	abδ(a	PROPN
ejpam-4344	93	16	)	)	PUNCT
ejpam-4344	93	17	=	=	PUNCT
ejpam-4344	94	1	δ(a)ab−	δ(a)ab−	PRON
ejpam-4344	94	2	abδ(a	abδ(a	PROPN
ejpam-4344	94	3	)	)	PUNCT
ejpam-4344	94	4	=	=	NOUN
ejpam-4344	95	1	[	[	X
ejpam-4344	95	2	δ(a	δ(a	PROPN
ejpam-4344	95	3	)	)	PUNCT
ejpam-4344	95	4	,	,	PUNCT
ejpam-4344	95	5	ab	ab	PROPN
ejpam-4344	95	6	]	]	X
ejpam-4344	95	7	=	=	PUNCT
ejpam-4344	96	1	[	[	X
ejpam-4344	96	2	a	a	PRON
ejpam-4344	96	3	,	,	PUNCT
ejpam-4344	96	4	δ(ab	δ(ab	NOUN
ejpam-4344	96	5	)	)	PUNCT
ejpam-4344	96	6	]	]	PUNCT
ejpam-4344	97	1	=	=	PUNCT
ejpam-4344	98	1	[	[	X
ejpam-4344	98	2	a	a	X
ejpam-4344	98	3	,	,	PUNCT
ejpam-4344	98	4	δ(a)b	δ(a)b	PROPN
ejpam-4344	98	5	]	]	X
ejpam-4344	99	1	+	+	CCONJ
ejpam-4344	99	2	[	[	X
ejpam-4344	99	3	a	a	PRON
ejpam-4344	99	4	,	,	PUNCT
ejpam-4344	99	5	aδ(b	aδ(b	NUM
ejpam-4344	99	6	)	)	PUNCT
ejpam-4344	99	7	]	]	PUNCT
ejpam-4344	99	8	.	.	PUNCT
ejpam-4344	100	1	hence	hence	ADV
ejpam-4344	100	2	δ(a)[a	δ(a)[a	NOUN
ejpam-4344	100	3	,	,	PUNCT
ejpam-4344	100	4	b	b	X
ejpam-4344	100	5	]	]	X
ejpam-4344	100	6	=	=	PUNCT
ejpam-4344	101	1	[	[	X
ejpam-4344	101	2	a	a	X
ejpam-4344	101	3	,	,	PUNCT
ejpam-4344	101	4	δ(a)b	δ(a)b	PROPN
ejpam-4344	101	5	]	]	X
ejpam-4344	101	6	=	=	SYM
ejpam-4344	101	7	0	0	X
ejpam-4344	101	8	.	.	PUNCT
ejpam-4344	102	1	(	(	PUNCT
ejpam-4344	102	2	2−	2−	NUM
ejpam-4344	102	3	3	3	NUM
ejpam-4344	102	4	)	)	PUNCT
ejpam-4344	102	5	now	now	ADV
ejpam-4344	102	6	replacing	replace	VERB
ejpam-4344	102	7	b	b	NUM
ejpam-4344	102	8	by	by	ADP
ejpam-4344	102	9	cb	cb	PROPN
ejpam-4344	102	10	in	in	ADP
ejpam-4344	102	11	(	(	PUNCT
ejpam-4344	102	12	2	2	NUM
ejpam-4344	102	13	-	-	SYM
ejpam-4344	102	14	3	3	NUM
ejpam-4344	102	15	)	)	PUNCT
ejpam-4344	102	16	we	we	PRON
ejpam-4344	102	17	obtain	obtain	VERB
ejpam-4344	102	18	that	that	PRON
ejpam-4344	102	19	0	0	NUM
ejpam-4344	103	1	=	=	SYM
ejpam-4344	103	2	δ(a)[a	δ(a)[a	NOUN
ejpam-4344	103	3	,	,	PUNCT
ejpam-4344	103	4	cb	cb	PROPN
ejpam-4344	103	5	]	]	X
ejpam-4344	103	6	=	=	SYM
ejpam-4344	103	7	δ(a)[a	δ(a)[a	NOUN
ejpam-4344	103	8	,	,	PUNCT
ejpam-4344	103	9	c]b+	c]b+	PROPN
ejpam-4344	103	10	δ(a)c[a	δ(a)c[a	NOUN
ejpam-4344	103	11	,	,	PUNCT
ejpam-4344	103	12	b	b	X
ejpam-4344	103	13	]	]	X
ejpam-4344	103	14	=	=	PUNCT
ejpam-4344	103	15	δ(a)c[a	δ(a)c[a	NOUN
ejpam-4344	103	16	,	,	PUNCT
ejpam-4344	103	17	b	b	NOUN
ejpam-4344	103	18	]	]	X
ejpam-4344	103	19	.	.	PUNCT
ejpam-4344	104	1	consequently	consequently	ADV
ejpam-4344	104	2	,	,	PUNCT
ejpam-4344	104	3	δ(a)i[a	δ(a)i[a	NOUN
ejpam-4344	104	4	,	,	PUNCT
ejpam-4344	104	5	b	b	NOUN
ejpam-4344	104	6	]	]	X
ejpam-4344	104	7	=	=	SYM
ejpam-4344	104	8	0	0	X
ejpam-4344	104	9	.	.	PUNCT
ejpam-4344	104	10	thus	thus	ADV
ejpam-4344	104	11	by	by	ADP
ejpam-4344	104	12	using	use	VERB
ejpam-4344	104	13	the	the	DET
ejpam-4344	104	14	δ	δ	NOUN
ejpam-4344	104	15	-	-	PUNCT
ejpam-4344	104	16	primenes	primene	NOUN
ejpam-4344	104	17	we	we	PRON
ejpam-4344	104	18	get	get	VERB
ejpam-4344	104	19	either	either	CCONJ
ejpam-4344	104	20	a	a	DET
ejpam-4344	104	21	=	=	SYM
ejpam-4344	104	22	0	0	NUM
ejpam-4344	104	23	or	or	CCONJ
ejpam-4344	104	24	[	[	X
ejpam-4344	104	25	a	a	X
ejpam-4344	104	26	,	,	PUNCT
ejpam-4344	104	27	b	b	NOUN
ejpam-4344	104	28	]	]	X
ejpam-4344	104	29	=	=	SYM
ejpam-4344	104	30	0	0	X
ejpam-4344	104	31	.	.	PUNCT
ejpam-4344	105	1	since	since	SCONJ
ejpam-4344	105	2	i	i	PRON
ejpam-4344	105	3	6=	6=	X
ejpam-4344	105	4	{	{	PUNCT
ejpam-4344	105	5	0	0	NUM
ejpam-4344	105	6	}	}	PUNCT
ejpam-4344	105	7	,	,	PUNCT
ejpam-4344	105	8	then	then	ADV
ejpam-4344	105	9	we	we	PRON
ejpam-4344	105	10	deduce	deduce	VERB
ejpam-4344	105	11	that	that	SCONJ
ejpam-4344	105	12	[	[	X
ejpam-4344	105	13	a	a	DET
ejpam-4344	105	14	,	,	PUNCT
ejpam-4344	105	15	b	b	NOUN
ejpam-4344	105	16	]	]	X
ejpam-4344	105	17	=	=	SYM
ejpam-4344	105	18	0	0	NUM
ejpam-4344	105	19	and	and	CCONJ
ejpam-4344	105	20	therefore	therefore	ADV
ejpam-4344	105	21	,	,	PUNCT
ejpam-4344	105	22	i	i	PRON
ejpam-4344	105	23	is	be	AUX
ejpam-4344	105	24	commutative	commutative	ADJ
ejpam-4344	105	25	.	.	PUNCT
ejpam-4344	106	1	then	then	ADV
ejpam-4344	106	2	we	we	PRON
ejpam-4344	106	3	have	have	VERB
ejpam-4344	106	4	i2c(r	i2c(r	NOUN
ejpam-4344	106	5	)	)	PUNCT
ejpam-4344	106	6	=	=	SYM
ejpam-4344	106	7	0	0	NUM
ejpam-4344	106	8	,	,	PUNCT
ejpam-4344	106	9	and	and	CCONJ
ejpam-4344	106	10	so	so	ADV
ejpam-4344	106	11	c(r	c(r	NOUN
ejpam-4344	106	12	)	)	PUNCT
ejpam-4344	107	1	=	=	SYM
ejpam-4344	107	2	0	0	X
ejpam-4344	107	3	.	.	PUNCT
ejpam-4344	108	1	hence	hence	ADV
ejpam-4344	108	2	r	r	NOUN
ejpam-4344	108	3	is	be	AUX
ejpam-4344	108	4	commutative	commutative	ADJ
ejpam-4344	108	5	.	.	PUNCT
ejpam-4344	109	1	i.	i.	PROPN
ejpam-4344	109	2	taha	taha	PROPN
ejpam-4344	109	3	et	et	PROPN
ejpam-4344	109	4	al	al	PROPN
ejpam-4344	109	5	.	.	PUNCT
ejpam-4344	109	6	/	/	SYM
ejpam-4344	109	7	eur	eur	PROPN
ejpam-4344	109	8	.	.	PUNCT
ejpam-4344	110	1	j.	j.	PROPN
ejpam-4344	110	2	pure	pure	PROPN
ejpam-4344	110	3	appl	appl	PROPN
ejpam-4344	110	4	.	.	PROPN
ejpam-4344	110	5	math	math	PROPN
ejpam-4344	110	6	,	,	PUNCT
ejpam-4344	110	7	15	15	NUM
ejpam-4344	110	8	(	(	PUNCT
ejpam-4344	110	9	2	2	NUM
ejpam-4344	110	10	)	)	PUNCT
ejpam-4344	110	11	(	(	PUNCT
ejpam-4344	110	12	2022	2022	NUM
ejpam-4344	110	13	)	)	PUNCT
ejpam-4344	110	14	,	,	PUNCT
ejpam-4344	110	15	454	454	NUM
ejpam-4344	110	16	-	-	SYM
ejpam-4344	110	17	466	466	NUM
ejpam-4344	110	18	458	458	NUM
ejpam-4344	110	19	3	3	NUM
ejpam-4344	110	20	.	.	PUNCT
ejpam-4344	111	1	δ	δ	NOUN
ejpam-4344	111	2	-	-	NOUN
ejpam-4344	111	3	derivation	derivation	NOUN
ejpam-4344	111	4	on	on	ADP
ejpam-4344	111	5	δ	δ	PROPN
ejpam-4344	111	6	-	-	PUNCT
ejpam-4344	111	7	ideal	ideal	NOUN
ejpam-4344	111	8	first	first	ADV
ejpam-4344	111	9	of	of	ADP
ejpam-4344	111	10	all	all	PRON
ejpam-4344	111	11	in	in	ADP
ejpam-4344	111	12	the	the	DET
ejpam-4344	111	13	next	next	ADJ
ejpam-4344	111	14	lemma	lemma	PROPN
ejpam-4344	111	15	we	we	PRON
ejpam-4344	111	16	give	give	VERB
ejpam-4344	111	17	a	a	DET
ejpam-4344	111	18	generalization	generalization	NOUN
ejpam-4344	111	19	of	of	ADP
ejpam-4344	111	20	lemma	lemma	PROPN
ejpam-4344	111	21	1	1	NUM
ejpam-4344	111	22	from	from	ADP
ejpam-4344	111	23	[	[	X
ejpam-4344	111	24	31	31	NUM
ejpam-4344	111	25	]	]	X
ejpam-4344	111	26	lemma	lemma	PROPN
ejpam-4344	111	27	3	3	X
ejpam-4344	111	28	.	.	PUNCT
ejpam-4344	112	1	let	let	VERB
ejpam-4344	112	2	δ	δ	PROPN
ejpam-4344	112	3	6=	6=	ADP
ejpam-4344	112	4	0	0	NUM
ejpam-4344	112	5	be	be	AUX
ejpam-4344	112	6	a	a	DET
ejpam-4344	112	7	derivation	derivation	NOUN
ejpam-4344	112	8	of	of	ADP
ejpam-4344	112	9	a	a	DET
ejpam-4344	112	10	ring	ring	NOUN
ejpam-4344	112	11	r	r	NOUN
ejpam-4344	112	12	.	.	PUNCT
ejpam-4344	113	1	if	if	SCONJ
ejpam-4344	113	2	r	r	NOUN
ejpam-4344	113	3	is	be	AUX
ejpam-4344	113	4	δ	δ	NOUN
ejpam-4344	113	5	-	-	ADJ
ejpam-4344	113	6	prime	prime	ADJ
ejpam-4344	113	7	ring	ring	NOUN
ejpam-4344	113	8	such	such	ADJ
ejpam-4344	113	9	that	that	SCONJ
ejpam-4344	113	10	a[δn(a	a[δn(a	PROPN
ejpam-4344	113	11	)	)	PUNCT
ejpam-4344	113	12	,	,	PUNCT
ejpam-4344	113	13	r	r	X
ejpam-4344	113	14	]	]	X
ejpam-4344	113	15	=	=	SYM
ejpam-4344	113	16	0	0	NUM
ejpam-4344	113	17	,	,	PUNCT
ejpam-4344	113	18	(	(	PUNCT
ejpam-4344	113	19	respectively	respectively	ADV
ejpam-4344	113	20	[	[	X
ejpam-4344	113	21	δn(b	δn(b	NOUN
ejpam-4344	113	22	)	)	PUNCT
ejpam-4344	113	23	,	,	PUNCT
ejpam-4344	113	24	r]a	r]a	NOUN
ejpam-4344	113	25	=	=	NOUN
ejpam-4344	113	26	0	0	NUM
ejpam-4344	113	27	)	)	PUNCT
ejpam-4344	113	28	∀a	∀a	NOUN
ejpam-4344	113	29	,	,	PUNCT
ejpam-4344	113	30	b	b	X
ejpam-4344	113	31	∈	∈	PROPN
ejpam-4344	113	32	r	r	NOUN
ejpam-4344	113	33	,	,	PUNCT
ejpam-4344	113	34	and	and	CCONJ
ejpam-4344	113	35	for	for	ADP
ejpam-4344	113	36	all	all	DET
ejpam-4344	113	37	integers	integer	NOUN
ejpam-4344	113	38	n	n	PRON
ejpam-4344	113	39	≥	≥	NOUN
ejpam-4344	113	40	0	0	NUM
ejpam-4344	113	41	,	,	PUNCT
ejpam-4344	113	42	then	then	ADV
ejpam-4344	113	43	either	either	CCONJ
ejpam-4344	113	44	a	a	DET
ejpam-4344	113	45	=	=	SYM
ejpam-4344	113	46	0	0	NUM
ejpam-4344	113	47	or	or	CCONJ
ejpam-4344	113	48	b	b	NOUN
ejpam-4344	113	49	∈	∈	PROPN
ejpam-4344	113	50	z(r	z(r	PROPN
ejpam-4344	113	51	)	)	PUNCT
ejpam-4344	113	52	.	.	PUNCT
ejpam-4344	114	1	proof	proof	NOUN
ejpam-4344	114	2	.	.	PUNCT
ejpam-4344	115	1	suppose	suppose	VERB
ejpam-4344	115	2	that	that	SCONJ
ejpam-4344	115	3	x	x	NOUN
ejpam-4344	115	4	,	,	PUNCT
ejpam-4344	115	5	y	y	PROPN
ejpam-4344	115	6	∈	∈	PROPN
ejpam-4344	115	7	r	r	NOUN
ejpam-4344	115	8	and	and	CCONJ
ejpam-4344	115	9	n	n	CCONJ
ejpam-4344	115	10	,	,	PUNCT
ejpam-4344	115	11	k	k	X
ejpam-4344	115	12	are	be	AUX
ejpam-4344	115	13	a	a	DET
ejpam-4344	115	14	nonnegative	nonnegative	ADJ
ejpam-4344	115	15	integers	integer	NOUN
ejpam-4344	115	16	.	.	PUNCT
ejpam-4344	116	1	from	from	ADP
ejpam-4344	116	2	[	[	X
ejpam-4344	116	3	31	31	NUM
ejpam-4344	116	4	]	]	PUNCT
ejpam-4344	116	5	we	we	PRON
ejpam-4344	116	6	have	have	VERB
ejpam-4344	116	7	a∂δn(b)(r	a∂δn(b)(r	NOUN
ejpam-4344	116	8	)	)	PUNCT
ejpam-4344	117	1	=	=	SYM
ejpam-4344	117	2	0	0	NUM
ejpam-4344	117	3	,	,	PUNCT
ejpam-4344	117	4	then	then	ADV
ejpam-4344	117	5	0	0	X
ejpam-4344	117	6	=	=	SYM
ejpam-4344	117	7	a∂δn(b)(xy	a∂δn(b)(xy	PROPN
ejpam-4344	117	8	)	)	PUNCT
ejpam-4344	117	9	=	=	PUNCT
ejpam-4344	118	1	a∂δn(b)(x)y	a∂δn(b)(x)y	NOUN
ejpam-4344	118	2	+	+	CCONJ
ejpam-4344	118	3	ax∂δn(b)(y	ax∂δn(b)(y	NUM
ejpam-4344	118	4	)	)	PUNCT
ejpam-4344	118	5	=	=	SYM
ejpam-4344	118	6	ax∂δn(b)(y	ax∂δn(b)(y	PROPN
ejpam-4344	118	7	)	)	PUNCT
ejpam-4344	118	8	.	.	PUNCT
ejpam-4344	119	1	this	this	PRON
ejpam-4344	119	2	means	mean	VERB
ejpam-4344	119	3	that	that	SCONJ
ejpam-4344	119	4	ar[δn(b	ar[δn(b	PROPN
ejpam-4344	119	5	)	)	PUNCT
ejpam-4344	119	6	,	,	PUNCT
ejpam-4344	119	7	y	y	PROPN
ejpam-4344	119	8	]	]	X
ejpam-4344	119	9	=	=	PUNCT
ejpam-4344	119	10	0	0	X
ejpam-4344	119	11	.	.	PUNCT
ejpam-4344	120	1	consequently	consequently	ADV
ejpam-4344	120	2	,	,	PUNCT
ejpam-4344	120	3	arδk([δn(b	arδk([δn(b	PROPN
ejpam-4344	120	4	)	)	PUNCT
ejpam-4344	120	5	,	,	PUNCT
ejpam-4344	120	6	y	y	NOUN
ejpam-4344	120	7	]	]	X
ejpam-4344	120	8	)	)	PUNCT
ejpam-4344	121	1	=	=	SYM
ejpam-4344	121	2	0	0	NUM
ejpam-4344	121	3	,	,	PUNCT
ejpam-4344	121	4	what	what	PRON
ejpam-4344	121	5	forces	force	VERB
ejpam-4344	121	6	that	that	SCONJ
ejpam-4344	121	7	a	a	DET
ejpam-4344	121	8	=	=	SYM
ejpam-4344	121	9	0	0	NUM
ejpam-4344	121	10	or	or	CCONJ
ejpam-4344	121	11	[	[	X
ejpam-4344	121	12	δn(b	δn(b	NOUN
ejpam-4344	121	13	)	)	PUNCT
ejpam-4344	121	14	,	,	PUNCT
ejpam-4344	121	15	y	y	PROPN
ejpam-4344	121	16	]	]	X
ejpam-4344	121	17	=	=	SYM
ejpam-4344	121	18	0	0	PUNCT
ejpam-4344	121	19	(	(	PUNCT
ejpam-4344	121	20	and	and	CCONJ
