id	sid	eid	entity	type
ejpam-6011	1	1	european journal	ORG
ejpam-6011	1	2	2025	DATE
ejpam-6011	1	3	18	CARDINAL
ejpam-6011	1	4	2	CARDINAL
ejpam-6011	1	5	6011	CARDINAL
ejpam-6011	1	6	new york	GPE
ejpam-6011	1	7	nj-abelian	NORP
ejpam-6011	1	8	abelian	NORP
ejpam-6011	1	9	muhammad saad1	PERSON
ejpam-6011	1	10	samia m. abdelwahab2,3,∗	PERSON
ejpam-6011	1	11	1	CARDINAL
ejpam-6011	1	12	science	ORG
ejpam-6011	1	13	alexandria university	ORG
ejpam-6011	1	14	21511	DATE
ejpam-6011	1	15	alexandria	GPE
ejpam-6011	1	16	egypt 2	ORG
ejpam-6011	1	17	ain helwan	PERSON
ejpam-6011	1	18	11790	CARDINAL
ejpam-6011	1	19	egypt 3department	ORG
ejpam-6011	1	20	p.o.	ORG
ejpam-6011	1	21	6644	DATE
ejpam-6011	1	22	51452	DATE
ejpam-6011	1	23	saudi arabia	GPE
ejpam-6011	2	1	nj-abelian	NORP
ejpam-6011	2	2	jacobson	PERSON
ejpam-6011	3	1	nj-abelian	NORP
ejpam-6011	3	2	abelian	NORP
ejpam-6011	4	1	nj-abelian	NORP
ejpam-6011	4	2	abelian	NORP
ejpam-6011	5	1	2020	DATE
ejpam-6011	5	2	16u80	CARDINAL
ejpam-6011	5	3	16u99	CARDINAL
ejpam-6011	5	4	16u40	CARDINAL
ejpam-6011	5	5	nj-abelian	NORP
ejpam-6011	5	6	j-abelian	PERSON
ejpam-6011	5	7	nj	ORG
ejpam-6011	5	8	1	CARDINAL
ejpam-6011	5	9	j(r	PERSON
ejpam-6011	5	10	n(r	TIME
ejpam-6011	5	11	r.	NORP
ejpam-6011	8	1	0	CARDINAL
ejpam-6011	11	1	0	CARDINAL
ejpam-6011	13	1	abelian	NORP
ejpam-6011	14	1	j-abelian	PRODUCT
ejpam-6011	14	2	ea	CARDINAL
ejpam-6011	14	3	∈	ORG
ejpam-6011	14	4	r. abelian	NORP
ejpam-6011	14	5	j-abelian	PERSON
ejpam-6011	14	6	1	CARDINAL
ejpam-6011	14	7	2	CARDINAL
ejpam-6011	16	1	3	CARDINAL
ejpam-6011	16	2	0	CARDINAL
ejpam-6011	17	1	7	CARDINAL
ejpam-6011	17	2	nj-semicomutative	ORG
ejpam-6011	18	1	jacobson	PERSON
ejpam-6011	20	1	m.saad@alexu.edu.eg	PERSON
ejpam-6011	20	2	m. saad	PERSON
ejpam-6011	20	3	s. m. abdelwahab	PERSON
ejpam-6011	21	1	1	CARDINAL
ejpam-6011	21	2	2025	CARDINAL
ejpam-6011	22	1	m. saad	PERSON
ejpam-6011	22	2	s. m. abdelwahab	PERSON
ejpam-6011	23	1	j. pure	PERSON
ejpam-6011	23	2	18	CARDINAL
ejpam-6011	23	3	2	CARDINAL
ejpam-6011	23	4	2025	CARDINAL
ejpam-6011	23	5	6011 2	CARDINAL
ejpam-6011	23	6	13	CARDINAL
ejpam-6011	24	1	nj-abelian	NORP
ejpam-6011	25	1	nj-abelian	NORP
ejpam-6011	25	2	two	CARDINAL
ejpam-6011	26	1	nj-abelian	NORP
ejpam-6011	26	2	nj	ORG