ejpam-4344	121	21	then	then	ADV
ejpam-4344	121	22	b	b	PROPN
ejpam-4344	121	23	∈	∈	PROPN
ejpam-4344	121	24	z(r	z(r	PROPN
ejpam-4344	121	25	)	)	PUNCT
ejpam-4344	121	26	)	)	PUNCT
ejpam-4344	121	27	.	.	PUNCT
ejpam-4344	122	1	lemma	lemma	PROPN
ejpam-4344	122	2	4	4	X
ejpam-4344	122	3	.	.	PUNCT
ejpam-4344	123	1	let	let	VERB
ejpam-4344	123	2	i	i	PRON
ejpam-4344	123	3	6=	6=	PRON
ejpam-4344	123	4	{	{	PUNCT
ejpam-4344	123	5	0	0	NUM
ejpam-4344	123	6	}	}	PUNCT
ejpam-4344	123	7	be	be	AUX
ejpam-4344	123	8	a	a	DET
ejpam-4344	123	9	right	right	ADJ
ejpam-4344	123	10	δ	δ	NOUN
ejpam-4344	123	11	-	-	PUNCT
ejpam-4344	123	12	ideal	ideal	NOUN
ejpam-4344	123	13	of	of	ADP
ejpam-4344	123	14	a	a	DET
ejpam-4344	123	15	δ	δ	NOUN
ejpam-4344	123	16	-	-	ADJ
ejpam-4344	123	17	prime	prime	PROPN
ejpam-4344	123	18	ring	ring	NOUN
ejpam-4344	123	19	r.	r.	PROPN
ejpam-4344	123	20	if	if	SCONJ
ejpam-4344	123	21	i	i	PRON
ejpam-4344	123	22	is	be	AUX
ejpam-4344	123	23	commutative	commutative	ADJ
ejpam-4344	123	24	,	,	PUNCT
ejpam-4344	123	25	then	then	ADV
ejpam-4344	123	26	r	r	NOUN
ejpam-4344	123	27	is	be	AUX
ejpam-4344	123	28	commutative	commutative	ADJ
ejpam-4344	123	29	.	.	PUNCT
ejpam-4344	124	1	proof	proof	NOUN
ejpam-4344	124	2	.	.	PUNCT
ejpam-4344	125	1	suppose	suppose	VERB
ejpam-4344	125	2	that	that	SCONJ
ejpam-4344	125	3	a	a	DET
ejpam-4344	125	4	∈	∈	PROPN
ejpam-4344	125	5	i.	i.	NOUN
ejpam-4344	125	6	then	then	ADV
ejpam-4344	125	7	∂a(i	∂a(i	VERB
ejpam-4344	125	8	)	)	PUNCT
ejpam-4344	126	1	=	=	SYM
ejpam-4344	126	2	0	0	NUM
ejpam-4344	127	1	and	and	CCONJ
ejpam-4344	127	2	so	so	ADV
ejpam-4344	127	3	∂a(r	∂a(r	PROPN
ejpam-4344	127	4	)	)	PUNCT
ejpam-4344	128	1	⊆	⊆	NUM
ejpam-4344	128	2	anni	anni	PROPN
ejpam-4344	128	3	.	.	PUNCT
ejpam-4344	129	1	since	since	SCONJ
ejpam-4344	129	2	anni	anni	PROPN
ejpam-4344	129	3	is	be	AUX
ejpam-4344	129	4	a	a	DET
ejpam-4344	129	5	δ	δ	NOUN
ejpam-4344	129	6	-	-	PUNCT
ejpam-4344	129	7	ideal	ideal	NOUN
ejpam-4344	129	8	,	,	PUNCT
ejpam-4344	129	9	then	then	ADV
ejpam-4344	129	10	we	we	PRON
ejpam-4344	129	11	see	see	VERB
ejpam-4344	129	12	that	that	DET
ejpam-4344	129	13	anni	anni	PROPN
ejpam-4344	129	14	=	=	PROPN
ejpam-4344	129	15	0	0	PROPN
ejpam-4344	129	16	,	,	PUNCT
ejpam-4344	129	17	and	and	CCONJ
ejpam-4344	129	18	so	so	ADV
ejpam-4344	129	19	a	a	DET
ejpam-4344	129	20	∈	∈	PROPN
ejpam-4344	129	21	z(r	z(r	NOUN
ejpam-4344	129	22	)	)	PUNCT
ejpam-4344	129	23	.	.	PUNCT
ejpam-4344	130	1	hence	hence	ADV
ejpam-4344	130	2	i	i	PRON
ejpam-4344	130	3	⊆	⊆	NUM
ejpam-4344	130	4	z(r	z(r	NOUN
ejpam-4344	130	5	)	)	PUNCT
ejpam-4344	130	6	.	.	PUNCT
ejpam-4344	131	1	then	then	ADV
ejpam-4344	131	2	ic(r	ic(r	VERB
ejpam-4344	131	3	)	)	PUNCT
ejpam-4344	131	4	=	=	SYM
ejpam-4344	131	5	0	0	PUNCT
ejpam-4344	131	6	and	and	CCONJ
ejpam-4344	131	7	hence	hence	ADV
ejpam-4344	131	8	c(r	c(r	NOUN
ejpam-4344	131	9	)	)	PUNCT
ejpam-4344	132	1	=	=	SYM
ejpam-4344	132	2	0	0	X
ejpam-4344	132	3	.	.	PUNCT
ejpam-4344	132	4	i.	i.	PROPN
ejpam-4344	132	5	taha	taha	PROPN
ejpam-4344	132	6	et	et	PROPN
ejpam-4344	132	7	al	al	PROPN
ejpam-4344	132	8	.	.	PUNCT
ejpam-4344	132	9	/	/	SYM
ejpam-4344	132	10	eur	eur	PROPN
ejpam-4344	132	11	.	.	PUNCT
ejpam-4344	133	1	j.	j.	PROPN
ejpam-4344	133	2	pure	pure	PROPN
ejpam-4344	133	3	appl	appl	PROPN
ejpam-4344	133	4	.	.	PROPN
ejpam-4344	133	5	math	math	PROPN
ejpam-4344	133	6	,	,	PUNCT
ejpam-4344	133	7	15	15	NUM
ejpam-4344	133	8	(	(	PUNCT
ejpam-4344	133	9	2	2	NUM
ejpam-4344	133	10	)	)	PUNCT
ejpam-4344	133	11	(	(	PUNCT
ejpam-4344	133	12	2022	2022	NUM
ejpam-4344	133	13	)	)	PUNCT
ejpam-4344	133	14	,	,	PUNCT
ejpam-4344	133	15	454	454	NUM
ejpam-4344	133	16	-	-	SYM
ejpam-4344	133	17	466	466	NUM
ejpam-4344	133	18	459	459	NUM
ejpam-4344	133	19	lemma	lemma	PROPN
ejpam-4344	133	20	5	5	NUM
ejpam-4344	133	21	.	.	PUNCT
ejpam-4344	134	1	let	let	VERB
ejpam-4344	134	2	δ	δ	PROPN
ejpam-4344	134	3	6=	6=	ADP
ejpam-4344	134	4	0	0	NUM
ejpam-4344	134	5	be	be	AUX
ejpam-4344	134	6	a	a	DET
ejpam-4344	134	7	nonzero	nonzero	ADJ
ejpam-4344	134	8	derivation	derivation	NOUN
ejpam-4344	134	9	of	of	ADP
ejpam-4344	134	10	a	a	DET
ejpam-4344	134	11	δ	δ	NOUN
ejpam-4344	134	12	-	-	ADJ
ejpam-4344	134	13	prime	prime	PROPN
ejpam-4344	134	14	ring	ring	NOUN
ejpam-4344	134	15	r.	r.	PROPN
ejpam-4344	135	1	if	if	SCONJ
ejpam-4344	135	2	[	[	X
ejpam-4344	135	3	b	b	X
ejpam-4344	135	4	,	,	PUNCT
ejpam-4344	135	5	δn(a)b	δn(a)b	NUM
ejpam-4344	135	6	]	]	X
ejpam-4344	135	7	∈	∈	PROPN
ejpam-4344	135	8	z(r	z(r	PROPN
ejpam-4344	135	9	)	)	PUNCT
ejpam-4344	135	10	,	,	PUNCT
ejpam-4344	135	11	and	and	CCONJ
ejpam-4344	135	12	0	0	NUM
ejpam-4344	135	13	6=	6=	SYM
ejpam-4344	135	14	b	b	X
ejpam-4344	135	15	∈	∈	NOUN
ejpam-4344	135	16	r	r	NOUN
ejpam-4344	135	17	for	for	ADP
ejpam-4344	135	18	all	all	DET
ejpam-4344	135	19	integers	integer	NOUN
ejpam-4344	135	20	n	n	PRON
ejpam-4344	135	21	≥	≥	NOUN
ejpam-4344	135	22	0	0	NUM
ejpam-4344	135	23	,	,	PUNCT
ejpam-4344	135	24	then	then	ADV
ejpam-4344	135	25	a	a	DET
ejpam-4344	135	26	∈	∈	PROPN
ejpam-4344	135	27	z(r	z(r	PROPN
ejpam-4344	135	28	)	)	PUNCT
ejpam-4344	135	29	.	.	PUNCT
ejpam-4344	136	1	proof	proof	NOUN
ejpam-4344	136	2	.	.	PUNCT
ejpam-4344	137	1	since	since	SCONJ
ejpam-4344	137	2	for	for	ADP
ejpam-4344	137	3	all	all	PRON
ejpam-4344	137	4	x	x	SYM
ejpam-4344	137	5	∈	∈	NOUN
ejpam-4344	137	6	r	r	NOUN
ejpam-4344	137	7	we	we	PRON
ejpam-4344	137	8	have	have	VERB
ejpam-4344	137	9	0	0	NUM
ejpam-4344	137	10	=	=	PUNCT
ejpam-4344	138	1	[	[	X
ejpam-4344	138	2	δn(a)b	δn(a)b	X
ejpam-4344	138	3	,	,	PUNCT
ejpam-4344	138	4	x	x	X
ejpam-4344	138	5	]	]	X
ejpam-4344	138	6	=	=	SYM
ejpam-4344	138	7	δn(a)[b	δn(a)[b	PROPN
ejpam-4344	138	8	,	,	PUNCT
ejpam-4344	138	9	x	x	X
ejpam-4344	139	1	]	]	X
ejpam-4344	139	2	+	+	CCONJ
ejpam-4344	139	3	[	[	X
ejpam-4344	139	4	δn(a	δn(a	NUM
ejpam-4344	139	5	)	)	PUNCT
ejpam-4344	139	6	,	,	PUNCT
ejpam-4344	139	7	x]b	x]b	X
ejpam-4344	139	8	=	=	PUNCT
ejpam-4344	140	1	[	[	X
ejpam-4344	140	2	δn(a	δn(a	NUM
ejpam-4344	140	3	)	)	PUNCT
ejpam-4344	140	4	,	,	PUNCT
ejpam-4344	140	5	x]b	x]b	PROPN
ejpam-4344	140	6	.	.	PUNCT
ejpam-4344	141	1	then	then	ADV
ejpam-4344	141	2	by	by	ADP
ejpam-4344	141	3	lemma	lemma	PROPN
ejpam-4344	141	4	3	3	NUM
ejpam-4344	141	5	we	we	PRON
ejpam-4344	141	6	see	see	VERB
ejpam-4344	141	7	that	that	SCONJ
ejpam-4344	141	8	a	a	DET
ejpam-4344	141	9	∈	∈	PROPN
ejpam-4344	141	10	z(r	z(r	PROPN
ejpam-4344	141	11	)	)	PUNCT
ejpam-4344	141	12	.	.	PUNCT
ejpam-4344	142	1	lemma	lemma	PROPN
ejpam-4344	142	2	6	6	NUM
ejpam-4344	142	3	.	.	PUNCT
ejpam-4344	143	1	let	let	VERB
ejpam-4344	143	2	r	r	PRON
ejpam-4344	143	3	be	be	AUX
ejpam-4344	143	4	a	a	DET
ejpam-4344	143	5	δ−prime	δ−prime	NOUN
ejpam-4344	143	6	ring	ring	NOUN
ejpam-4344	143	7	of	of	ADP
ejpam-4344	143	8	characterstic	characterstic	ADJ
ejpam-4344	143	9	6=	6=	NUM
ejpam-4344	143	10	2	2	NUM
ejpam-4344	144	1	and	and	CCONJ
ejpam-4344	144	2	i	i	PRON
ejpam-4344	144	3	be	be	VERB
ejpam-4344	144	4	a	a	DET
ejpam-4344	144	5	δ−ideal	δ−ideal	NOUN
ejpam-4344	144	6	of	of	ADP
ejpam-4344	144	7	r.	r.	PROPN
ejpam-4344	144	8	if	if	SCONJ
ejpam-4344	144	9	[	[	X
ejpam-4344	144	10	x	x	X
ejpam-4344	144	11	,	,	PUNCT
ejpam-4344	144	12	δ(x	δ(x	ADJ
ejpam-4344	144	13	)	)	PUNCT
ejpam-4344	144	14	]	]	PUNCT
ejpam-4344	144	15	∈	∈	PROPN
ejpam-4344	144	16	z(r	z(r	PROPN
ejpam-4344	144	17	)	)	PUNCT
ejpam-4344	145	1	∀x	∀x	VERB
ejpam-4344	145	2	∈	∈	PROPN
ejpam-4344	146	1	i	i	PRON
ejpam-4344	146	2	,	,	PUNCT
ejpam-4344	146	3	(	(	PUNCT
ejpam-4344	146	4	3−	3−	NUM
ejpam-4344	146	5	1	1	NUM
ejpam-4344	146	6	)	)	PUNCT
ejpam-4344	146	7	then	then	ADV
ejpam-4344	146	8	[	[	X
ejpam-4344	146	9	x	x	X
ejpam-4344	146	10	,	,	PUNCT
ejpam-4344	146	11	δ(x	δ(x	ADJ
ejpam-4344	146	12	)	)	PUNCT
ejpam-4344	146	13	]	]	PUNCT
ejpam-4344	147	1	=	=	PUNCT
ejpam-4344	147	2	0	0	X
ejpam-4344	147	3	.	.	PUNCT
ejpam-4344	147	4	proof	proof	NOUN
ejpam-4344	147	5	.	.	PUNCT
ejpam-4344	147	6	suppose	suppose	VERB
ejpam-4344	147	7	that	that	SCONJ
ejpam-4344	147	8	x	x	NOUN
ejpam-4344	147	9	,	,	PUNCT
ejpam-4344	147	10	y	y	PROPN
ejpam-4344	147	11	∈	∈	PROPN
ejpam-4344	147	12	i.	i.	NOUN
ejpam-4344	147	13	now	now	ADV
ejpam-4344	147	14	replace	replace	VERB
ejpam-4344	147	15	x	x	PUNCT
ejpam-4344	147	16	by	by	ADP
ejpam-4344	147	17	x+	x+	PROPN
ejpam-4344	147	18	y	y	PROPN
ejpam-4344	147	19	in	in	ADP
ejpam-4344	147	20	(	(	PUNCT
ejpam-4344	147	21	3	3	NUM
ejpam-4344	147	22	-	-	SYM
ejpam-4344	147	23	1	1	NUM
ejpam-4344	147	24	)	)	PUNCT
ejpam-4344	147	25	we	we	PRON
ejpam-4344	147	26	get	get	VERB
ejpam-4344	147	27	[	[	PUNCT
ejpam-4344	147	28	x+	x+	ADJ
ejpam-4344	147	29	y	y	NOUN
ejpam-4344	147	30	,	,	PUNCT
ejpam-4344	147	31	δ(x+	δ(x+	X
ejpam-4344	147	32	y	y	NOUN
ejpam-4344	147	33	)	)	PUNCT
ejpam-4344	147	34	]	]	PUNCT
ejpam-4344	148	1	=	=	PUNCT
ejpam-4344	149	1	[	[	X
ejpam-4344	149	2	x	x	X
ejpam-4344	149	3	,	,	PUNCT
ejpam-4344	149	4	δ(x	δ(x	NOUN
ejpam-4344	149	5	)	)	PUNCT
ejpam-4344	149	6	]	]	PUNCT
ejpam-4344	150	1	+	+	CCONJ
ejpam-4344	150	2	[	[	X
ejpam-4344	150	3	x	x	X
ejpam-4344	150	4	,	,	PUNCT
ejpam-4344	150	5	δ(y	δ(y	ADV
ejpam-4344	150	6	)	)	PUNCT
ejpam-4344	150	7	]	]	PUNCT
ejpam-4344	151	1	+	+	CCONJ
ejpam-4344	151	2	[	[	X
ejpam-4344	151	3	y	y	INTJ
ejpam-4344	151	4	,	,	PUNCT
ejpam-4344	151	5	δ(x	δ(x	NOUN
ejpam-4344	151	6	)	)	PUNCT
ejpam-4344	151	7	]	]	PUNCT
ejpam-4344	152	1	+	+	CCONJ
ejpam-4344	152	2	[	[	X
ejpam-4344	152	3	y	y	INTJ
ejpam-4344	152	4	,	,	PUNCT
ejpam-4344	152	5	δ(y	δ(y	ADV
ejpam-4344	152	6	)	)	PUNCT
ejpam-4344	152	7	]	]	PUNCT
ejpam-4344	152	8	,	,	PUNCT
ejpam-4344	152	9	and	and	CCONJ
ejpam-4344	152	10	so	so	ADV
ejpam-4344	152	11	[	[	X
ejpam-4344	152	12	x	x	X
ejpam-4344	152	13	,	,	PUNCT
ejpam-4344	152	14	δ(y	δ(y	ADV
ejpam-4344	152	15	)	)	PUNCT
ejpam-4344	152	16	]	]	PUNCT
ejpam-4344	153	1	+	+	CCONJ
ejpam-4344	153	2	[	[	X
ejpam-4344	153	3	y	y	INTJ
ejpam-4344	153	4	,	,	PUNCT
ejpam-4344	153	5	δ(x	δ(x	NOUN
ejpam-4344	153	6	)	)	PUNCT
ejpam-4344	153	7	]	]	PUNCT
ejpam-4344	153	8	∈	∈	PROPN
ejpam-4344	153	9	z(r	z(r	PROPN
ejpam-4344	153	10	)	)	PUNCT
ejpam-4344	153	11	.	.	PUNCT
ejpam-4344	154	1	(	(	PUNCT
ejpam-4344	154	2	3−	3−	NUM
ejpam-4344	154	3	2	2	NUM
ejpam-4344	154	4	)	)	PUNCT
ejpam-4344	154	5	.	.	PUNCT
ejpam-4344	155	1	now	now	ADV
ejpam-4344	155	2	substituting	substitute	VERB
ejpam-4344	155	3	y	y	PROPN
ejpam-4344	155	4	by	by	ADP
ejpam-4344	155	5	x2	x2	PROPN
ejpam-4344	155	6	in	in	ADP
ejpam-4344	155	7	(	(	PUNCT
ejpam-4344	155	8	3	3	NUM
ejpam-4344	155	9	-	-	SYM
ejpam-4344	155	10	2	2	NUM
ejpam-4344	155	11	)	)	PUNCT
ejpam-4344	155	12	,	,	PUNCT
ejpam-4344	155	13	we	we	PRON
ejpam-4344	155	14	obtain	obtain	VERB
ejpam-4344	155	15	4x[x	4x[x	NUM
ejpam-4344	155	16	,	,	PUNCT
ejpam-4344	155	17	δ(x	δ(x	ADJ
ejpam-4344	155	18	)	)	PUNCT
ejpam-4344	155	19	]	]	PUNCT
ejpam-4344	156	1	=	=	PUNCT
ejpam-4344	157	1	[	[	X
ejpam-4344	157	2	x	x	NOUN
ejpam-4344	157	3	,	,	PUNCT
ejpam-4344	157	4	δ(x2	δ(x2	NOUN
ejpam-4344	157	5	)	)	PUNCT
ejpam-4344	157	6	]	]	PUNCT
ejpam-4344	158	1	+	+	CCONJ
ejpam-4344	159	1	[	[	X
ejpam-4344	159	2	x2	x2	X
ejpam-4344	159	3	,	,	PUNCT
ejpam-4344	159	4	δ(x	δ(x	ADJ
ejpam-4344	159	5	)	)	PUNCT
ejpam-4344	159	6	]	]	PUNCT
ejpam-4344	159	7	∈	∈	PROPN
ejpam-4344	159	8	z(r	z(r	PROPN
ejpam-4344	159	9	)	)	PUNCT
ejpam-4344	159	10	.	.	PUNCT
ejpam-4344	160	1	consequently	consequently	ADV
ejpam-4344	160	2	,	,	PUNCT
ejpam-4344	160	3	x[x	x[x	PROPN
ejpam-4344	160	4	,	,	PUNCT
ejpam-4344	160	5	δ(x	δ(x	NOUN
ejpam-4344	160	6	)	)	PUNCT
ejpam-4344	160	7	]	]	PUNCT
ejpam-4344	160	8	∈	∈	PROPN
ejpam-4344	160	9	z(r	z(r	PROPN
ejpam-4344	160	10	)	)	PUNCT
ejpam-4344	160	11	(	(	PUNCT
ejpam-4344	160	12	3−	3−	NUM
ejpam-4344	160	13	3	3	NUM
ejpam-4344	160	14	)	)	PUNCT
ejpam-4344	160	15	.	.	PUNCT
ejpam-4344	161	1	then	then	ADV
ejpam-4344	161	2	0	0	NUM
ejpam-4344	161	3	=	=	PUNCT
ejpam-4344	162	1	[	[	X
ejpam-4344	162	2	x[x	x[x	X
ejpam-4344	162	3	,	,	PUNCT
ejpam-4344	162	4	δ(x	δ(x	PROPN
ejpam-4344	162	5	)	)	PUNCT
ejpam-4344	162	6	]	]	X
ejpam-4344	162	7	,	,	PUNCT
ejpam-4344	162	8	δ(x	δ(x	NOUN
ejpam-4344	162	9	)	)	PUNCT
ejpam-4344	162	10	]	]	PUNCT
ejpam-4344	163	1	=	=	PUNCT
ejpam-4344	164	1	[	[	X
ejpam-4344	164	2	x	x	X
ejpam-4344	164	3	,	,	PUNCT
ejpam-4344	164	4	δ(x)]2	δ(x)]2	ADV
ejpam-4344	164	5	.	.	PUNCT
ejpam-4344	165	1	obviously	obviously	ADV
ejpam-4344	165	2	that	that	DET
ejpam-4344	165	3	δ([x	δ([x	ADJ
ejpam-4344	165	4	,	,	PUNCT
ejpam-4344	165	5	δ(x	δ(x	NOUN
ejpam-4344	165	6	)	)	PUNCT
ejpam-4344	165	7	]	]	PUNCT
ejpam-4344	165	8	)	)	PUNCT
ejpam-4344	165	9	∈	∈	PROPN
ejpam-4344	165	10	z(r	z(r	PROPN
ejpam-4344	165	11	)	)	PUNCT
ejpam-4344	165	12	.	.	PUNCT
ejpam-4344	166	1	and	and	CCONJ
ejpam-4344	166	2	δ([x	δ([x	NOUN
ejpam-4344	166	3	,	,	PUNCT
ejpam-4344	166	4	δ(x	δ(x	NOUN
ejpam-4344	166	5	)	)	PUNCT
ejpam-4344	166	6	]	]	PUNCT
ejpam-4344	166	7	)	)	PUNCT
ejpam-4344	167	1	=	=	PUNCT
ejpam-4344	168	1	[	[	X
ejpam-4344	168	2	δ(x	δ(x	NOUN
ejpam-4344	168	3	)	)	PUNCT
ejpam-4344	168	4	,	,	PUNCT
ejpam-4344	168	5	δ(x	δ(x	NOUN
ejpam-4344	168	6	)	)	PUNCT
ejpam-4344	168	7	]	]	PUNCT
ejpam-4344	169	1	+	+	CCONJ
ejpam-4344	169	2	[	[	X
ejpam-4344	169	3	x	x	X
ejpam-4344	169	4	,	,	PUNCT
ejpam-4344	169	5	δ2(x	δ2(x	NOUN
ejpam-4344	169	6	)	)	PUNCT
ejpam-4344	169	7	]	]	PUNCT
ejpam-4344	170	1	=	=	PUNCT
ejpam-4344	170	2	i.	i.	PROPN
ejpam-4344	170	3	taha	taha	PROPN
ejpam-4344	170	4	et	et	PROPN
ejpam-4344	170	5	al	al	PROPN
ejpam-4344	170	6	.	.	PUNCT
ejpam-4344	170	7	/	/	SYM
ejpam-4344	170	8	eur	eur	PROPN
ejpam-4344	170	9	.	.	PUNCT
ejpam-4344	171	1	j.	j.	PROPN
ejpam-4344	171	2	pure	pure	PROPN
ejpam-4344	171	3	appl	appl	PROPN
ejpam-4344	171	4	.	.	PROPN
ejpam-4344	171	5	math	math	PROPN
ejpam-4344	171	6	,	,	PUNCT
ejpam-4344	171	7	15	15	NUM
ejpam-4344	171	8	(	(	PUNCT
ejpam-4344	171	9	2	2	NUM
ejpam-4344	171	10	)	)	PUNCT
ejpam-4344	171	11	(	(	PUNCT
ejpam-4344	171	12	2022	2022	NUM
ejpam-4344	171	13	)	)	PUNCT
ejpam-4344	171	14	,	,	PUNCT
ejpam-4344	171	15	454	454	NUM
ejpam-4344	171	16	-	-	SYM
ejpam-4344	171	17	466	466	NUM
ejpam-4344	171	18	460	460	NUM
ejpam-4344	172	1	[	[	X
ejpam-4344	172	2	x	x	X
ejpam-4344	172	3	,	,	PUNCT
ejpam-4344	172	4	δ2(x	δ2(x	NOUN
ejpam-4344	172	5	)	)	PUNCT
ejpam-4344	172	6	]	]	PUNCT
ejpam-4344	172	7	and	and	CCONJ
ejpam-4344	172	8	δ([x	δ([x	PROPN
ejpam-4344	172	9	,	,	PUNCT
ejpam-4344	172	10	δ2(x	δ2(x	NOUN
ejpam-4344	172	11	)	)	PUNCT
ejpam-4344	172	12	]	]	PUNCT
ejpam-4344	172	13	)	)	PUNCT
ejpam-4344	172	14	∈	∈	PROPN
ejpam-4344	172	15	z(r	z(r	PROPN
ejpam-4344	172	16	)	)	PUNCT
ejpam-4344	172	17	.	.	PUNCT
ejpam-4344	173	1	δ([x	δ([x	ADJ
ejpam-4344	173	2	,	,	PUNCT
ejpam-4344	173	3	δ2(x	δ2(x	NOUN
ejpam-4344	173	4	)	)	PUNCT
ejpam-4344	173	5	]	]	PUNCT
ejpam-4344	173	6	)	)	PUNCT
ejpam-4344	174	1	=	=	PUNCT
ejpam-4344	175	1	[	[	X
ejpam-4344	175	2	δ(x	δ(x	NOUN
ejpam-4344	175	3	)	)	PUNCT
ejpam-4344	175	4	,	,	PUNCT
ejpam-4344	175	5	δ2(x	δ2(x	NOUN
ejpam-4344	175	6	)	)	PUNCT
ejpam-4344	175	7	]	]	PUNCT
ejpam-4344	176	1	+	+	CCONJ
ejpam-4344	176	2	[	[	X
ejpam-4344	176	3	x	x	X
ejpam-4344	176	4	,	,	PUNCT
ejpam-4344	176	5	δ3(x	δ3(x	PROPN
ejpam-4344	176	6	)	)	PUNCT
ejpam-4344	176	7	]	]	PUNCT
ejpam-4344	176	8	.	.	PUNCT
ejpam-4344	177	1	hence	hence	ADV
ejpam-4344	177	2	[	[	X
ejpam-4344	177	3	δ(x	δ(x	PROPN
ejpam-4344	177	4	)	)	PUNCT
ejpam-4344	177	5	,	,	PUNCT
ejpam-4344	177	6	δ2(x	δ2(x	NOUN
ejpam-4344	177	7	)	)	PUNCT
ejpam-4344	177	8	]	]	PUNCT
ejpam-4344	177	9	∈	∈	PROPN
ejpam-4344	177	10	z(g	z(g	NOUN
ejpam-4344	177	11	)	)	PUNCT
ejpam-4344	177	12	we	we	PRON
ejpam-4344	177	13	have	have	VERB
ejpam-4344	177	14	[	[	X
ejpam-4344	177	15	x	x	X
ejpam-4344	177	16	,	,	PUNCT
ejpam-4344	177	17	δ3(x	δ3(x	NOUN
ejpam-4344	177	18	)	)	PUNCT
ejpam-4344	177	19	]	]	PUNCT
ejpam-4344	177	20	∈	∈	PROPN
ejpam-4344	177	21	z(r	z(r	PROPN
ejpam-4344	177	22	)	)	PUNCT
ejpam-4344	177	23	.	.	PUNCT
ejpam-4344	178	1	in	in	ADP
ejpam-4344	178	2	addition	addition	NOUN
ejpam-4344	178	3	,	,	PUNCT
ejpam-4344	178	4	by	by	ADP
ejpam-4344	178	5	induction	induction	NOUN
ejpam-4344	178	6	on	on	ADP
ejpam-4344	178	7	n	n	CCONJ
ejpam-4344	178	8	we	we	PRON
ejpam-4344	178	9	obtain	obtain	VERB
ejpam-4344	178	10	that	that	SCONJ
ejpam-4344	178	11	[	[	X
ejpam-4344	178	12	x	x	X
ejpam-4344	178	13	,	,	PUNCT
ejpam-4344	178	14	δn(x	δn(x	X
ejpam-4344	178	15	)	)	PUNCT
ejpam-4344	178	16	]	]	PUNCT
ejpam-4344	179	1	∈	∈	PROPN
ejpam-4344	179	2	z(r	z(r	PROPN
ejpam-4344	179	3	)	)	PUNCT
ejpam-4344	179	4	,	,	PUNCT
ejpam-4344	179	5	(	(	PUNCT
ejpam-4344	179	6	3−	3−	NUM
ejpam-4344	179	7	4	4	NUM
ejpam-4344	179	8	)	)	PUNCT
ejpam-4344	179	9	.	.	PUNCT
ejpam-4344	180	1	now	now	ADV
ejpam-4344	180	2	substituting	substitute	VERB
ejpam-4344	180	3	y	y	NOUN
ejpam-4344	180	4	by	by	ADP
ejpam-4344	180	5	xδn(x	xδn(x	NOUN
ejpam-4344	180	6	)	)	PUNCT
ejpam-4344	180	7	in	in	ADP
ejpam-4344	180	8	(	(	PUNCT
ejpam-4344	180	9	3	3	NUM
ejpam-4344	180	10	-	-	SYM
ejpam-4344	180	11	2	2	NUM
ejpam-4344	180	12	)	)	PUNCT
ejpam-4344	180	13	we	we	PRON
ejpam-4344	180	14	get	get	VERB
ejpam-4344	180	15	(	(	PUNCT
ejpam-4344	180	16	since	since	SCONJ
ejpam-4344	180	17	[	[	X
ejpam-4344	180	18	x	x	X
ejpam-4344	180	19	,	,	PUNCT
ejpam-4344	180	20	δ(xδn(x	δ(xδn(x	NUM
ejpam-4344	180	21	)	)	PUNCT
ejpam-4344	180	22	]	]	PUNCT
ejpam-4344	181	1	+	+	CCONJ
ejpam-4344	182	1	[	[	X
ejpam-4344	182	2	xδn(x	xδn(x	X
ejpam-4344	182	3	)	)	PUNCT
ejpam-4344	182	4	,	,	PUNCT
ejpam-4344	182	5	δ(x	δ(x	NOUN
ejpam-4344	182	6	)	)	PUNCT
ejpam-4344	182	7	]	]	PUNCT
ejpam-4344	182	8	∈	∈	PROPN
ejpam-4344	182	9	z(g	z(g	NOUN
ejpam-4344	182	10	)	)	PUNCT
ejpam-4344	182	11	)	)	PUNCT
ejpam-4344	183	1	[	[	X
ejpam-4344	183	2	x	x	X
ejpam-4344	183	3	,	,	PUNCT
ejpam-4344	183	4	δ(xδn(x	δ(xδn(x	NUM
ejpam-4344	183	5	)	)	PUNCT
ejpam-4344	183	6	]	]	PUNCT
ejpam-4344	184	1	+	+	CCONJ
ejpam-4344	185	1	[	[	X
ejpam-4344	185	2	xδn(x	xδn(x	X
ejpam-4344	185	3	)	)	PUNCT
ejpam-4344	185	4	,	,	PUNCT
ejpam-4344	185	5	δ(x	δ(x	NOUN
ejpam-4344	185	6	)	)	PUNCT
ejpam-4344	185	7	]	]	PUNCT
ejpam-4344	186	1	=	=	PUNCT
ejpam-4344	187	1	[	[	X
ejpam-4344	187	2	x	x	X
ejpam-4344	187	3	,	,	PUNCT
ejpam-4344	187	4	δ(x)δn(x	δ(x)δn(x	ADJ
ejpam-4344	187	5	)	)	PUNCT
ejpam-4344	187	6	]	]	PUNCT
ejpam-4344	188	1	+	+	CCONJ
ejpam-4344	189	1	[	[	X
ejpam-4344	189	2	x	x	X
ejpam-4344	189	3	,	,	PUNCT
ejpam-4344	189	4	xδn+1(x)]−	xδn+1(x)]−	PROPN
ejpam-4344	190	1	[	[	X
ejpam-4344	190	2	δ(x	δ(x	PROPN
ejpam-4344	190	3	)	)	PUNCT
ejpam-4344	190	4	,	,	PUNCT
ejpam-4344	190	5	xδn(x	xδn(x	PROPN
ejpam-4344	190	6	)	)	PUNCT
ejpam-4344	190	7	]	]	PUNCT
ejpam-4344	191	1	=	=	PUNCT
ejpam-4344	192	1	[	[	X
ejpam-4344	192	2	x	x	X
ejpam-4344	192	3	,	,	PUNCT
ejpam-4344	192	4	δ(x)]δn(x	δ(x)]δn(x	PROPN
ejpam-4344	192	5	)	)	PUNCT
ejpam-4344	192	6	+	+	CCONJ
ejpam-4344	192	7	δ(x)[x	δ(x)[x	PROPN
ejpam-4344	192	8	,	,	PUNCT
ejpam-4344	192	9	xδn(x)]+	xδn(x)]+	PUNCT
ejpam-4344	193	1	+	+	NOUN
ejpam-4344	193	2	x[x	x[x	PROPN
ejpam-4344	193	3	,	,	PUNCT
ejpam-4344	193	4	xδn+1(x)]−	xδn+1(x)]−	PROPN
ejpam-4344	194	1	[	[	X
ejpam-4344	194	2	δ(x	δ(x	PROPN
ejpam-4344	194	3	)	)	PUNCT
ejpam-4344	194	4	,	,	PUNCT
ejpam-4344	194	5	x]δn(x)−	x]δn(x)−	PROPN
ejpam-4344	194	6	−x[δ(x	−x[δ(x	NOUN
ejpam-4344	194	7	)	)	PUNCT
ejpam-4344	194	8	,	,	PUNCT
ejpam-4344	194	9	δn(x	δn(x	X
ejpam-4344	194	10	)	)	PUNCT
ejpam-4344	194	11	]	]	PUNCT
ejpam-4344	195	1	=	=	X
ejpam-4344	195	2	:	:	PUNCT
ejpam-4344	195	3	t.	t.	NOUN
ejpam-4344	195	4	then	then	ADV
ejpam-4344	195	5	,	,	PUNCT
ejpam-4344	195	6	0	0	PUNCT
ejpam-4344	195	7	=	=	SYM
ejpam-4344	196	1	[	[	X
ejpam-4344	196	2	t	t	X
ejpam-4344	196	3	,	,	PUNCT
ejpam-4344	196	4	δn(x	δn(x	X
ejpam-4344	196	5	)	)	PUNCT
ejpam-4344	196	6	]	]	PUNCT
ejpam-4344	197	1	=	=	PUNCT
ejpam-4344	198	1	[	[	X
ejpam-4344	198	2	δ(x	δ(x	NOUN
ejpam-4344	198	3	)	)	PUNCT
ejpam-4344	198	4	,	,	PUNCT
ejpam-4344	198	5	δn(x)].[x	δn(x)].[x	PROPN
ejpam-4344	198	6	,	,	PUNCT
ejpam-4344	198	7	δn(x)]+	δn(x)]+	X
ejpam-4344	199	1	[	[	X
ejpam-4344	199	2	x	x	NOUN
ejpam-4344	199	3	,	,	PUNCT
ejpam-4344	199	4	δn(x)].[x	δn(x)].[x	NOUN
ejpam-4344	199	5	,	,	PUNCT
ejpam-4344	199	6	δn+1(x)]−	δn+1(x)]−	PROPN
ejpam-4344	199	7	[	[	X
ejpam-4344	199	8	x	x	X
ejpam-4344	199	9	,	,	PUNCT
ejpam-4344	199	10	δn(x)].[δ(x	δn(x)].[δ(x	PROPN
ejpam-4344	199	11	)	)	PUNCT
ejpam-4344	199	12	,	,	PUNCT
ejpam-4344	199	13	δn(x	δn(x	X
ejpam-4344	199	14	)	)	PUNCT
ejpam-4344	199	15	]	]	PUNCT
ejpam-4344	200	1	=	=	PUNCT
ejpam-4344	201	1	[	[	X
ejpam-4344	201	2	x	x	X
ejpam-4344	201	3	,	,	PUNCT
ejpam-4344	201	4	δn(x)][x	δn(x)][x	PROPN
ejpam-4344	201	5	,	,	PUNCT
ejpam-4344	201	6	δn+1(x	δn+1(x	NOUN
ejpam-4344	201	7	)	)	PUNCT
ejpam-4344	201	8	]	]	PUNCT
ejpam-4344	201	9	.	.	PUNCT
ejpam-4344	202	1	(	(	PUNCT
ejpam-4344	202	2	3−	3−	NUM
ejpam-4344	202	3	5	5	NUM
ejpam-4344	202	4	)	)	PUNCT
ejpam-4344	202	5	substituting	substitute	VERB
ejpam-4344	202	6	y	y	NOUN
ejpam-4344	202	7	by	by	ADP
ejpam-4344	202	8	x2δn(x	x2δn(x	NOUN
ejpam-4344	202	9	)	)	PUNCT
ejpam-4344	202	10	in	in	ADP
ejpam-4344	202	11	(	(	PUNCT
ejpam-4344	202	12	3	3	NUM
ejpam-4344	202	13	-	-	SYM
ejpam-4344	202	14	2	2	NUM
ejpam-4344	202	15	)	)	PUNCT
ejpam-4344	202	16	,	,	PUNCT
ejpam-4344	202	17	we	we	PRON
ejpam-4344	202	18	will	will	AUX
ejpam-4344	202	19	obtain	obtain	VERB
ejpam-4344	202	20	[	[	X
ejpam-4344	202	21	x	x	NOUN
ejpam-4344	202	22	,	,	PUNCT
ejpam-4344	202	23	δ(x2δn(x	δ(x2δn(x	NUM
ejpam-4344	202	24	)	)	PUNCT
ejpam-4344	202	25	)	)	PUNCT
ejpam-4344	202	26	]	]	PUNCT
ejpam-4344	203	1	+	+	CCONJ
ejpam-4344	203	2	[	[	X
ejpam-4344	203	3	x2δn(x	x2δn(x	NOUN
ejpam-4344	203	4	)	)	PUNCT