ejpam-6011	27	1	nj-abelian	NORP
ejpam-6011	27	2	abelian	NORP
ejpam-6011	28	1	nj-abelian	NORP
ejpam-6011	30	1	2	CARDINAL
ejpam-6011	30	2	1	CARDINAL
ejpam-6011	33	1	r. 2	PERSON
ejpam-6011	33	2	nj-abelian	NORP
ejpam-6011	33	3	the j-abelian	ORG
ejpam-6011	33	4	nj	ORG
ejpam-6011	34	1	1	CARDINAL
ejpam-6011	35	1	nj-abelian	NORP
ejpam-6011	35	2	∈	ORG
ejpam-6011	35	3	ae ∈	ORG
ejpam-6011	35	4	⊆	CARDINAL
ejpam-6011	36	1	nj-abelian	NORP
ejpam-6011	36	2	j-abelian	PERSON
ejpam-6011	37	1	1	CARDINAL
ejpam-6011	38	1	j-abelian	PERSON
ejpam-6011	39	1	⊆	CARDINAL
ejpam-6011	41	1	r.	NORP
ejpam-6011	42	1	e(1 − e	PERSON
ejpam-6011	42	2	⊆	CARDINAL
ejpam-6011	43	1	⊆	CARDINAL
ejpam-6011	44	1	∈	ORG
ejpam-6011	45	1	1− e)(−r)e ∈ er(1− e	DATE
ejpam-6011	45	2	1−	ORDINAL
ejpam-6011	45	3	⊆	CARDINAL
ejpam-6011	45	4	j-abelian	PERSON
ejpam-6011	46	1	1−f+(1−f)erf	CARDINAL
ejpam-6011	46	2	r.	NORP
ejpam-6011	46	3	1−f)erf	CARDINAL
ejpam-6011	48	1	∈ j(r	LOC
ejpam-6011	51	1	m. saad	PERSON
ejpam-6011	51	2	s. m. abdelwahab	PERSON
ejpam-6011	52	1	j. pure	PERSON
ejpam-6011	52	2	18	CARDINAL
ejpam-6011	52	3	2	CARDINAL
ejpam-6011	52	4	2025	CARDINAL
ejpam-6011	52	5	6011 3	DATE
ejpam-6011	52	6	∈	ORG
ejpam-6011	52	7	⊆	CARDINAL
ejpam-6011	53	1	1	CARDINAL
ejpam-6011	54	1	nj-abelian	NORP
ejpam-6011	54	2	j-abelian	PERSON
ejpam-6011	55	1	nj-abelian	NORP
ejpam-6011	56	1	1	CARDINAL
ejpam-6011	58	1	n(s	GPE
ejpam-6011	59	1	1x	CARDINAL
ejpam-6011	59	2	1sx	ORDINAL
ejpam-6011	60	1	nj-abelian	NORP
ejpam-6011	60	2	j-abelian	PERSON
ejpam-6011	61	1	nj-abelian	NORP
ejpam-6011	62	1	2	CARDINAL
ejpam-6011	63	1	nj-abelian	NORP
ejpam-6011	63	2	∈	ORG
ejpam-6011	63	3	∈	ORG
ejpam-6011	63	4	ea	CARDINAL
ejpam-6011	63	5	⊆	CARDINAL
ejpam-6011	63	6	∈	ORG
ejpam-6011	63	7	r.	NORP
ejpam-6011	64	1	ae ∈	ORG
ejpam-6011	64	2	⊆	CARDINAL
ejpam-6011	64	3	r.	NORP
ejpam-6011	64	4	∈	ORG
ejpam-6011	65	1	j-abelian	PERSON
ejpam-6011	65	2	1	CARDINAL
ejpam-6011	66	1	ae	ORG
ejpam-6011	66	2	ea	CARDINAL
ejpam-6011	67	1	1	CARDINAL
ejpam-6011	67	2	j-abelian	PERSON
ejpam-6011	68	1	∈	ORG
ejpam-6011	68	2	⊆	CARDINAL
ejpam-6011	70	1	nj-abelian	NORP
ejpam-6011	71	1	8	CARDINAL
ejpam-6011	71	2	⊆	CARDINAL
ejpam-6011	72	1	9	CARDINAL
ejpam-6011	72	2	nj	ORG
ejpam-6011	73	1	nj-abelian	NORP