ejpam-4344	203	5	,	,	PUNCT
ejpam-4344	203	6	δ(x	δ(x	NOUN
ejpam-4344	203	7	)	)	PUNCT
ejpam-4344	203	8	]	]	PUNCT
ejpam-4344	203	9	∈	∈	PROPN
ejpam-4344	203	10	z(r	z(r	PROPN
ejpam-4344	203	11	)	)	PUNCT
ejpam-4344	203	12	)	)	PUNCT
ejpam-4344	204	1	[	[	X
ejpam-4344	204	2	x	x	X
ejpam-4344	204	3	,	,	PUNCT
ejpam-4344	204	4	δ(x2δn(x	δ(x2δn(x	NUM
ejpam-4344	204	5	)	)	PUNCT
ejpam-4344	204	6	)	)	PUNCT
ejpam-4344	204	7	]	]	PUNCT
ejpam-4344	205	1	+	+	CCONJ
ejpam-4344	205	2	[	[	X
ejpam-4344	205	3	x2δn(x	x2δn(x	NOUN
ejpam-4344	205	4	)	)	PUNCT
ejpam-4344	205	5	,	,	PUNCT
ejpam-4344	205	6	δ(x	δ(x	NOUN
ejpam-4344	205	7	)	)	PUNCT
ejpam-4344	205	8	]	]	PUNCT
ejpam-4344	205	9	=	=	PUNCT
ejpam-4344	205	10	i.	i.	PROPN
ejpam-4344	205	11	taha	taha	PROPN
ejpam-4344	205	12	et	et	PROPN
ejpam-4344	205	13	al	al	PROPN
ejpam-4344	205	14	.	.	PUNCT
ejpam-4344	205	15	/	/	SYM
ejpam-4344	205	16	eur	eur	PROPN
ejpam-4344	205	17	.	.	PUNCT
ejpam-4344	206	1	j.	j.	PROPN
ejpam-4344	206	2	pure	pure	PROPN
ejpam-4344	206	3	appl	appl	PROPN
ejpam-4344	206	4	.	.	PROPN
ejpam-4344	206	5	math	math	PROPN
ejpam-4344	206	6	,	,	PUNCT
ejpam-4344	206	7	15	15	NUM
ejpam-4344	206	8	(	(	PUNCT
ejpam-4344	206	9	2	2	NUM
ejpam-4344	206	10	)	)	PUNCT
ejpam-4344	206	11	(	(	PUNCT
ejpam-4344	206	12	2022	2022	NUM
ejpam-4344	206	13	)	)	PUNCT
ejpam-4344	206	14	,	,	PUNCT
ejpam-4344	206	15	454	454	NUM
ejpam-4344	206	16	-	-	SYM
ejpam-4344	206	17	466	466	NUM
ejpam-4344	206	18	461	461	NUM
ejpam-4344	206	19	[	[	X
ejpam-4344	206	20	x	x	NOUN
ejpam-4344	206	21	,	,	PUNCT
ejpam-4344	206	22	δ(x)xδn(x	δ(x)xδn(x	NOUN
ejpam-4344	206	23	)	)	PUNCT
ejpam-4344	206	24	]	]	PUNCT
ejpam-4344	207	1	+	+	CCONJ
ejpam-4344	208	1	[	[	X
ejpam-4344	208	2	x	x	X
ejpam-4344	208	3	,	,	PUNCT
ejpam-4344	208	4	xδ(x)δn(x)]+	xδ(x)δn(x)]+	PROPN
ejpam-4344	209	1	+	+	PROPN
ejpam-4344	209	2	[	[	X
ejpam-4344	209	3	x	x	X
ejpam-4344	209	4	,	,	PUNCT
ejpam-4344	209	5	x2δn+1(x)]−	x2δn+1(x)]−	PROPN
ejpam-4344	210	1	[	[	X
ejpam-4344	210	2	δ(x	δ(x	PROPN
ejpam-4344	210	3	)	)	PUNCT
ejpam-4344	210	4	,	,	PUNCT
ejpam-4344	210	5	x2δn(x	x2δn(x	PROPN
ejpam-4344	210	6	)	)	PUNCT
ejpam-4344	210	7	]	]	PUNCT
ejpam-4344	211	1	=	=	PUNCT
ejpam-4344	212	1	[	[	X
ejpam-4344	212	2	x	x	X
ejpam-4344	212	3	,	,	PUNCT
ejpam-4344	212	4	δ(x)x]δn(x	δ(x)x]δn(x	PROPN
ejpam-4344	212	5	)	)	PUNCT
ejpam-4344	212	6	+	+	CCONJ
ejpam-4344	213	1	[	[	X
ejpam-4344	213	2	x	x	X
ejpam-4344	213	3	,	,	PUNCT
ejpam-4344	213	4	δn(x)]δ(x)x+	δn(x)]δ(x)x+	X
ejpam-4344	213	5	[	[	X
ejpam-4344	213	6	x	x	X
ejpam-4344	213	7	,	,	PUNCT
ejpam-4344	213	8	xδ(x)]δn(x	xδ(x)]δn(x	NUM
ejpam-4344	213	9	)	)	PUNCT
ejpam-4344	213	10	+	+	CCONJ
ejpam-4344	213	11	[	[	X
ejpam-4344	213	12	x	x	X
ejpam-4344	213	13	,	,	PUNCT
ejpam-4344	213	14	δn(x)]xδ(x)+	δn(x)]xδ(x)+	ADJ
ejpam-4344	213	15	[	[	X
ejpam-4344	213	16	x	x	X
ejpam-4344	213	17	,	,	PUNCT
ejpam-4344	213	18	x2]δn+1(x	x2]δn+1(x	NUM
ejpam-4344	213	19	)	)	PUNCT
ejpam-4344	214	1	+	+	CCONJ
ejpam-4344	215	1	[	[	X
ejpam-4344	215	2	x	x	X
ejpam-4344	215	3	,	,	PUNCT
ejpam-4344	215	4	δn+1(x)]x2−	δn+1(x)]x2−	PROPN
ejpam-4344	215	5	−[δ(x	−[δ(x	PROPN
ejpam-4344	215	6	)	)	PUNCT
ejpam-4344	215	7	,	,	PUNCT
ejpam-4344	215	8	x2]δn(x)−	x2]δn(x)−	PROPN
ejpam-4344	216	1	[	[	X
ejpam-4344	216	2	δ(x	δ(x	PROPN
ejpam-4344	216	3	)	)	PUNCT
ejpam-4344	216	4	,	,	PUNCT
ejpam-4344	216	5	δn(x)]x2	δn(x)]x2	X
ejpam-4344	217	1	=	=	PUNCT
ejpam-4344	218	1	[	[	X
ejpam-4344	218	2	x	x	X
ejpam-4344	218	3	,	,	PUNCT
ejpam-4344	218	4	δ(x)]xδn(x	δ(x)]xδn(x	ADJ
ejpam-4344	218	5	)	)	PUNCT
ejpam-4344	218	6	+	+	PROPN
ejpam-4344	219	1	[	[	X
ejpam-4344	219	2	x	x	X
ejpam-4344	219	3	,	,	PUNCT
ejpam-4344	219	4	x]δ(x)δn(x)+	x]δ(x)δn(x)+	PUNCT
ejpam-4344	220	1	[	[	X
ejpam-4344	220	2	x	x	X
ejpam-4344	220	3	,	,	PUNCT
ejpam-4344	220	4	δn(x)]δ(x)x+	δn(x)]δ(x)x+	X
ejpam-4344	221	1	[	[	X
ejpam-4344	221	2	x	x	X
ejpam-4344	221	3	,	,	PUNCT
ejpam-4344	221	4	x]δ(x)δn(x)+	x]δ(x)δn(x)+	PUNCT
ejpam-4344	222	1	[	[	X
ejpam-4344	222	2	x	x	X
ejpam-4344	222	3	,	,	PUNCT
ejpam-4344	222	4	δ(x)]xδn(x	δ(x)]xδn(x	ADJ
ejpam-4344	222	5	)	)	PUNCT
ejpam-4344	222	6	+	+	PROPN
ejpam-4344	223	1	[	[	X
ejpam-4344	223	2	x	x	X
ejpam-4344	223	3	,	,	PUNCT
ejpam-4344	223	4	δn(x)]xδ(x)+	δn(x)]xδ(x)+	ADJ
ejpam-4344	223	5	[	[	X
ejpam-4344	223	6	x	x	X
ejpam-4344	223	7	,	,	PUNCT
ejpam-4344	223	8	δn+1(x)]x2	δn+1(x)]x2	PROPN
ejpam-4344	223	9	−	−	PROPN
ejpam-4344	223	10	2[δ(x	2[δ(x	NUM
ejpam-4344	223	11	)	)	PUNCT
ejpam-4344	223	12	,	,	PUNCT
ejpam-4344	223	13	x]xδn(x)−	x]xδn(x)−	PROPN
ejpam-4344	223	14	−[δ(x	−[δ(x	PROPN
ejpam-4344	223	15	)	)	PUNCT
ejpam-4344	223	16	,	,	PUNCT
ejpam-4344	223	17	δn(x)]x2	δn(x)]x2	X
ejpam-4344	223	18	=	=	SYM
ejpam-4344	223	19	4[x	4[x	NUM
ejpam-4344	223	20	,	,	PUNCT
ejpam-4344	223	21	δ(x)]xδn(x	δ(x)]xδn(x	PROPN
ejpam-4344	223	22	)	)	PUNCT
ejpam-4344	223	23	+	+	PROPN
ejpam-4344	224	1	[	[	X
ejpam-4344	224	2	x	x	X
ejpam-4344	224	3	,	,	PUNCT
ejpam-4344	224	4	δn(x)]xδ(x)+	δn(x)]xδ(x)+	ADJ
ejpam-4344	224	5	+	+	PROPN
ejpam-4344	224	6	[	[	X
ejpam-4344	224	7	x	x	NOUN
ejpam-4344	224	8	,	,	PUNCT
ejpam-4344	224	9	δn(x)]xδ(x)x+	δn(x)]xδ(x)x+	NOUN
ejpam-4344	224	10	[	[	X
ejpam-4344	224	11	x	x	NOUN
ejpam-4344	224	12	,	,	PUNCT
ejpam-4344	224	13	δn+1(x)]x2−	δn+1(x)]x2−	ADP
ejpam-4344	224	14	+	+	PROPN
ejpam-4344	224	15	[	[	X
ejpam-4344	224	16	δ(x	δ(x	ADJ
ejpam-4344	224	17	)	)	PUNCT
ejpam-4344	224	18	,	,	PUNCT
ejpam-4344	224	19	δn(x)]x2	δn(x)]x2	X
ejpam-4344	225	1	=	=	PRON
ejpam-4344	225	2	:	:	PUNCT
ejpam-4344	225	3	q.	q.	PROPN
ejpam-4344	225	4	(	(	PUNCT
ejpam-4344	225	5	3−	3−	NUM
ejpam-4344	225	6	6	6	NUM
ejpam-4344	225	7	)	)	PUNCT
ejpam-4344	225	8	multiplying	multiply	VERB
ejpam-4344	225	9	q	q	PUNCT
ejpam-4344	225	10	by	by	ADP
ejpam-4344	225	11	[	[	X
ejpam-4344	225	12	x	x	X
ejpam-4344	225	13	,	,	PUNCT
ejpam-4344	225	14	δn(x	δn(x	X
ejpam-4344	225	15	)	)	PUNCT
ejpam-4344	225	16	]	]	PUNCT
ejpam-4344	225	17	in	in	ADP
ejpam-4344	225	18	(	(	PUNCT
ejpam-4344	225	19	3	3	NUM
ejpam-4344	225	20	-	-	SYM
ejpam-4344	225	21	6	6	NUM
ejpam-4344	225	22	)	)	PUNCT
ejpam-4344	225	23	a	a	PRON
ejpam-4344	225	24	in	in	ADP
ejpam-4344	225	25	view	view	NOUN
ejpam-4344	225	26	of	of	ADP
ejpam-4344	225	27	(	(	PUNCT
ejpam-4344	225	28	3	3	NUM
ejpam-4344	225	29	-	-	SYM
ejpam-4344	225	30	2	2	NUM
ejpam-4344	225	31	)	)	PUNCT
ejpam-4344	225	32	we	we	PRON
ejpam-4344	225	33	obtain	obtain	VERB
ejpam-4344	225	34	[	[	X
ejpam-4344	225	35	x	x	NOUN
ejpam-4344	225	36	,	,	PUNCT
ejpam-4344	225	37	δn(x)]2xδ(x	δn(x)]2xδ(x	NOUN
ejpam-4344	225	38	)	)	PUNCT
ejpam-4344	226	1	+	+	PUNCT
ejpam-4344	227	1	[	[	X
ejpam-4344	227	2	x	x	X
ejpam-4344	227	3	,	,	PUNCT
ejpam-4344	227	4	δn(x)]2δ(x)x−	δn(x)]2δ(x)x−	PROPN
ejpam-4344	227	5	−[δ(x	−[δ(x	PROPN
ejpam-4344	227	6	)	)	PUNCT
ejpam-4344	227	7	,	,	PUNCT
ejpam-4344	227	8	δn(x)][x	δn(x)][x	PROPN
ejpam-4344	227	9	,	,	PUNCT
ejpam-4344	227	10	δn(x)]x2	δn(x)]x2	NOUN
ejpam-4344	227	11	∈	∈	PROPN
ejpam-4344	227	12	z(r	z(r	PROPN
ejpam-4344	227	13	)	)	PUNCT
ejpam-4344	227	14	.	.	PUNCT
ejpam-4344	228	1	then	then	ADV
ejpam-4344	228	2	,	,	PUNCT
ejpam-4344	228	3	i.	i.	PROPN
ejpam-4344	228	4	taha	taha	PROPN
ejpam-4344	228	5	et	et	PROPN
ejpam-4344	228	6	al	al	PROPN
ejpam-4344	228	7	.	.	PUNCT
ejpam-4344	228	8	/	/	SYM
ejpam-4344	228	9	eur	eur	PROPN
ejpam-4344	228	10	.	.	PUNCT
ejpam-4344	229	1	j.	j.	PROPN
ejpam-4344	229	2	pure	pure	PROPN
ejpam-4344	229	3	appl	appl	PROPN
ejpam-4344	229	4	.	.	PROPN
ejpam-4344	229	5	math	math	PROPN
ejpam-4344	229	6	,	,	PUNCT
ejpam-4344	229	7	15	15	NUM
ejpam-4344	229	8	(	(	PUNCT
ejpam-4344	229	9	2	2	NUM
ejpam-4344	229	10	)	)	PUNCT
ejpam-4344	229	11	(	(	PUNCT
ejpam-4344	229	12	2022	2022	NUM
ejpam-4344	229	13	)	)	PUNCT
ejpam-4344	229	14	,	,	PUNCT
ejpam-4344	229	15	454	454	NUM
ejpam-4344	229	16	-	-	SYM
ejpam-4344	229	17	466	466	NUM
ejpam-4344	229	18	462	462	NUM
ejpam-4344	229	19	0	0	NUM
ejpam-4344	230	1	=	=	PUNCT
ejpam-4344	231	1	[	[	X
ejpam-4344	231	2	δn(x	δn(x	X
ejpam-4344	231	3	)	)	PUNCT
ejpam-4344	231	4	,	,	PUNCT
ejpam-4344	231	5	f	f	X
ejpam-4344	231	6	]	]	X
ejpam-4344	232	1	=	=	PUNCT
ejpam-4344	233	1	[	[	X
ejpam-4344	233	2	δn(x	δn(x	X
ejpam-4344	233	3	)	)	PUNCT
ejpam-4344	233	4	,	,	PUNCT
ejpam-4344	233	5	xδ(x)][x	xδ(x)][x	PROPN
ejpam-4344	233	6	,	,	PUNCT
ejpam-4344	233	7	δn(x)]2	δn(x)]2	NOUN
ejpam-4344	233	8	+	+	NOUN
ejpam-4344	233	9	+	+	ADJ
ejpam-4344	233	10	[	[	X
ejpam-4344	233	11	δn(x	δn(x	X
ejpam-4344	233	12	)	)	PUNCT
ejpam-4344	233	13	,	,	PUNCT
ejpam-4344	233	14	δ(x)x][xδn(x)]2−	δ(x)x][xδn(x)]2−	NOUN
ejpam-4344	233	15	−[δ(x	−[δ(x	PROPN
ejpam-4344	233	16	)	)	PUNCT
ejpam-4344	233	17	,	,	PUNCT
ejpam-4344	233	18	δn(x)][x	δn(x)][x	PROPN
ejpam-4344	233	19	,	,	PUNCT
ejpam-4344	233	20	δn(x)][δn(x	δn(x)][δn(x	PROPN
ejpam-4344	233	21	)	)	PUNCT
ejpam-4344	233	22	,	,	PUNCT
ejpam-4344	233	23	x2	x2	PROPN
ejpam-4344	233	24	]	]	X
ejpam-4344	234	1	=	=	PUNCT
ejpam-4344	234	2	=	=	PUNCT
ejpam-4344	234	3	[	[	X
ejpam-4344	234	4	δn(x	δn(x	X
ejpam-4344	234	5	)	)	PUNCT
ejpam-4344	234	6	,	,	PUNCT
ejpam-4344	234	7	x][x	x][x	NOUN
ejpam-4344	234	8	,	,	PUNCT
ejpam-4344	234	9	δn(x)]2δ(x)+	δn(x)]2δ(x)+	PROPN
ejpam-4344	234	10	=	=	PUNCT
ejpam-4344	234	11	[	[	X
ejpam-4344	234	12	δn(x	δn(x	X
ejpam-4344	234	13	)	)	PUNCT
ejpam-4344	234	14	,	,	PUNCT
ejpam-4344	234	15	δ(x)][x	δ(x)][x	NOUN
ejpam-4344	234	16	,	,	PUNCT
ejpam-4344	234	17	δn(x)]2δ(x)+	δn(x)]2δ(x)+	NOUN
ejpam-4344	234	18	+	+	PROPN
ejpam-4344	234	19	[	[	X
ejpam-4344	234	20	δn(x	δn(x	X
ejpam-4344	234	21	)	)	PUNCT
ejpam-4344	234	22	,	,	PUNCT
ejpam-4344	234	23	δ(x)][x	δ(x)][x	PROPN
ejpam-4344	234	24	,	,	PUNCT
ejpam-4344	234	25	δn(x)]2x+	δn(x)]2x+	PROPN
ejpam-4344	235	1	+	+	PROPN
ejpam-4344	235	2	[	[	X
ejpam-4344	235	3	δn(x	δn(x	X
ejpam-4344	235	4	)	)	PUNCT
ejpam-4344	235	5	,	,	PUNCT
ejpam-4344	235	6	δ(x)][x	δ(x)][x	PROPN
ejpam-4344	235	7	,	,	PUNCT
ejpam-4344	236	1	δn(x)]2x+	δn(x)]2x+	PROPN
ejpam-4344	237	1	+	+	PROPN
ejpam-4344	237	2	[	[	X
ejpam-4344	237	3	δn(x	δn(x	X
ejpam-4344	237	4	)	)	PUNCT
ejpam-4344	237	5	,	,	PUNCT
ejpam-4344	237	6	x][x	x][x	PROPN
ejpam-4344	237	7	,	,	PUNCT
ejpam-4344	237	8	δn(x)]2δ(x)−	δn(x)]2δ(x)−	NOUN
ejpam-4344	237	9	−2[δ(x	−2[δ(x	NOUN
ejpam-4344	237	10	)	)	PUNCT
ejpam-4344	237	11	,	,	PUNCT
ejpam-4344	237	12	δn(x)][x	δn(x)][x	PROPN
ejpam-4344	237	13	,	,	PUNCT
ejpam-4344	237	14	δn(x)][δn(x	δn(x)][δn(x	PROPN
ejpam-4344	237	15	)	)	PUNCT
ejpam-4344	237	16	,	,	PUNCT
ejpam-4344	238	1	x]x	x]x	NOUN
ejpam-4344	238	2	=	=	SYM
ejpam-4344	238	3	2[δn(x	2[δn(x	NUM
ejpam-4344	238	4	)	)	PUNCT
ejpam-4344	238	5	,	,	PUNCT
ejpam-4344	238	6	δ(x)][x	δ(x)][x	NOUN
ejpam-4344	238	7	,	,	PUNCT
ejpam-4344	238	8	δn(x)]2−	δn(x)]2−	NOUN
ejpam-4344	238	9	−2[x	−2[x	NOUN
ejpam-4344	238	10	,	,	PUNCT
ejpam-4344	238	11	δn(x)]3δ(x	δn(x)]3δ(x	NOUN
ejpam-4344	238	12	)	)	PUNCT
ejpam-4344	238	13	+	+	NUM
ejpam-4344	238	14	2[δ(x	2[δ(x	NUM
ejpam-4344	238	15	)	)	PUNCT
ejpam-4344	238	16	,	,	PUNCT
ejpam-4344	238	17	δn(x)][x	δn(x)][x	PROPN
ejpam-4344	238	18	,	,	PUNCT
ejpam-4344	238	19	δn(x)]2x	δn(x)]2x	NOUN
ejpam-4344	238	20	=	=	PUNCT
ejpam-4344	238	21	=	=	SYM
ejpam-4344	238	22	2[x	2[x	NUM
ejpam-4344	238	23	,	,	PUNCT
ejpam-4344	238	24	δn(x)]3δ(x	δn(x)]3δ(x	NOUN
ejpam-4344	238	25	)	)	PUNCT
ejpam-4344	238	26	]	]	PUNCT
ejpam-4344	239	1	=	=	SYM
ejpam-4344	239	2	:	:	PUNCT
ejpam-4344	239	3	x	x	X
ejpam-4344	239	4	then	then	ADV
ejpam-4344	239	5	[	[	X
ejpam-4344	239	6	x	x	X
ejpam-4344	239	7	,	,	PUNCT
ejpam-4344	239	8	δn(x)]3δ(x	δn(x)]3δ(x	NOUN
ejpam-4344	239	9	)	)	PUNCT
ejpam-4344	239	10	]	]	PUNCT
ejpam-4344	240	1	=	=	PUNCT
ejpam-4344	240	2	0	0	PUNCT
ejpam-4344	241	1	thus	thus	ADV
ejpam-4344	241	2	[	[	X
ejpam-4344	241	3	x	x	X
ejpam-4344	241	4	,	,	PUNCT
ejpam-4344	241	5	δn+1(x)]3δ(x	δn+1(x)]3δ(x	PROPN
ejpam-4344	241	6	)	)	PUNCT
ejpam-4344	241	7	]	]	PUNCT
ejpam-4344	242	1	=	=	PUNCT
ejpam-4344	242	2	0	0	PUNCT
ejpam-4344	243	1	hence	hence	ADV
ejpam-4344	243	2	[	[	X
ejpam-4344	243	3	x	x	X
ejpam-4344	243	4	,	,	PUNCT
ejpam-4344	243	5	δn+1(x)]3[δ(x	δn+1(x)]3[δ(x	PROPN
ejpam-4344	243	6	)	)	PUNCT
ejpam-4344	243	7	,	,	PUNCT
ejpam-4344	243	8	δn(x	δn(x	X
ejpam-4344	243	9	)	)	PUNCT
ejpam-4344	243	10	]	]	PUNCT
ejpam-4344	244	1	=	=	PUNCT
ejpam-4344	245	1	[	[	X
ejpam-4344	245	2	x	x	X
ejpam-4344	245	3	,	,	PUNCT
ejpam-4344	245	4	δn+1(x)]3δ(x)δn(x)−	δn+1(x)]3δ(x)δn(x)−	PROPN
ejpam-4344	245	5	i.	i.	PROPN
ejpam-4344	245	6	taha	taha	PROPN
ejpam-4344	245	7	et	et	PROPN
ejpam-4344	245	8	al	al	PROPN
ejpam-4344	245	9	.	.	PUNCT
ejpam-4344	245	10	/	/	SYM
ejpam-4344	245	11	eur	eur	PROPN
ejpam-4344	245	12	.	.	PUNCT
ejpam-4344	246	1	j.	j.	PROPN
ejpam-4344	246	2	pure	pure	PROPN
ejpam-4344	246	3	appl	appl	PROPN
ejpam-4344	246	4	.	.	PROPN
ejpam-4344	246	5	math	math	PROPN
ejpam-4344	246	6	,	,	PUNCT
ejpam-4344	246	7	15	15	NUM
ejpam-4344	246	8	(	(	PUNCT
ejpam-4344	246	9	2	2	NUM
ejpam-4344	246	10	)	)	PUNCT
ejpam-4344	246	11	(	(	PUNCT
ejpam-4344	246	12	2022	2022	NUM
ejpam-4344	246	13	)	)	PUNCT
ejpam-4344	246	14	,	,	PUNCT
ejpam-4344	246	15	454	454	NUM
ejpam-4344	246	16	-	-	SYM
ejpam-4344	246	17	466	466	NUM
ejpam-4344	246	18	463	463	NUM
ejpam-4344	246	19	−δn(x)[x	−δn(x)[x	NOUN
ejpam-4344	246	20	,	,	PUNCT
ejpam-4344	246	21	δn+1(x)]3δ(x	δn+1(x)]3δ(x	NOUN
ejpam-4344	246	22	)	)	PUNCT
ejpam-4344	246	23	=	=	SYM
ejpam-4344	246	24	0	0	X
ejpam-4344	246	25	.	.	PUNCT
ejpam-4344	247	1	(	(	PUNCT
ejpam-4344	247	2	3−	3−	NUM
ejpam-4344	247	3	7	7	NUM
ejpam-4344	247	4	)	)	PUNCT
ejpam-4344	247	5	multiplying	multiplying	NOUN
ejpam-4344	247	6	(	(	PUNCT
ejpam-4344	247	7	3	3	NUM
ejpam-4344	247	8	-	-	SYM
ejpam-4344	247	9	7	7	NUM
ejpam-4344	247	10	)	)	PUNCT
ejpam-4344	247	11	by	by	ADP
ejpam-4344	247	12	[	[	X
ejpam-4344	247	13	x	x	X
ejpam-4344	247	14	,	,	PUNCT
ejpam-4344	247	15	δn+1(x)]2	δn+1(x)]2	PROPN
ejpam-4344	247	16	we	we	PRON
ejpam-4344	247	17	obtain	obtain	VERB
ejpam-4344	247	18	[	[	X
ejpam-4344	247	19	x	x	X
ejpam-4344	247	20	,	,	PUNCT
ejpam-4344	247	21	δn+1(x)]4	δn+1(x)]4	PROPN
ejpam-4344	247	22	=	=	SYM
ejpam-4344	247	23	0	0	X
ejpam-4344	247	24	.	.	PUNCT
ejpam-4344	248	1	thus	thus	ADV
ejpam-4344	248	2	(	(	PUNCT
ejpam-4344	248	3	[	[	X
ejpam-4344	248	4	x	x	NOUN
ejpam-4344	248	5	,	,	PUNCT
ejpam-4344	248	6	δn+1(x)]r4	δn+1(x)]r4	PROPN
ejpam-4344	248	7	=	=	PROPN
ejpam-4344	248	8	0	0	PROPN
ejpam-4344	248	9	.	.	PUNCT
ejpam-4344	249	1	this	this	PRON
ejpam-4344	249	2	means	mean	VERB
ejpam-4344	249	3	that	that	SCONJ
ejpam-4344	249	4	a	a	DET
ejpam-4344	249	5	=	=	SYM
ejpam-4344	249	6	∞∑	∞∑	NUM
ejpam-4344	249	7	n=1	n=1	PUNCT
ejpam-4344	249	8	∑	∑	ADP
ejpam-4344	249	9	x∈i	x∈i	NOUN
ejpam-4344	250	1	[	[	X
ejpam-4344	250	2	x	x	NOUN
ejpam-4344	250	3	,	,	PUNCT
ejpam-4344	250	4	δn(x)]r	δn(x)]r	NOUN
ejpam-4344	250	5	.	.	PUNCT
ejpam-4344	251	1	(	(	PUNCT
ejpam-4344	251	2	δ([x	δ([x	ADJ
ejpam-4344	251	3	,	,	PUNCT
ejpam-4344	251	4	δn+1(x)]r	δn+1(x)]r	NOUN
ejpam-4344	251	5	)	)	PUNCT
ejpam-4344	251	6	=	=	PUNCT
ejpam-4344	252	1	[	[	X
ejpam-4344	252	2	δ(x	δ(x	NOUN
ejpam-4344	252	3	)	)	PUNCT
ejpam-4344	252	4	,	,	PUNCT
ejpam-4344	252	5	δn+1(x)]r+	δn+1(x)]r+	VERB
ejpam-4344	253	1	[	[	X
ejpam-4344	253	2	x	x	X
ejpam-4344	253	3	,	,	PUNCT
ejpam-4344	253	4	δn+2(x)]r+	δn+2(x)]r+	PROPN
ejpam-4344	253	5	[	[	X
ejpam-4344	253	6	x	x	X
ejpam-4344	253	7	,	,	PUNCT
ejpam-4344	253	8	δn(x)]δ(r	δn(x)]δ(r	NOUN
ejpam-4344	253	9	)	)	PUNCT
ejpam-4344	253	10	⊆	⊆	PROPN
ejpam-4344	253	11	a	a	PRON
ejpam-4344	253	12	)	)	PUNCT
ejpam-4344	253	13	is	be	AUX
ejpam-4344	253	14	a	a	DET
ejpam-4344	253	15	sum	sum	NOUN
ejpam-4344	253	16	of	of	ADP
ejpam-4344	253	17	nilpotent	nilpotent	ADJ
ejpam-4344	253	18	ideals	ideal	NOUN
ejpam-4344	253	19	and	and	CCONJ
ejpam-4344	253	20	i	i	PRON
ejpam-4344	253	21	is	be	AUX
ejpam-4344	253	22	a	a	DET
ejpam-4344	253	23	nil	nil	ADJ
ejpam-4344	253	24	ideal	ideal	NOUN
ejpam-4344	253	25	,	,	PUNCT
ejpam-4344	253	26	since	since	SCONJ
ejpam-4344	253	27	a	a	PRON
ejpam-4344	253	28	is	be	AUX
ejpam-4344	253	29	δ	δ	NOUN
ejpam-4344	253	30	-	-	PUNCT
ejpam-4344	253	31	ideal	ideal	ADJ
ejpam-4344	253	32	,	,	PUNCT
ejpam-4344	253	33	we	we	PRON
ejpam-4344	253	34	deduce	deduce	VERB
ejpam-4344	253	35	that	that	SCONJ
ejpam-4344	253	36	a	a	DET
ejpam-4344	253	37	=	=	NOUN
ejpam-4344	253	38	0	0	NUM
ejpam-4344	253	39	.	.	PUNCT
ejpam-4344	254	1	this	this	PRON
ejpam-4344	254	2	gives	give	VERB
ejpam-4344	254	3	that	that	PRON
ejpam-4344	254	4	[	[	X
ejpam-4344	254	5	x	x	X
ejpam-4344	254	6	,	,	PUNCT
ejpam-4344	254	7	δ(x	δ(x	NOUN
ejpam-4344	254	8	)	)	PUNCT
ejpam-4344	254	9	]	]	PUNCT
ejpam-4344	255	1	=	=	PUNCT
ejpam-4344	255	2	0	0	X
ejpam-4344	255	3	.	.	PUNCT
ejpam-4344	256	1	lemma	lemma	PROPN
ejpam-4344	256	2	7	7	X
ejpam-4344	256	3	.	.	PUNCT
ejpam-4344	257	1	let	let	VERB
ejpam-4344	257	2	r	r	NOUN
ejpam-4344	257	3	be	be	AUX
ejpam-4344	257	4	δ	δ	NOUN
ejpam-4344	257	5	-	-	ADJ
ejpam-4344	257	6	prime	prime	ADJ
ejpam-4344	257	7	ring	ring	NOUN
ejpam-4344	257	8	of	of	ADP
ejpam-4344	257	9	charr	charr	NOUN
ejpam-4344	257	10	6=	6=	ADP
ejpam-4344	257	11	2	2	NUM
ejpam-4344	257	12	and	and	CCONJ
ejpam-4344	257	13	[	[	X
ejpam-4344	257	14	δ(x	δ(x	PROPN
ejpam-4344	257	15	)	)	PUNCT
ejpam-4344	257	16	,	,	PUNCT
ejpam-4344	257	17	x	x	X
ejpam-4344	257	18	]	]	X
ejpam-4344	257	19	∈	∈	PROPN
ejpam-4344	257	20	z(r	z(r	PROPN
ejpam-4344	257	21	)	)	PUNCT
ejpam-4344	257	22	∀x	∀x	VERB
ejpam-4344	257	23	∈	∈	PROPN
ejpam-4344	257	24	r.	r.	NOUN
ejpam-4344	257	25	then	then	ADV
ejpam-4344	257	26	r	r	NOUN
ejpam-4344	257	27	is	be	AUX
ejpam-4344	257	28	commutative	commutative	ADJ
ejpam-4344	257	29	.	.	PUNCT
ejpam-4344	258	1	proof	proof	NOUN
ejpam-4344	258	2	.	.	PUNCT
ejpam-4344	259	1	it	it	PRON
ejpam-4344	259	2	is	be	AUX
ejpam-4344	259	3	well	well	ADV
ejpam-4344	259	4	known	known	ADJ
ejpam-4344	259	5	that	that	SCONJ
ejpam-4344	259	6	[	[	X
ejpam-4344	259	7	r	r	X
ejpam-4344	259	8	,	,	PUNCT
ejpam-4344	259	9	r	r	NOUN
ejpam-4344	259	10	]	]	X
ejpam-4344	259	11	is	be	AUX
ejpam-4344	259	12	a	a	DET
ejpam-4344	259	13	lie	lie	NOUN
ejpam-4344	259	14	ideal	ideal	NOUN
ejpam-4344	259	15	of	of	ADP
ejpam-4344	259	16	r.	r.	PROPN
ejpam-4344	259	17	moreover	moreover	ADV
ejpam-4344	259	18	,	,	PUNCT
ejpam-4344	259	19	δ([r	δ([r	PROPN
ejpam-4344	259	20	,	,	PUNCT
ejpam-4344	259	21	r	r	NOUN
ejpam-4344	259	22	]	]	PUNCT
ejpam-4344	259	23	)	)	PUNCT
ejpam-4344	260	1	⊆	⊆	NUM
ejpam-4344	260	2	[	[	X
ejpam-4344	260	3	r	r	NOUN
ejpam-4344	260	4	,	,	PUNCT
ejpam-4344	260	5	r	r	NOUN
ejpam-4344	260	6	]	]	PUNCT
ejpam-4344	260	7	.	.	PUNCT
ejpam-4344	261	1	now	now	ADV
ejpam-4344	261	2	on	on	ADP
ejpam-4344	261	3	the	the	DET
ejpam-4344	261	4	one	one	NUM
ejpam-4344	261	5	hand	hand	NOUN
ejpam-4344	261	6	if	if	SCONJ
ejpam-4344	261	7	[	[	X
ejpam-4344	261	8	r	r	NOUN
ejpam-4344	261	9	,	,	PUNCT
ejpam-4344	261	10	r	r	NOUN
ejpam-4344	261	11	]	]	X
ejpam-4344	261	12	is	be	AUX
ejpam-4344	261	13	commutative	commutative	ADJ
ejpam-4344	261	14	,	,	PUNCT
ejpam-4344	261	15	then	then	ADV
ejpam-4344	261	16	by	by	ADP
ejpam-4344	261	17	lemma	lemma	PROPN
ejpam-4344	261	18	(	(	PUNCT
ejpam-4344	261	19	1	1	NUM
ejpam-4344	261	20	-	-	SYM
ejpam-4344	261	21	7	7	NUM
ejpam-4344	261	22	)	)	PUNCT
ejpam-4344	261	23	in	in	ADP
ejpam-4344	261	24	[	[	X
ejpam-4344	261	25	5	5	NUM
ejpam-4344	261	26	]	]	PUNCT
ejpam-4344	261	27	c(r	c(r	NOUN
ejpam-4344	261	28	)	)	PUNCT
ejpam-4344	261	29	is	be	AUX
ejpam-4344	261	30	a	a	DET
ejpam-4344	261	31	nil	nil	ADJ
ejpam-4344	261	32	ideal	ideal	NOUN
ejpam-4344	261	33	,	,	PUNCT
ejpam-4344	261	34	thus	thus	ADV
ejpam-4344	261	35	c(r	c(r	NOUN
ejpam-4344	261	36	)	)	PUNCT
ejpam-4344	262	1	=	=	SYM
ejpam-4344	262	2	0	0	NUM
ejpam-4344	262	3	,	,	PUNCT
ejpam-4344	262	4	and	and	CCONJ
ejpam-4344	262	5	r	r	NOUN
ejpam-4344	262	6	is	be	AUX
ejpam-4344	262	7	commutative	commutative	ADJ
ejpam-4344	262	8	.	.	PUNCT
ejpam-4344	263	1	on	on	ADP
ejpam-4344	263	2	the	the	DET
ejpam-4344	263	3	other	other	ADJ
ejpam-4344	263	4	hand	hand	NOUN
ejpam-4344	263	5	by	by	ADP
ejpam-4344	263	6	lemma	lemma	PROPN
ejpam-4344	263	7	13	13	NUM
ejpam-4344	264	1	[	[	X
ejpam-4344	264	2	3	3	X
ejpam-4344	264	3	]	]	X
ejpam-4344	264	4	[	[	X
ejpam-4344	264	5	r	r	X
ejpam-4344	264	6	,	,	PUNCT
ejpam-4344	264	7	r	r	NOUN
ejpam-4344	264	8	]	]	PUNCT
ejpam-4344	264	9	contains	contain	VERB
ejpam-4344	264	10	a	a	DET
ejpam-4344	264	11	nonzro	nonzro	ADJ
ejpam-4344	264	12	δ	δ	NOUN
ejpam-4344	264	13	-	-	PUNCT
ejpam-4344	264	14	ideal	ideal	NOUN
ejpam-4344	264	15	i	i	PROPN
ejpam-4344	264	16	of	of	ADP
ejpam-4344	264	17	r.	r.	PROPN
ejpam-4344	264	18	thus	thus	ADV
ejpam-4344	264	19	by(3	by(3	NOUN
ejpam-4344	264	20	-	-	SYM
ejpam-4344	264	21	2	2	NUM
ejpam-4344	264	22	)	)	PUNCT
ejpam-4344	264	23	we	we	PRON
ejpam-4344	264	24	have	have	VERB
ejpam-4344	264	25	[	[	X
ejpam-4344	264	26	δ(x	δ(x	NOUN
ejpam-4344	264	27	)	)	PUNCT
ejpam-4344	264	28	,	,	PUNCT
ejpam-4344	264	29	y	y	X
ejpam-4344	264	30	]	]	X
ejpam-4344	264	31	∈	∈	PROPN
ejpam-4344	264	32	z(r	z(r	PROPN
ejpam-4344	264	33	)	)	PUNCT
ejpam-4344	264	34	∀x	∀x	NUM
ejpam-4344	264	35	,	,	PUNCT
ejpam-4344	264	36	y	y	PROPN
ejpam-4344	264	37	∈	∈	PROPN
ejpam-4344	264	38	r.	r.	PROPN
ejpam-4344	264	39	references	reference	VERB
ejpam-4344	264	40	464	464	NUM
ejpam-4344	264	41	this	this	PRON
ejpam-4344	264	42	means	mean	VERB
ejpam-4344	264	43	that	that	SCONJ
ejpam-4344	264	44	δ(i	δ(i	PROPN
ejpam-4344	264	45	)	)	PUNCT
ejpam-4344	264	46	⊆	⊆	NUM
ejpam-4344	264	47	z(r).then	z(r).then	NOUN
ejpam-4344	264	48	for	for	ADP
ejpam-4344	264	49	all	all	DET
ejpam-4344	264	50	a	a	DET
ejpam-4344	264	51	∈	∈	NOUN
ejpam-4344	265	1	i	i	PRON
ejpam-4344	266	1	[	[	X