ejpam-6011	74	1	example 1	DATE
ejpam-6011	75	1	abelian	NORP
ejpam-6011	76	1	nj-abelian	NORP
ejpam-6011	77	1	nj-abelian	NORP
ejpam-6011	78	1	3	CARDINAL
ejpam-6011	79	1	nj-abelian	NORP
ejpam-6011	80	1	j-abelian	PERSON
ejpam-6011	83	1	j-abelian	NORP
ejpam-6011	84	1	ae ∈	ORG
ejpam-6011	84	2	∈	ORG
ejpam-6011	85	1	ea	CARDINAL
ejpam-6011	85	2	r.	NORP
ejpam-6011	85	3	∈	ORG
ejpam-6011	86	1	j-abelian	PERSON
ejpam-6011	87	1	⊆	CARDINAL
ejpam-6011	87	2	nj-abelian	NORP
ejpam-6011	88	1	nj-abelian	NORP
ejpam-6011	88	2	abelian	NORP
ejpam-6011	89	1	nj-abelian	NORP
ejpam-6011	89	2	abelian	NORP
ejpam-6011	90	1	m. saad	PERSON
ejpam-6011	90	2	s. m. abdelwahab	PERSON
ejpam-6011	91	1	j. pure	PERSON
ejpam-6011	91	2	18	CARDINAL
ejpam-6011	91	3	2	CARDINAL
ejpam-6011	91	4	2025	CARDINAL
ejpam-6011	91	5	6011 4	DATE
ejpam-6011	91	6	13	CARDINAL
ejpam-6011	91	7	2	CARDINAL
ejpam-6011	92	1	2	CARDINAL
ejpam-6011	93	1	abelian	NORP
ejpam-6011	95	1	0 2	CARDINAL
ejpam-6011	95	2	αr1	CARDINAL
ejpam-6011	95	3	2z 2z	CARDINAL
ejpam-6011	98	1	nj-abelian	NORP
ejpam-6011	99	1	3	CARDINAL
ejpam-6011	99	2	abelian	NORP
ejpam-6011	99	3	1	CARDINAL
ejpam-6011	99	4	0	CARDINAL
ejpam-6011	99	5	0 1 ] |	QUANTITY
ejpam-6011	99	6	∈	ORG
ejpam-6011	100	1	∈	ORG
ejpam-6011	100	2	∈	ORG
ejpam-6011	101	1	∈	ORG
ejpam-6011	102	1	αre	CARDINAL
ejpam-6011	102	2	0	CARDINAL
ejpam-6011	103	1	nj-abelian	NORP
ejpam-6011	104	1	two	CARDINAL
ejpam-6011	104	2	abelian	NORP
ejpam-6011	104	3	nj-abelian	NORP
ejpam-6011	105	1	abelian	NORP
ejpam-6011	105	2	nj-abelian	NORP
ejpam-6011	106	1	abelian	NORP
ejpam-6011	106	2	nj-abelian	NORP
ejpam-6011	107	1	abelian	NORP
ejpam-6011	107	2	nj-abelian	NORP
ejpam-6011	109	1	4	CARDINAL
ejpam-6011	110	1	2−1	CARDINAL
ejpam-6011	110	2	∈	ORG
ejpam-6011	110	3	j2 = 1.	ORG
ejpam-6011	111	1	0	CARDINAL
ejpam-6011	111	2	1	CARDINAL
ejpam-6011	111	3	12(1 + j	DATE
ejpam-6011	111	4	12(1	CARDINAL
ejpam-6011	112	1	σ(a +	LOC
ejpam-6011	113	1	r.	NORP
ejpam-6011	115	1	1 + j)x	QUANTITY
ejpam-6011	116	1	nj-abelian	NORP
ejpam-6011	117	1	r.	NORP
ejpam-6011	119	1	nj-abelian	NORP
ejpam-6011	120	1	4	CARDINAL
ejpam-6011	121	1	nj-abelian	NORP
ejpam-6011	121	2	abelian	NORP
ejpam-6011	123	1	e(1 − e	PERSON
ejpam-6011	124	1	er(1− e	PERSON
ejpam-6011	124	2	⊆	CARDINAL
ejpam-6011	125	1	0	CARDINAL
ejpam-6011	128	1	abelian	NORP
ejpam-6011	129	1	nj-abelian	NORP
ejpam-6011	132	1	5	CARDINAL
ejpam-6011	133	1	10	CARDINAL
ejpam-6011	133	2	3.7	CARDINAL
ejpam-6011	133	3	zero	CARDINAL
ejpam-6011	134	1	7	CARDINAL
ejpam-6011	134	2	4	CARDINAL
ejpam-6011	136	1	nj-abelian	NORP
ejpam-6011	137	1	m. saad	PERSON
ejpam-6011	137	2	s. m. abdelwahab	PERSON
ejpam-6011	138	1	j. pure	PERSON
ejpam-6011	138	2	18	CARDINAL
ejpam-6011	138	3	2	CARDINAL
ejpam-6011	138	4	2025	CARDINAL
ejpam-6011	138	5	6011 5	DATE
ejpam-6011	138	6	13	CARDINAL
ejpam-6011	138	7	1	CARDINAL
ejpam-6011	138	8	1	CARDINAL
ejpam-6011	138	9	r.	NORP
ejpam-6011	138	10	nj-abelian	NORP
ejpam-6011	139	1	5	CARDINAL
ejpam-6011	140	1	nj-abelian	NORP
ejpam-6011	142	1	nj-abelian	NORP
ejpam-6011	142	2	1	CARDINAL
ejpam-6011	143	1	1−	LANGUAGE
ejpam-6011	143	2	1− 2ba+	TIME
ejpam-6011	143	3	1− ba	PERSON
ejpam-6011	143	4	r.	NORP
ejpam-6011	143	5	1−	WORK_OF_ART
ejpam-6011	143	6	1− ba	QUANTITY
ejpam-6011	143	7	1− ba)ab ∈	MONEY
ejpam-6011	143	8	1− ba)rb ⊆	MONEY
ejpam-6011	143	9	r.	NORP
ejpam-6011	143	10	1−	LANGUAGE
ejpam-6011	144	1	1	CARDINAL
ejpam-6011	145	1	11	CARDINAL
ejpam-6011	145	2	r.	NORP
ejpam-6011	145	3	r.	NORP
ejpam-6011	146	1	nj-abelian	NORP
ejpam-6011	147	1	6	CARDINAL
ejpam-6011	148	1	nj-abelian	NORP
ejpam-6011	150	1	∈	ORG
ejpam-6011	151	1	⊆	CARDINAL
ejpam-6011	151	2	r.	NORP
ejpam-6011	151	3	r.	NORP
ejpam-6011	152	1	0	CARDINAL
ejpam-6011	153	1	xe	ORG
ejpam-6011	153	2	⊆	CARDINAL
ejpam-6011	153	3	r.	NORP
ejpam-6011	154	1	⊆	CARDINAL
ejpam-6011	154	2	0	CARDINAL
ejpam-6011	156	1	1−	ORDINAL
ejpam-6011	156	2	0	CARDINAL
ejpam-6011	158	1	∈	ORG
ejpam-6011	160	1	nj-abelian	NORP
ejpam-6011	162	1	nj-abelian	NORP
ejpam-6011	165	1	0	CARDINAL
ejpam-6011	166	1	∈	ORG
ejpam-6011	167	1	0	CARDINAL
ejpam-6011	168	1	nj-abelian	NORP
ejpam-6011	168	2	1	CARDINAL
ejpam-6011	168	3	lemma 2.4	ORG
ejpam-6011	168	4	3	CARDINAL
ejpam-6011	169	1	2	CARDINAL
ejpam-6011	169	2	1	CARDINAL
ejpam-6011	169	3	2.4	CARDINAL
ejpam-6011	170	1	j-abelian	PERSON
ejpam-6011	171	1	5	CARDINAL
ejpam-6011	172	1	3	CARDINAL
ejpam-6011	172	2	1	CARDINAL
ejpam-6011	172	3	2.10	CARDINAL
ejpam-6011	174	1	12	CARDINAL
ejpam-6011	175	1	∈	ORG
ejpam-6011	176	1	j(r	PERSON