ejpam-4344	266	2	δ(a	δ(a	PROPN
ejpam-4344	266	3	)	)	PUNCT
ejpam-4344	266	4	,	,	PUNCT
ejpam-4344	266	5	a	a	PRON
ejpam-4344	266	6	]	]	X
ejpam-4344	266	7	=	=	SYM
ejpam-4344	266	8	0	0	NUM
ejpam-4344	266	9	,	,	PUNCT
ejpam-4344	266	10	and	and	CCONJ
ejpam-4344	266	11	by	by	ADP
ejpam-4344	266	12	lemma	lemma	PROPN
ejpam-4344	266	13	2	2	NUM
ejpam-4344	266	14	r	r	NOUN
ejpam-4344	266	15	is	be	AUX
ejpam-4344	266	16	commutative	commutative	ADJ
ejpam-4344	266	17	.	.	PUNCT
ejpam-4344	267	1	proof	proof	NOUN
ejpam-4344	267	2	of	of	ADP
ejpam-4344	267	3	theorem	theorem	NOUN
ejpam-4344	267	4	(	(	PUNCT
ejpam-4344	267	5	1	1	NUM
ejpam-4344	267	6	)	)	PUNCT
ejpam-4344	267	7	since	since	SCONJ
ejpam-4344	267	8	[	[	X
ejpam-4344	267	9	x	x	X
ejpam-4344	267	10	,	,	PUNCT
ejpam-4344	267	11	δ(x	δ(x	ADJ
ejpam-4344	267	12	)	)	PUNCT
ejpam-4344	267	13	]	]	PUNCT
ejpam-4344	268	1	∈	∈	PROPN
ejpam-4344	268	2	z(r	z(r	PROPN
ejpam-4344	268	3	)	)	PUNCT
ejpam-4344	268	4	for	for	ADP
ejpam-4344	268	5	all	all	DET
ejpam-4344	268	6	x	x	SYM
ejpam-4344	268	7	∈	∈	PROPN
ejpam-4344	268	8	i	i	PRON
ejpam-4344	268	9	,	,	PUNCT
ejpam-4344	268	10	then	then	ADV
ejpam-4344	268	11	by	by	ADP
ejpam-4344	268	12	lemma	lemma	PROPN
ejpam-4344	268	13	7	7	NUM
ejpam-4344	268	14	we	we	PRON
ejpam-4344	268	15	get	get	VERB
ejpam-4344	268	16	[	[	X
ejpam-4344	268	17	x	x	NOUN
ejpam-4344	268	18	,	,	PUNCT
ejpam-4344	268	19	δ(x	δ(x	NOUN
ejpam-4344	268	20	)	)	PUNCT
ejpam-4344	268	21	]	]	PUNCT
ejpam-4344	269	1	=	=	PUNCT
ejpam-4344	269	2	0	0	X
ejpam-4344	269	3	.	.	PUNCT
ejpam-4344	269	4	now	now	ADV
ejpam-4344	269	5	using	use	VERB
ejpam-4344	269	6	lemma	lemma	PROPN
ejpam-4344	269	7	2	2	NUM
ejpam-4344	269	8	and	and	CCONJ
ejpam-4344	269	9	since	since	SCONJ
ejpam-4344	269	10	r	r	NOUN
ejpam-4344	269	11	is	be	AUX
ejpam-4344	269	12	a	a	DET
ejpam-4344	269	13	δ	δ	NOUN
ejpam-4344	269	14	-	-	ADJ
ejpam-4344	269	15	prime	prime	ADJ
ejpam-4344	269	16	ring	ring	NOUN
ejpam-4344	269	17	and	and	CCONJ
ejpam-4344	269	18	[	[	X
ejpam-4344	269	19	x	x	X
ejpam-4344	269	20	,	,	PUNCT
ejpam-4344	269	21	δ(x	δ(x	NOUN
ejpam-4344	269	22	)	)	PUNCT
ejpam-4344	269	23	]	]	PUNCT
ejpam-4344	270	1	=	=	PUNCT
ejpam-4344	270	2	0	0	NUM
ejpam-4344	270	3	,	,	PUNCT
ejpam-4344	270	4	then	then	ADV
ejpam-4344	270	5	r	r	NOUN
ejpam-4344	270	6	is	be	AUX
ejpam-4344	270	7	commutative	commutative	ADJ
ejpam-4344	270	8	.	.	PUNCT
ejpam-4344	271	1	acknowledgements	acknowledgement	NOUN
ejpam-4344	271	2	this	this	DET
ejpam-4344	271	3	project	project	NOUN
ejpam-4344	271	4	was	be	AUX
ejpam-4344	271	5	funded	fund	VERB
ejpam-4344	271	6	by	by	ADP
ejpam-4344	271	7	national	national	ADJ
ejpam-4344	271	8	plan	plan	NOUN
ejpam-4344	271	9	for	for	ADP
ejpam-4344	271	10	science	science	NOUN
ejpam-4344	271	11	,	,	PUNCT
ejpam-4344	271	12	technology	technology	NOUN
ejpam-4344	271	13	and	and	CCONJ
ejpam-4344	271	14	innovation	innovation	NOUN
ejpam-4344	271	15	(	(	PUNCT
ejpam-4344	271	16	maarifah	maarifah	NOUN
ejpam-4344	271	17	)	)	PUNCT
ejpam-4344	271	18	—	—	PUNCT
ejpam-4344	271	19	king	king	PROPN
ejpam-4344	271	20	abdul	abdul	PROPN
ejpam-4344	271	21	aziz	aziz	PROPN
ejpam-4344	271	22	city	city	PROPN
ejpam-4344	271	23	for	for	ADP
ejpam-4344	271	24	science	science	NOUN
ejpam-4344	271	25	and	and	CCONJ
ejpam-4344	271	26	technology	technology	NOUN
ejpam-4344	271	27	—	—	PUNCT
ejpam-4344	271	28	the	the	DET
ejpam-4344	271	29	kingdom	kingdom	NOUN
ejpam-4344	271	30	of	of	ADP
ejpam-4344	271	31	saudi	saudi	PROPN
ejpam-4344	271	32	arabia	arabia	PROPN
ejpam-4344	271	33	,	,	PUNCT
ejpam-4344	271	34	award	award	NOUN
ejpam-4344	271	35	number	number	NOUN
ejpam-4344	271	36	(	(	PUNCT
ejpam-4344	271	37	14	14	NUM
ejpam-4344	271	38	-	-	PUNCT
ejpam-4344	271	39	mat273	mat273	NOUN
ejpam-4344	271	40	-	-	PUNCT
ejpam-4344	271	41	08	08	NUM
ejpam-4344	271	42	r	r	NOUN
ejpam-4344	271	43	)	)	PUNCT
ejpam-4344	271	44	.	.	PUNCT
ejpam-4344	272	1	references	reference	NOUN
ejpam-4344	272	2	[	[	X
ejpam-4344	272	3	1	1	NUM
ejpam-4344	272	4	]	]	PUNCT
ejpam-4344	272	5	�	�	PROPN
ejpam-4344	272	6	�	�	PROPN
ejpam-4344	272	7	a	a	DET
ejpam-4344	272	8	alkhalaf	alkhalaf	PROPN
ejpam-4344	272	9	,	,	PUNCT
ejpam-4344	272	10	o	o	NOUN
ejpam-4344	272	11	artemovych	artemovych	NOUN
ejpam-4344	272	12	,	,	PUNCT
ejpam-4344	272	13	and	and	CCONJ
ejpam-4344	272	14	i	i	PRON
ejpam-4344	272	15	taha	taha	PROPN
ejpam-4344	272	16	.	.	PUNCT
ejpam-4344	273	1	derivations	derivation	NOUN
ejpam-4344	273	2	in	in	ADP
ejpam-4344	273	3	differentially	differentially	ADV
ejpam-4344	273	4	prime	prime	ADJ
ejpam-4344	273	5	rings	ring	NOUN
ejpam-4344	273	6	.	.	PUNCT
ejpam-4344	274	1	journal	journal	PROPN
ejpam-4344	274	2	of	of	ADP
ejpam-4344	274	3	algebra	algebra	PROPN
ejpam-4344	274	4	and	and	CCONJ
ejpam-4344	274	5	its	its	PRON
ejpam-4344	274	6	applications	application	NOUN
ejpam-4344	274	7	,	,	PUNCT
ejpam-4344	274	8	17(07):1850129	17(07):1850129	NUM
ejpam-4344	274	9	,	,	PUNCT
ejpam-4344	274	10	2018	2018	NUM
ejpam-4344	274	11	.	.	PUNCT
ejpam-4344	275	1	[	[	X
ejpam-4344	275	2	2	2	NUM
ejpam-4344	275	3	]	]	PUNCT
ejpam-4344	275	4	�	�	PROPN
ejpam-4344	275	5	�	�	PROPN
ejpam-4344	275	6	a	a	DET
ejpam-4344	275	7	alkhalaf	alkhalaf	PROPN
ejpam-4344	275	8	,	,	PUNCT
ejpam-4344	275	9	o	o	PROPN
ejpam-4344	275	10	artemovych	artemovych	NOUN
ejpam-4344	275	11	,	,	PUNCT
ejpam-4344	275	12	i	i	PRON
ejpam-4344	275	13	taha	taha	PROPN
ejpam-4344	275	14	,	,	PUNCT
ejpam-4344	275	15	and	and	CCONJ
ejpam-4344	275	16	a	a	DET
ejpam-4344	275	17	aljouiiee	aljouiiee	NOUN
ejpam-4344	275	18	.	.	PUNCT
ejpam-4344	276	1	derivations	derivation	NOUN
ejpam-4344	276	2	of	of	ADP
ejpam-4344	276	3	differentially	differentially	ADV
ejpam-4344	276	4	semiprime	semiprime	NOUN
ejpam-4344	276	5	rings	ring	NOUN
ejpam-4344	276	6	.	.	PUNCT
ejpam-4344	277	1	asian	asian	ADJ
ejpam-4344	277	2	-	-	PUNCT
ejpam-4344	277	3	european	european	ADJ
ejpam-4344	277	4	journal	journal	NOUN
ejpam-4344	277	5	of	of	ADP
ejpam-4344	277	6	mathematics	mathematic	NOUN
ejpam-4344	277	7	,	,	PUNCT
ejpam-4344	277	8	12(05):1950079	12(05):1950079	NUM
ejpam-4344	277	9	,	,	PUNCT
ejpam-4344	277	10	2019	2019	NUM
ejpam-4344	277	11	.	.	PUNCT
ejpam-4344	278	1	[	[	X
ejpam-4344	278	2	3	3	NUM
ejpam-4344	278	3	]	]	X
ejpam-4344	278	4	o	o	X
ejpam-4344	278	5	artemovych	artemovych	NOUN
ejpam-4344	278	6	and	and	CCONJ
ejpam-4344	278	7	m	m	PROPN
ejpam-4344	278	8	lukashenko	lukashenko	PROPN
ejpam-4344	278	9	.	.	PUNCT
ejpam-4344	279	1	lie	lie	NOUN
ejpam-4344	279	2	and	and	CCONJ
ejpam-4344	279	3	jordan	jordan	PROPN
ejpam-4344	279	4	structures	structure	NOUN
ejpam-4344	279	5	of	of	ADP
ejpam-4344	279	6	differentially	differentially	ADV
ejpam-4344	279	7	semiprime	semiprime	NOUN
ejpam-4344	279	8	rings	ring	NOUN
ejpam-4344	279	9	.	.	PUNCT
ejpam-4344	280	1	algebra	algebra	NOUN
ejpam-4344	280	2	and	and	CCONJ
ejpam-4344	280	3	discrete	discrete	ADJ
ejpam-4344	280	4	mathematics	mathematic	NOUN
ejpam-4344	280	5	,	,	PUNCT
ejpam-4344	280	6	20(1	20(1	NUM
ejpam-4344	280	7	)	)	PUNCT
ejpam-4344	280	8	,	,	PUNCT
ejpam-4344	280	9	2015	2015	NUM
ejpam-4344	280	10	.	.	PUNCT
ejpam-4344	281	1	[	[	X
ejpam-4344	281	2	4	4	NUM
ejpam-4344	281	3	]	]	SYM
ejpam-4344	281	4	r	r	NOUN
ejpam-4344	281	5	awtar	awtar	NOUN
ejpam-4344	281	6	.	.	PUNCT
ejpam-4344	282	1	lie	lie	NOUN
ejpam-4344	282	2	and	and	CCONJ
ejpam-4344	282	3	jordan	jordan	PROPN
ejpam-4344	282	4	structure	structure	PROPN
ejpam-4344	282	5	in	in	ADP
ejpam-4344	282	6	prime	prime	ADJ
ejpam-4344	282	7	rings	ring	NOUN
ejpam-4344	282	8	with	with	ADP
ejpam-4344	282	9	derivations	derivation	NOUN
ejpam-4344	282	10	.	.	PUNCT
ejpam-4344	283	1	proceedings	proceeding	NOUN
ejpam-4344	283	2	of	of	ADP
ejpam-4344	283	3	the	the	DET
ejpam-4344	283	4	american	american	PROPN
ejpam-4344	283	5	mathematical	mathematical	PROPN
ejpam-4344	283	6	society	society	NOUN
ejpam-4344	283	7	,	,	PUNCT
ejpam-4344	283	8	41(1):67–74	41(1):67–74	NUM
ejpam-4344	283	9	,	,	PUNCT
ejpam-4344	283	10	1973	1973	NUM
ejpam-4344	283	11	.	.	PUNCT
ejpam-4344	284	1	[	[	X
ejpam-4344	284	2	5	5	NUM
ejpam-4344	284	3	]	]	PUNCT
ejpam-4344	284	4	h	h	NOUN
ejpam-4344	284	5	bell	bell	NOUN
ejpam-4344	284	6	and	and	CCONJ
ejpam-4344	284	7	a	a	DET
ejpam-4344	284	8	klein	klein	PROPN
ejpam-4344	284	9	.	.	PUNCT
ejpam-4344	285	1	combinatorial	combinatorial	PROPN
ejpam-4344	285	2	commutativity	commutativity	NOUN
ejpam-4344	285	3	and	and	CCONJ
ejpam-4344	285	4	finiteness	finiteness	NOUN
ejpam-4344	285	5	conditions	condition	NOUN
ejpam-4344	285	6	for	for	ADP
ejpam-4344	285	7	rings	ring	NOUN
ejpam-4344	285	8	.	.	PUNCT
ejpam-4344	286	1	communications	communication	NOUN
ejpam-4344	286	2	in	in	ADP
ejpam-4344	286	3	algebra	algebra	NOUN
ejpam-4344	286	4	,	,	PUNCT
ejpam-4344	286	5	29(7):2935–2943	29(7):2935–2943	PROPN
ejpam-4344	286	6	,	,	PUNCT
ejpam-4344	286	7	2001	2001	NUM
ejpam-4344	286	8	.	.	PUNCT
ejpam-4344	287	1	[	[	X
ejpam-4344	287	2	6	6	NUM
ejpam-4344	287	3	]	]	X
ejpam-4344	287	4	j	j	PROPN
ejpam-4344	287	5	bergen	bergen	PROPN
ejpam-4344	287	6	.	.	PUNCT
ejpam-4344	288	1	lie	lie	VERB
ejpam-4344	288	2	ideals	ideal	NOUN
ejpam-4344	288	3	with	with	ADP
ejpam-4344	288	4	regular	regular	ADJ
ejpam-4344	288	5	and	and	CCONJ
ejpam-4344	288	6	nilpotent	nilpotent	ADJ
ejpam-4344	288	7	elements	element	NOUN
ejpam-4344	288	8	and	and	CCONJ
ejpam-4344	288	9	a	a	DET
ejpam-4344	288	10	result	result	NOUN
ejpam-4344	288	11	on	on	ADP
ejpam-4344	288	12	derivations	derivation	NOUN
ejpam-4344	288	13	.	.	PUNCT
ejpam-4344	289	1	rendiconti	rendiconti	ADJ
ejpam-4344	289	2	del	del	PROPN
ejpam-4344	289	3	circolo	circolo	PROPN
ejpam-4344	289	4	matematico	matematico	NOUN
ejpam-4344	289	5	di	di	NOUN
ejpam-4344	289	6	palermo	palermo	NOUN
ejpam-4344	289	7	,	,	PUNCT
ejpam-4344	289	8	33(1):99–108	33(1):99–108	NUM
ejpam-4344	289	9	,	,	PUNCT
ejpam-4344	289	10	1984	1984	NUM
ejpam-4344	289	11	.	.	PUNCT
ejpam-4344	290	1	[	[	X
ejpam-4344	290	2	7	7	NUM
ejpam-4344	290	3	]	]	PUNCT
ejpam-4344	290	4	m	m	AUX
ejpam-4344	290	5	brešar	brešar	NOUN
ejpam-4344	290	6	.	.	PUNCT
ejpam-4344	291	1	on	on	ADP
ejpam-4344	291	2	a	a	DET
ejpam-4344	291	3	generalization	generalization	NOUN
ejpam-4344	291	4	of	of	ADP
ejpam-4344	291	5	the	the	DET
ejpam-4344	291	6	notion	notion	NOUN
ejpam-4344	291	7	of	of	ADP
ejpam-4344	291	8	centralizing	centralize	VERB
ejpam-4344	291	9	mappings	mapping	NOUN
ejpam-4344	291	10	.	.	PUNCT
ejpam-4344	292	1	proceedings	proceeding	NOUN
ejpam-4344	292	2	of	of	ADP
ejpam-4344	292	3	the	the	DET
ejpam-4344	292	4	american	american	PROPN
ejpam-4344	292	5	mathematical	mathematical	PROPN
ejpam-4344	292	6	society	society	NOUN
ejpam-4344	292	7	,	,	PUNCT
ejpam-4344	292	8	114(3):641–649	114(3):641–649	NUM
ejpam-4344	292	9	,	,	PUNCT
ejpam-4344	292	10	1992	1992	NUM
ejpam-4344	292	11	.	.	PUNCT