ejpam-6011	177	1	13	CARDINAL
ejpam-6011	178	1	1	CARDINAL
ejpam-6011	178	2	nj-abelian	NORP
ejpam-6011	179	1	m. saad	PERSON
ejpam-6011	179	2	s. m. abdelwahab	PERSON
ejpam-6011	180	1	j. pure	PERSON
ejpam-6011	180	2	18	CARDINAL
ejpam-6011	180	3	2	CARDINAL
ejpam-6011	180	4	2025	CARDINAL
ejpam-6011	180	5	6011 6	DATE
ejpam-6011	180	6	13	CARDINAL
ejpam-6011	181	1	nj-abelian	NORP
ejpam-6011	183	1	13	CARDINAL
ejpam-6011	183	2	2.6	CARDINAL
ejpam-6011	184	1	ea	CARDINAL
ejpam-6011	184	2	∈	ORG
ejpam-6011	184	3	∈	ORG
ejpam-6011	184	4	1)are	CARDINAL
ejpam-6011	184	5	ea	CARDINAL
ejpam-6011	184	6	1)are	CARDINAL
ejpam-6011	185	1	j(r	PERSON
ejpam-6011	186	1	1)are	CARDINAL
ejpam-6011	186	2	∈ j(r	LOC
ejpam-6011	186	3	∈	ORG
ejpam-6011	186	4	⊆	CARDINAL
ejpam-6011	186	5	nj-abelian	NORP
ejpam-6011	187	1	only one	CARDINAL
ejpam-6011	188	1	12	CARDINAL
ejpam-6011	188	2	1	CARDINAL
ejpam-6011	189	1	4	CARDINAL
ejpam-6011	190	1	nj-abelian	NORP
ejpam-6011	191	1	nj-abelian	NORP
ejpam-6011	192	1	nj-abelian	NORP
ejpam-6011	192	2	3	CARDINAL
ejpam-6011	193	1	nj-abelian	NORP
ejpam-6011	194	1	abelian	NORP
ejpam-6011	196	1	nj-abelian	NORP
ejpam-6011	196	2	nj	ORG
ejpam-6011	198	1	6	CARDINAL
ejpam-6011	199	1	z⊕z	GPE
ejpam-6011	199	2	σ	ORG
ejpam-6011	199	3	σ(a	ORG
ejpam-6011	200	1	∈	ORG
ejpam-6011	200	2	r.	NORP
ejpam-6011	200	3	σ	ORG
ejpam-6011	201	1	1	CARDINAL
ejpam-6011	201	2	0	DATE
ejpam-6011	201	3	0	CARDINAL
ejpam-6011	201	4	1	CARDINAL
ejpam-6011	201	5	0	CARDINAL
ejpam-6011	201	6	1	CARDINAL
ejpam-6011	201	7	0	CARDINAL
ejpam-6011	201	8	1	CARDINAL
ejpam-6011	201	9	ea	CARDINAL
ejpam-6011	201	10	0	CARDINAL
ejpam-6011	201	11	0	DATE
ejpam-6011	203	1	nj-abelian	NORP
ejpam-6011	203	2	nj-abelian	NORP
ejpam-6011	203	3	nj-abelian	NORP
ejpam-6011	203	4	non-nj	NORP
ejpam-6011	204	1	7	CARDINAL
ejpam-6011	204	2	14	CARDINAL
ejpam-6011	204	3	4.8	CARDINAL
ejpam-6011	204	4	r.	NORP
ejpam-6011	204	5	9	CARDINAL
ejpam-6011	205	1	nj-abelian	NORP
ejpam-6011	206	1	nj-abelian	NORP
ejpam-6011	206	2	nj	ORG
ejpam-6011	207	1	m. saad	PERSON
ejpam-6011	207	2	s. m. abdelwahab	PERSON
ejpam-6011	208	1	j. pure	PERSON
ejpam-6011	208	2	18	CARDINAL
ejpam-6011	208	3	2	CARDINAL
ejpam-6011	208	4	2025	CARDINAL
ejpam-6011	208	5	6011 7	DATE
ejpam-6011	208	6	13	CARDINAL