ejpam-4344	293	1	[	[	X
ejpam-4344	293	2	8	8	NUM
ejpam-4344	293	3	]	]	PUNCT
ejpam-4344	293	4	m	m	VERB
ejpam-4344	293	5	brešar	brešar	NOUN
ejpam-4344	293	6	.	.	PUNCT
ejpam-4344	294	1	centralizing	centralize	VERB
ejpam-4344	294	2	mappings	mapping	NOUN
ejpam-4344	294	3	and	and	CCONJ
ejpam-4344	294	4	derivations	derivation	NOUN
ejpam-4344	294	5	in	in	ADP
ejpam-4344	294	6	prime	prime	ADJ
ejpam-4344	294	7	rings	ring	NOUN
ejpam-4344	294	8	.	.	PUNCT
ejpam-4344	295	1	j.	j.	PROPN
ejpam-4344	295	2	algebra	algebra	PROPN
ejpam-4344	295	3	,	,	PUNCT
ejpam-4344	295	4	156(2):385–394	156(2):385–394	NUM
ejpam-4344	295	5	,	,	PUNCT
ejpam-4344	295	6	1993	1993	NUM
ejpam-4344	295	7	.	.	PUNCT
ejpam-4344	295	8	references	reference	NOUN
ejpam-4344	295	9	465	465	NUM
ejpam-4344	296	1	[	[	X
ejpam-4344	296	2	9	9	NUM
ejpam-4344	296	3	]	]	PUNCT
ejpam-4344	296	4	m	m	AUX
ejpam-4344	296	5	brešar	brešar	ADJ
ejpam-4344	296	6	,	,	PUNCT
ejpam-4344	296	7	m	m	NOUN
ejpam-4344	296	8	chebotar	chebotar	ADJ
ejpam-4344	296	9	,	,	PUNCT
ejpam-4344	296	10	and	and	CCONJ
ejpam-4344	296	11	w	w	PROPN
ejpam-4344	296	12	martindale	martindale	PROPN
ejpam-4344	296	13	.	.	PUNCT
ejpam-4344	297	1	functional	functional	ADJ
ejpam-4344	297	2	identities	identity	NOUN
ejpam-4344	297	3	.	.	PUNCT
ejpam-4344	298	1	springer	springer	NOUN
ejpam-4344	298	2	science	science	PROPN
ejpam-4344	298	3	&	&	CCONJ
ejpam-4344	298	4	business	business	NOUN
ejpam-4344	298	5	media	medium	NOUN
ejpam-4344	298	6	,	,	PUNCT
ejpam-4344	298	7	2007	2007	NUM
ejpam-4344	298	8	.	.	PUNCT
ejpam-4344	299	1	[	[	X
ejpam-4344	299	2	10	10	NUM
ejpam-4344	299	3	]	]	X
ejpam-4344	299	4	m	m	AUX
ejpam-4344	299	5	bresar	bresar	VERB
ejpam-4344	299	6	and	and	CCONJ
ejpam-4344	299	7	j	j	PROPN
ejpam-4344	299	8	vukman	vukman	PROPN
ejpam-4344	299	9	.	.	PUNCT
ejpam-4344	300	1	orthogonal	orthogonal	ADJ
ejpam-4344	300	2	derivations	derivation	NOUN
ejpam-4344	300	3	and	and	CCONJ
ejpam-4344	300	4	an	an	DET
ejpam-4344	300	5	extension	extension	NOUN
ejpam-4344	300	6	of	of	ADP
ejpam-4344	300	7	a	a	DET
ejpam-4344	300	8	theorem	theorem	NOUN
ejpam-4344	300	9	of	of	ADP
ejpam-4344	300	10	posner	posner	NOUN
ejpam-4344	300	11	,	,	PUNCT
ejpam-4344	300	12	radovi	radovi	PROPN
ejpam-4344	300	13	mat	mat	PROPN
ejpam-4344	300	14	.	.	PROPN
ejpam-4344	300	15	vol	vol	NOUN
ejpam-4344	300	16	.	.	PROPN
ejpam-4344	300	17	5	5	NUM
ejpam-4344	300	18	(	(	PUNCT
ejpam-4344	300	19	1989	1989	NUM
ejpam-4344	300	20	)	)	PUNCT
ejpam-4344	300	21	,	,	PUNCT
ejpam-4344	300	22	237	237	NUM
ejpam-4344	300	23	,	,	PUNCT
ejpam-4344	300	24	246	246	NUM
ejpam-4344	300	25	,	,	PUNCT
ejpam-4344	300	26	1989	1989	NUM
ejpam-4344	300	27	.	.	PUNCT
ejpam-4344	301	1	[	[	X
ejpam-4344	301	2	11	11	NUM
ejpam-4344	301	3	]	]	PUNCT
ejpam-4344	301	4	m	m	VERB
ejpam-4344	301	5	chebotar	chebotar	ADJ
ejpam-4344	301	6	.	.	PUNCT
ejpam-4344	302	1	on	on	ADP
ejpam-4344	302	2	the	the	DET
ejpam-4344	302	3	composition	composition	NOUN
ejpam-4344	302	4	of	of	ADP
ejpam-4344	302	5	derivations	derivation	NOUN
ejpam-4344	302	6	of	of	ADP
ejpam-4344	302	7	prime	prime	ADJ
ejpam-4344	302	8	rings	ring	NOUN
ejpam-4344	302	9	.	.	PUNCT
ejpam-4344	303	1	vestnik	vestnik	PROPN
ejpam-4344	303	2	moskovskogo	moskovskogo	PROPN
ejpam-4344	303	3	universiteta	universiteta	PROPN
ejpam-4344	303	4	.	.	PUNCT
ejpam-4344	304	1	seriya	seriya	PROPN
ejpam-4344	304	2	1	1	NUM
ejpam-4344	304	3	.	.	PUNCT
ejpam-4344	304	4	matematika	matematika	PROPN
ejpam-4344	304	5	.	.	PUNCT
ejpam-4344	304	6	mekhanika	mekhanika	PROPN
ejpam-4344	304	7	,	,	PUNCT
ejpam-4344	304	8	(	(	PUNCT
ejpam-4344	304	9	2):22–25	2):22–25	NUM
ejpam-4344	304	10	,	,	PUNCT
ejpam-4344	304	11	1995	1995	NUM
ejpam-4344	304	12	.	.	PUNCT
ejpam-4344	305	1	[	[	X
ejpam-4344	305	2	12	12	NUM
ejpam-4344	305	3	]	]	X
ejpam-4344	305	4	c	c	PROPN
ejpam-4344	305	5	chuang	chuang	PROPN
ejpam-4344	305	6	.	.	PUNCT
ejpam-4344	306	1	on	on	ADP
ejpam-4344	306	2	compositions	composition	NOUN
ejpam-4344	306	3	of	of	ADP
ejpam-4344	306	4	derivations	derivation	NOUN
ejpam-4344	306	5	of	of	ADP
ejpam-4344	306	6	prime	prime	ADJ
ejpam-4344	306	7	rings	ring	NOUN
ejpam-4344	306	8	.	.	PUNCT
ejpam-4344	307	1	proceedings	proceeding	NOUN
ejpam-4344	307	2	of	of	ADP
ejpam-4344	307	3	the	the	DET
ejpam-4344	307	4	american	american	PROPN
ejpam-4344	307	5	mathematical	mathematical	PROPN
ejpam-4344	307	6	society	society	NOUN
ejpam-4344	307	7	,	,	PUNCT
ejpam-4344	307	8	108(3):647–652	108(3):647–652	NUM
ejpam-4344	307	9	,	,	PUNCT
ejpam-4344	307	10	1990	1990	NUM
ejpam-4344	307	11	.	.	PUNCT
ejpam-4344	308	1	[	[	X
ejpam-4344	308	2	13	13	NUM
ejpam-4344	308	3	]	]	X
ejpam-4344	308	4	c	c	PROPN
ejpam-4344	308	5	chuang	chuang	PROPN
ejpam-4344	308	6	and	and	CCONJ
ejpam-4344	308	7	t	t	PROPN
ejpam-4344	308	8	lee	lee	PROPN
ejpam-4344	308	9	.	.	PROPN
ejpam-4344	309	1	finite	finite	PROPN
ejpam-4344	309	2	products	product	NOUN
ejpam-4344	309	3	of	of	ADP
ejpam-4344	309	4	derivations	derivation	NOUN
ejpam-4344	309	5	in	in	ADP
ejpam-4344	309	6	prime	prime	ADJ
ejpam-4344	309	7	rings	ring	NOUN
ejpam-4344	309	8	.	.	PUNCT
ejpam-4344	310	1	communications	communication	NOUN
ejpam-4344	310	2	in	in	ADP
ejpam-4344	310	3	algebra	algebra	NOUN
ejpam-4344	310	4	,	,	PUNCT
ejpam-4344	310	5	30(5):2183–2190	30(5):2183–2190	NUM
ejpam-4344	310	6	,	,	PUNCT
ejpam-4344	310	7	2002	2002	NUM
ejpam-4344	310	8	.	.	PUNCT
ejpam-4344	311	1	[	[	X
ejpam-4344	311	2	14	14	NUM
ejpam-4344	311	3	]	]	PUNCT
ejpam-4344	311	4	l	l	NOUN
ejpam-4344	311	5	chung	chung	PROPN
ejpam-4344	311	6	and	and	CCONJ
ejpam-4344	311	7	j	j	PROPN
ejpam-4344	311	8	luh	luh	PROPN
ejpam-4344	311	9	.	.	PUNCT
ejpam-4344	312	1	derivations	derivation	NOUN
ejpam-4344	312	2	of	of	ADP
ejpam-4344	312	3	higher	high	ADJ
ejpam-4344	312	4	order	order	NOUN
ejpam-4344	312	5	and	and	CCONJ
ejpam-4344	312	6	commutativity	commutativity	NOUN
ejpam-4344	312	7	of	of	ADP
ejpam-4344	312	8	rings	ring	NOUN
ejpam-4344	312	9	.	.	PUNCT
ejpam-4344	313	1	pacific	pacific	PROPN
ejpam-4344	313	2	journal	journal	PROPN
ejpam-4344	313	3	of	of	ADP
ejpam-4344	313	4	mathematics	mathematic	NOUN
ejpam-4344	313	5	,	,	PUNCT
ejpam-4344	313	6	99(2):317–326	99(2):317–326	NOUN
ejpam-4344	313	7	,	,	PUNCT
ejpam-4344	313	8	1982	1982	NUM
ejpam-4344	313	9	.	.	PUNCT
ejpam-4344	314	1	[	[	X
ejpam-4344	314	2	15	15	NUM
ejpam-4344	314	3	]	]	X
ejpam-4344	314	4	t	t	PROPN
ejpam-4344	314	5	creedon	creedon	NOUN
ejpam-4344	314	6	.	.	PUNCT
ejpam-4344	315	1	products	product	NOUN
ejpam-4344	315	2	of	of	ADP
ejpam-4344	315	3	derivations	derivation	NOUN
ejpam-4344	315	4	.	.	PUNCT
ejpam-4344	316	1	proceedings	proceeding	NOUN
ejpam-4344	316	2	of	of	ADP
ejpam-4344	316	3	the	the	DET
ejpam-4344	316	4	edinburgh	edinburgh	PROPN
ejpam-4344	316	5	mathematical	mathematical	PROPN
ejpam-4344	316	6	society	society	NOUN
ejpam-4344	316	7	,	,	PUNCT
ejpam-4344	316	8	41(2):407–410	41(2):407–410	PROPN
ejpam-4344	316	9	,	,	PUNCT
ejpam-4344	316	10	1998	1998	NUM
ejpam-4344	316	11	.	.	PUNCT
ejpam-4344	317	1	[	[	X
ejpam-4344	317	2	16	16	NUM
ejpam-4344	317	3	]	]	PUNCT
ejpam-4344	317	4	n	n	PRON
ejpam-4344	317	5	divinsky	divinsky	NOUN
ejpam-4344	317	6	.	.	PUNCT
ejpam-4344	318	1	on	on	ADP
ejpam-4344	318	2	commuting	commute	VERB
ejpam-4344	318	3	automorphisms	automorphism	NOUN
ejpam-4344	318	4	of	of	ADP
ejpam-4344	318	5	rings	ring	NOUN
ejpam-4344	318	6	.	.	PUNCT
ejpam-4344	319	1	trans	trans	PROPN
ejpam-4344	319	2	.	.	PROPN
ejpam-4344	319	3	roy	roy	PROPN
ejpam-4344	319	4	.	.	PROPN
ejpam-4344	319	5	soc	soc	PROPN
ejpam-4344	319	6	.	.	PUNCT
ejpam-4344	320	1	canada	canada	PROPN
ejpam-4344	320	2	.	.	PUNCT
ejpam-4344	321	1	sect	sect	PROPN
ejpam-4344	321	2	,	,	PUNCT
ejpam-4344	321	3	3(3):49	3(3):49	NUM
ejpam-4344	321	4	,	,	PUNCT
ejpam-4344	321	5	1955	1955	NUM
ejpam-4344	321	6	.	.	PUNCT
ejpam-4344	322	1	[	[	X
ejpam-4344	322	2	17	17	NUM
ejpam-4344	322	3	]	]	X
ejpam-4344	322	4	i	i	PROPN
ejpam-4344	322	5	herstein	herstein	NOUN
ejpam-4344	322	6	.	.	PUNCT
ejpam-4344	323	1	on	on	ADP
ejpam-4344	323	2	the	the	DET
ejpam-4344	323	3	lie	lie	NOUN
ejpam-4344	323	4	and	and	CCONJ
ejpam-4344	323	5	jordan	jordan	PROPN
ejpam-4344	323	6	rings	ring	NOUN
ejpam-4344	323	7	of	of	ADP
ejpam-4344	323	8	a	a	DET
ejpam-4344	323	9	simple	simple	ADJ
ejpam-4344	323	10	associative	associative	ADJ
ejpam-4344	323	11	ring	ring	NOUN
ejpam-4344	323	12	.	.	PUNCT
ejpam-4344	324	1	american	american	PROPN
ejpam-4344	324	2	journal	journal	PROPN
ejpam-4344	324	3	of	of	ADP
ejpam-4344	324	4	mathematics	mathematic	NOUN
ejpam-4344	324	5	,	,	PUNCT
ejpam-4344	324	6	77(2):279–285	77(2):279–285	PROPN
ejpam-4344	324	7	,	,	PUNCT
ejpam-4344	324	8	1955	1955	NUM
ejpam-4344	324	9	.	.	PUNCT
ejpam-4344	325	1	[	[	X
ejpam-4344	325	2	18	18	NUM
ejpam-4344	325	3	]	]	X
ejpam-4344	325	4	i	i	PROPN
ejpam-4344	325	5	herstein	herstein	NOUN
ejpam-4344	325	6	.	.	PUNCT
ejpam-4344	326	1	topics	topic	NOUN
ejpam-4344	326	2	in	in	ADP
ejpam-4344	326	3	ring	ring	NOUN
ejpam-4344	326	4	theory	theory	NOUN
ejpam-4344	326	5	.	.	PUNCT
ejpam-4344	327	1	e	e	PROPN
ejpam-4344	327	2	university	university	PROPN
ejpam-4344	327	3	of	of	ADP
ejpam-4344	327	4	chicago	chicago	PROPN
ejpam-4344	327	5	press	press	NOUN
ejpam-4344	327	6	.	.	PUNCT
ejpam-4344	328	1	chicago	chicago	PROPN
ejpam-4344	328	2	,	,	PUNCT
ejpam-4344	328	3	il	il	PROPN
ejpam-4344	328	4	,	,	PUNCT
ejpam-4344	328	5	1965	1965	NUM
ejpam-4344	328	6	.	.	PUNCT
ejpam-4344	329	1	[	[	X
ejpam-4344	329	2	19	19	NUM
ejpam-4344	329	3	]	]	X
ejpam-4344	329	4	i	i	PROPN
ejpam-4344	329	5	herstein	herstein	PROPN
ejpam-4344	329	6	.	.	PUNCT
ejpam-4344	330	1	rings	ring	NOUN
ejpam-4344	330	2	with	with	ADP
ejpam-4344	330	3	involution	involution	NOUN
ejpam-4344	330	4	,	,	PUNCT
ejpam-4344	330	5	volume	volume	NOUN
ejpam-4344	330	6	111	111	NUM
ejpam-4344	330	7	.	.	PUNCT
ejpam-4344	331	1	university	university	NOUN
ejpam-4344	331	2	of	of	ADP
ejpam-4344	331	3	chicago	chicago	PROPN
ejpam-4344	331	4	press	press	PROPN
ejpam-4344	331	5	chicago	chicago	PROPN
ejpam-4344	331	6	,	,	PUNCT
ejpam-4344	331	7	1976	1976	NUM
ejpam-4344	331	8	.	.	PUNCT
ejpam-4344	332	1	[	[	X
ejpam-4344	332	2	20	20	NUM
ejpam-4344	332	3	]	]	X
ejpam-4344	332	4	y	y	PROPN
ejpam-4344	332	5	hirano	hirano	PROPN
ejpam-4344	332	6	,	,	PUNCT
ejpam-4344	332	7	a	a	DET
ejpam-4344	332	8	kaya	kaya	PROPN
ejpam-4344	332	9	,	,	PUNCT
ejpam-4344	332	10	and	and	CCONJ
ejpam-4344	332	11	h	h	PROPN
ejpam-4344	332	12	tominaga	tominaga	NOUN
ejpam-4344	332	13	.	.	PUNCT
ejpam-4344	333	1	on	on	ADP
ejpam-4344	333	2	a	a	DET
ejpam-4344	333	3	theorem	theorem	NOUN
ejpam-4344	333	4	of	of	ADP
ejpam-4344	333	5	mayne	mayne	NOUN
ejpam-4344	333	6	.	.	PUNCT
ejpam-4344	334	1	mathematical	mathematical	ADJ
ejpam-4344	334	2	journal	journal	PROPN
ejpam-4344	334	3	of	of	ADP
ejpam-4344	334	4	okayama	okayama	PROPN
ejpam-4344	334	5	university	university	PROPN
ejpam-4344	334	6	,	,	PUNCT
ejpam-4344	334	7	25(2):125–132	25(2):125–132	PROPN
ejpam-4344	334	8	,	,	PUNCT
ejpam-4344	334	9	1983	1983	NUM
ejpam-4344	334	10	.	.	PUNCT
ejpam-4344	335	1	[	[	X
ejpam-4344	335	2	21	21	NUM
ejpam-4344	335	3	]	]	X
ejpam-4344	335	4	y	y	PROPN
ejpam-4344	335	5	hirano	hirano	PROPN
ejpam-4344	335	6	,	,	PUNCT
ejpam-4344	335	7	h	h	NOUN
ejpam-4344	335	8	tominaga	tominaga	NOUN
ejpam-4344	335	9	,	,	PUNCT
ejpam-4344	335	10	and	and	CCONJ
ejpam-4344	335	11	a	a	DET
ejpam-4344	335	12	trzepizur	trzepizur	NOUN
ejpam-4344	335	13	.	.	PUNCT
ejpam-4344	336	1	on	on	ADP
ejpam-4344	336	2	a	a	DET
ejpam-4344	336	3	theorem	theorem	NOUN
ejpam-4344	336	4	of	of	ADP
ejpam-4344	336	5	posner	posner	NOUN
ejpam-4344	336	6	.	.	PUNCT
ejpam-4344	337	1	mathematical	mathematical	ADJ
ejpam-4344	337	2	journal	journal	PROPN
ejpam-4344	337	3	of	of	ADP
ejpam-4344	337	4	okayama	okayama	PROPN
ejpam-4344	337	5	university	university	PROPN
ejpam-4344	337	6	,	,	PUNCT
ejpam-4344	337	7	27(1):19–23	27(1):19–23	NUM
ejpam-4344	337	8	,	,	PUNCT
ejpam-4344	337	9	1985	1985	NUM
ejpam-4344	337	10	.	.	PUNCT
ejpam-4344	338	1	[	[	X
ejpam-4344	338	2	22	22	NUM
ejpam-4344	338	3	]	]	X
ejpam-4344	338	4	m	m	VERB
ejpam-4344	338	5	hongan	hongan	ADJ
ejpam-4344	338	6	and	and	CCONJ
ejpam-4344	338	7	a	a	DET
ejpam-4344	338	8	trzepizur	trzepizur	NOUN
ejpam-4344	338	9	.	.	PUNCT
ejpam-4344	339	1	on	on	ADP
ejpam-4344	339	2	generalization	generalization	NOUN
ejpam-4344	339	3	of	of	ADP
ejpam-4344	339	4	a	a	DET
ejpam-4344	339	5	theorem	theorem	NOUN
ejpam-4344	339	6	of	of	ADP
ejpam-4344	339	7	posner	posner	NOUN
ejpam-4344	339	8	.	.	PUNCT
ejpam-4344	340	1	mathematical	mathematical	ADJ
ejpam-4344	340	2	journal	journal	PROPN
ejpam-4344	340	3	of	of	ADP
ejpam-4344	340	4	okayama	okayama	PROPN
ejpam-4344	340	5	university	university	PROPN
ejpam-4344	340	6	,	,	PUNCT
ejpam-4344	340	7	27(1):19–23	27(1):19–23	NUM
ejpam-4344	340	8	,	,	PUNCT
ejpam-4344	340	9	1985	1985	NUM
ejpam-4344	340	10	.	.	PUNCT
ejpam-4344	341	1	[	[	X
ejpam-4344	341	2	23	23	NUM
ejpam-4344	341	3	]	]	X
ejpam-4344	341	4	j	j	PROPN
ejpam-4344	341	5	lambek	lambek	PROPN
ejpam-4344	341	6	.	.	PUNCT
ejpam-4344	342	1	lectures	lecture	NOUN
ejpam-4344	342	2	on	on	ADP
ejpam-4344	342	3	rings	ring	NOUN
ejpam-4344	342	4	and	and	CCONJ
ejpam-4344	342	5	modules	module	NOUN
ejpam-4344	342	6	,	,	PUNCT
ejpam-4344	342	7	blaisdell	blaisdell	PROPN
ejpam-4344	342	8	publ	publ	PROPN
ejpam-4344	342	9	.	.	PUNCT
ejpam-4344	343	1	com	com	PROPN
ejpam-4344	343	2	.	.	PROPN
ejpam-4344	343	3	,	,	PUNCT
ejpam-4344	343	4	waltham	waltham	PROPN
ejpam-4344	343	5	,	,	PUNCT
ejpam-4344	343	6	toronto	toronto	PROPN
ejpam-4344	343	7	,	,	PUNCT
ejpam-4344	343	8	london	london	PROPN
ejpam-4344	343	9	,	,	PUNCT
ejpam-4344	343	10	1966	1966	NUM
ejpam-4344	343	11	.	.	PUNCT
ejpam-4344	344	1	[	[	X
ejpam-4344	344	2	24	24	NUM
ejpam-4344	344	3	]	]	X
ejpam-4344	344	4	c	c	NOUN
ejpam-4344	344	5	lanski	lanski	NOUN
ejpam-4344	344	6	.	.	PUNCT
ejpam-4344	345	1	differential	differential	ADJ
ejpam-4344	345	2	identities	identity	NOUN
ejpam-4344	345	3	,	,	PUNCT
ejpam-4344	345	4	lie	lie	NOUN
ejpam-4344	345	5	ideals	ideal	NOUN
ejpam-4344	345	6	,	,	PUNCT
ejpam-4344	345	7	and	and	CCONJ
ejpam-4344	345	8	posner	posner	NOUN
ejpam-4344	345	9	’s	’s	PART
ejpam-4344	345	10	theorems	theorem	NOUN
ejpam-4344	345	11	.	.	PUNCT
ejpam-4344	346	1	pacific	pacific	PROPN
ejpam-4344	346	2	journal	journal	PROPN
ejpam-4344	346	3	of	of	ADP
ejpam-4344	346	4	mathematics	mathematic	NOUN
ejpam-4344	346	5	,	,	PUNCT
ejpam-4344	346	6	134(2):275–297	134(2):275–297	PROPN
ejpam-4344	346	7	,	,	PUNCT
ejpam-4344	346	8	1988	1988	NUM
ejpam-4344	346	9	.	.	PUNCT
ejpam-4344	347	1	[	[	X
ejpam-4344	347	2	25	25	NUM
ejpam-4344	347	3	]	]	X
ejpam-4344	347	4	w	w	PROPN
ejpam-4344	347	5	martindale	martindale	PROPN
ejpam-4344	347	6	and	and	CCONJ
ejpam-4344	347	7	c	c	PROPN
ejpam-4344	347	8	miers	mier	NOUN
ejpam-4344	347	9	.	.	PUNCT
ejpam-4344	348	1	on	on	ADP
ejpam-4344	348	2	the	the	DET
ejpam-4344	348	3	iterates	iterate	NOUN
ejpam-4344	348	4	of	of	ADP
ejpam-4344	348	5	derivations	derivation	NOUN
ejpam-4344	348	6	of	of	ADP
ejpam-4344	348	7	prime	prime	ADJ
ejpam-4344	348	8	rings	ring	NOUN
ejpam-4344	348	9	.	.	PUNCT
ejpam-4344	349	1	pacific	pacific	PROPN
ejpam-4344	349	2	journal	journal	PROPN
ejpam-4344	349	3	of	of	ADP
ejpam-4344	349	4	mathematics	mathematic	NOUN
ejpam-4344	349	5	,	,	PUNCT
ejpam-4344	349	6	104(1):179–190	104(1):179–190	NUM
ejpam-4344	349	7	,	,	PUNCT
ejpam-4344	349	8	1983	1983	NUM
ejpam-4344	349	9	.	.	PUNCT
ejpam-4344	350	1	references	reference	NOUN
ejpam-4344	350	2	466	466	NUM
ejpam-4344	350	3	[	[	X
ejpam-4344	350	4	26	26	NUM
ejpam-4344	350	5	]	]	X
ejpam-4344	350	6	j	j	PROPN
ejpam-4344	350	7	mayne	mayne	NOUN
ejpam-4344	350	8	.	.	PUNCT
ejpam-4344	351	1	centralizing	centralize	VERB
ejpam-4344	351	2	automorphisms	automorphism	NOUN
ejpam-4344	351	3	of	of	ADP
ejpam-4344	351	4	prime	prime	ADJ
ejpam-4344	351	5	rings	ring	NOUN
ejpam-4344	351	6	.	.	PUNCT
ejpam-4344	352	1	canadian	canadian	ADJ
ejpam-4344	352	2	mathematical	mathematical	ADJ
ejpam-4344	352	3	bulletin	bulletin	NOUN
ejpam-4344	352	4	,	,	PUNCT
ejpam-4344	352	5	19(1):113–115	19(1):113–115	PROPN
ejpam-4344	352	6	,	,	PUNCT
ejpam-4344	352	7	1976	1976	NUM
ejpam-4344	352	8	.	.	PUNCT
ejpam-4344	353	1	[	[	X
ejpam-4344	353	2	27	27	NUM
ejpam-4344	353	3	]	]	X
ejpam-4344	353	4	j	j	PROPN
ejpam-4344	353	5	mayne	mayne	PROPN
ejpam-4344	353	6	.	.	PUNCT
ejpam-4344	354	1	ideals	ideal	NOUN
ejpam-4344	354	2	and	and	CCONJ
ejpam-4344	354	3	centralizing	centralize	VERB
ejpam-4344	354	4	mappings	mapping	NOUN
ejpam-4344	354	5	in	in	ADP
ejpam-4344	354	6	prime	prime	ADJ
ejpam-4344	354	7	rings	ring	NOUN
ejpam-4344	354	8	.	.	PUNCT
ejpam-4344	355	1	proceedings	proceeding	NOUN
ejpam-4344	355	2	of	of	ADP
ejpam-4344	355	3	the	the	DET
ejpam-4344	355	4	american	american	PROPN
ejpam-4344	355	5	mathematical	mathematical	PROPN
ejpam-4344	355	6	society	society	NOUN
ejpam-4344	355	7	,	,	PUNCT
ejpam-4344	355	8	86(2):211–212	86(2):211–212	NUM
ejpam-4344	355	9	,	,	PUNCT
ejpam-4344	355	10	1982	1982	NUM
ejpam-4344	355	11	.	.	PUNCT
ejpam-4344	356	1	[	[	X
ejpam-4344	356	2	28	28	NUM
ejpam-4344	356	3	]	]	X
ejpam-4344	356	4	j	j	PROPN
ejpam-4344	356	5	mayne	mayne	NOUN
ejpam-4344	356	6	.	.	PUNCT
ejpam-4344	357	1	centralizing	centralize	VERB
ejpam-4344	357	2	mappings	mapping	NOUN
ejpam-4344	357	3	of	of	ADP
ejpam-4344	357	4	prime	prime	ADJ
ejpam-4344	357	5	rings	ring	NOUN
ejpam-4344	357	6	.	.	PUNCT
ejpam-4344	358	1	canadian	canadian	ADJ
ejpam-4344	358	2	mathematical	mathematical	ADJ
ejpam-4344	358	3	bulletin	bulletin	NOUN
ejpam-4344	358	4	,	,	PUNCT
ejpam-4344	358	5	27(1):122–126	27(1):122–126	NOUN
ejpam-4344	358	6	,	,	PUNCT
ejpam-4344	358	7	1984	1984	NUM
ejpam-4344	358	8	.	.	PUNCT
ejpam-4344	359	1	[	[	X
ejpam-4344	359	2	29	29	NUM
ejpam-4344	359	3	]	]	X
ejpam-4344	359	4	k	k	PROPN
ejpam-4344	359	5	mccrimmon	mccrimmon	PROPN
ejpam-4344	359	6	.	.	PUNCT
ejpam-4344	360	1	the	the	DET
ejpam-4344	360	2	zelmanov	zelmanov	PROPN
ejpam-4344	360	3	approach	approach	NOUN
ejpam-4344	360	4	to	to	ADP
ejpam-4344	360	5	jordan	jordan	PROPN
ejpam-4344	360	6	homomorphisms	homomorphisms	PROPN
ejpam-4344	360	7	of	of	ADP
ejpam-4344	360	8	associative	associative	ADJ
ejpam-4344	360	9	algebras	algebra	NOUN
ejpam-4344	360	10	.	.	PUNCT
ejpam-4344	360	11	journal	journal	PROPN
ejpam-4344	360	12	of	of	ADP
ejpam-4344	360	13	algebra	algebra	PROPN
ejpam-4344	360	14	,	,	PUNCT
ejpam-4344	360	15	123(2):457–477	123(2):457–477	NUM
ejpam-4344	360	16	,	,	PUNCT
ejpam-4344	360	17	1989	1989	NUM
ejpam-4344	360	18	.	.	PUNCT
ejpam-4344	361	1	[	[	X
ejpam-4344	361	2	30	30	NUM
ejpam-4344	361	3	]	]	X
ejpam-4344	361	4	r	r	NOUN
ejpam-4344	361	5	miers	mier	NOUN
ejpam-4344	361	6	.	.	PUNCT
ejpam-4344	362	1	centralizing	centralize	VERB
ejpam-4344	362	2	mappings	mapping	NOUN
ejpam-4344	362	3	of	of	ADP
ejpam-4344	362	4	operator	operator	NOUN
ejpam-4344	362	5	algebras	algebra	NOUN
ejpam-4344	362	6	.	.	PUNCT
ejpam-4344	362	7	journal	journal	PROPN
ejpam-4344	362	8	of	of	ADP
ejpam-4344	362	9	algebra	algebra	PROPN
ejpam-4344	362	10	,	,	PUNCT
ejpam-4344	362	11	59(1):56–64	59(1):56–64	NUM
ejpam-4344	362	12	,	,	PUNCT
ejpam-4344	362	13	1979	1979	NUM
ejpam-4344	362	14	.	.	PUNCT
ejpam-4344	363	1	[	[	X
ejpam-4344	363	2	31	31	NUM
ejpam-4344	363	3	]	]	PUNCT
ejpam-4344	363	4	e	e	NOUN
ejpam-4344	363	5	posner	posner	NOUN
ejpam-4344	363	6	.	.	PUNCT
ejpam-4344	364	1	derivations	derivation	NOUN
ejpam-4344	364	2	in	in	ADP
ejpam-4344	364	3	prime	prime	ADJ
ejpam-4344	364	4	rings	ring	NOUN
ejpam-4344	364	5	.	.	PUNCT
ejpam-4344	365	1	proceedings	proceeding	NOUN
ejpam-4344	365	2	of	of	ADP
ejpam-4344	365	3	the	the	DET
ejpam-4344	365	4	american	american	PROPN
ejpam-4344	365	5	mathematical	mathematical	PROPN
ejpam-4344	365	6	society	society	NOUN
ejpam-4344	365	7	,	,	PUNCT
ejpam-4344	365	8	8(6):1093–1100	8(6):1093–1100	PROPN
ejpam-4344	365	9	,	,	PUNCT
ejpam-4344	365	10	1957	1957	NUM
ejpam-4344	365	11	.	.	PUNCT
ejpam-4344	366	1	[	[	X
ejpam-4344	366	2	32	32	NUM
ejpam-4344	366	3	]	]	X
ejpam-4344	366	4	j	j	PROPN
ejpam-4344	366	5	vukman	vukman	NOUN
ejpam-4344	366	6	.	.	PUNCT
ejpam-4344	367	1	commuting	commute	VERB
ejpam-4344	367	2	and	and	CCONJ
ejpam-4344	367	3	centralizing	centralize	VERB
ejpam-4344	367	4	mappings	mapping	NOUN
ejpam-4344	367	5	in	in	ADP
ejpam-4344	367	6	prime	prime	ADJ
ejpam-4344	367	7	rings	ring	NOUN
ejpam-4344	367	8	.	.	PUNCT
ejpam-4344	368	1	proceedings	proceeding	NOUN
ejpam-4344	368	2	of	of	ADP
ejpam-4344	368	3	the	the	DET
ejpam-4344	368	4	american	american	PROPN
ejpam-4344	368	5	mathematical	mathematical	PROPN
ejpam-4344	368	6	society	society	NOUN
ejpam-4344	368	7	,	,	PUNCT
ejpam-4344	368	8	109(1):47–52	109(1):47–52	NUM
ejpam-4344	368	9	,	,	PUNCT
ejpam-4344	368	10	1990	1990	NUM
ejpam-4344	368	11	.	.	PUNCT
ejpam-4344	369	1	[	[	X
ejpam-4344	369	2	33	33	NUM
ejpam-4344	369	3	]	]	X
ejpam-4344	369	4	j	j	PROPN
ejpam-4344	369	5	vukman	vukman	NOUN
ejpam-4344	369	6	.	.	PUNCT
ejpam-4344	370	1	derivations	derivation	NOUN
ejpam-4344	370	2	on	on	ADP
ejpam-4344	370	3	semiprime	semiprime	NOUN
ejpam-4344	370	4	rings	ring	NOUN
ejpam-4344	370	5	.	.	PUNCT
ejpam-4344	371	1	bulletin	bulletin	NOUN
ejpam-4344	371	2	of	of	ADP
ejpam-4344	371	3	the	the	DET
ejpam-4344	371	4	australian	australian	ADJ
ejpam-4344	371	5	mathematical	mathematical	ADJ
ejpam-4344	371	6	society	society	NOUN
ejpam-4344	371	7	,	,	PUNCT
ejpam-4344	371	8	53(3):353–359	53(3):353–359	NUM
ejpam-4344	371	9	,	,	PUNCT
ejpam-4344	371	10	1996	1996	NUM
ejpam-4344	371	11	.	.	PUNCT