ejpam-6011	210	1	∏ i∈λri	PERCENT
ejpam-6011	210	2	nj-abelian	NORP
ejpam-6011	211	1	ri	GPE
ejpam-6011	211	2	nj-abelian	NORP
ejpam-6011	213	1	5	CARDINAL
ejpam-6011	214	1	r.	NORP
ejpam-6011	214	2	1−	ORDINAL
ejpam-6011	214	3	nj-abelian	NORP
ejpam-6011	215	1	nj-abelian	NORP
ejpam-6011	216	1	10	CARDINAL
ejpam-6011	217	1	nj-abelian	NORP
ejpam-6011	218	1	nj-abelian	NORP
ejpam-6011	221	1	∈	ORG
ejpam-6011	221	2	∈	ORG
ejpam-6011	222	1	nj-abelian	NORP
ejpam-6011	225	1	⊆	CARDINAL
ejpam-6011	225	2	nj-abelian	NORP
ejpam-6011	226	1	nj-abelian	NORP
ejpam-6011	226	2	nj-abelian	NORP
ejpam-6011	227	1	8	CARDINAL
ejpam-6011	228	1	integers z.	ORG
ejpam-6011	230	1	nj-abelian	NORP
ejpam-6011	230	2	nj-abelian	NORP
ejpam-6011	233	1	0 1	CARDINAL
ejpam-6011	235	1	nj-abelian	NORP
ejpam-6011	235	2	nj-abelian	NORP
ejpam-6011	236	1	11	CARDINAL
ejpam-6011	237	1	nj-abelian	NORP
ejpam-6011	237	2	nj-abelian	NORP
ejpam-6011	239	1	nj-abelian	NORP
ejpam-6011	239	2	r.	NORP
ejpam-6011	239	3	ea	CARDINAL
ejpam-6011	239	4	∈	ORG
ejpam-6011	239	5	n(i	GPE
ejpam-6011	239	6	nj-abelian	NORP
ejpam-6011	239	7	⊆	CARDINAL
ejpam-6011	240	1	aie ⊆	ORG
ejpam-6011	240	2	⊆	CARDINAL
ejpam-6011	241	1	j(r	PERSON
ejpam-6011	241	2	nj-abelian	NORP
ejpam-6011	242	1	12	CARDINAL
ejpam-6011	243	1	nj-abelian	NORP
ejpam-6011	244	1	nj-abelian	NORP
ejpam-6011	246	1	∈	ORG
ejpam-6011	246	2	ea	CARDINAL
ejpam-6011	246	3	⊆	CARDINAL
ejpam-6011	247	1	⊆	CARDINAL
ejpam-6011	247	2	1−	CARDINAL
ejpam-6011	247	3	r.	NORP
ejpam-6011	247	4	1−	CARDINAL
ejpam-6011	247	5	∈	ORG
ejpam-6011	247	6	1−	CARDINAL
ejpam-6011	247	7	r.	NORP
ejpam-6011	247	8	nj-abelian	NORP
ejpam-6011	248	1	nj-abelian	NORP
ejpam-6011	248	2	nj-abelian	NORP
ejpam-6011	250	1	m. saad	PERSON
ejpam-6011	250	2	s. m. abdelwahab	PERSON
ejpam-6011	251	1	j. pure	PERSON
ejpam-6011	251	2	18	CARDINAL
ejpam-6011	251	3	2	CARDINAL
ejpam-6011	251	4	2025	CARDINAL
ejpam-6011	251	5	6011 8	DATE
ejpam-6011	251	6	13	CARDINAL
ejpam-6011	251	7	9	CARDINAL
ejpam-6011	252	1	s.	ORG
ejpam-6011	252	2	nj-abelian	NORP
ejpam-6011	253	1	1 1	CARDINAL
ejpam-6011	253	2	1 1	CARDINAL
ejpam-6011	253	3	ea ∈ n(r	QUANTITY
ejpam-6011	255	1	nj-abelian	NORP
ejpam-6011	257	1	13	CARDINAL
ejpam-6011	258	1	nj-abelian	NORP
ejpam-6011	258	2	nj-abelian	NORP
ejpam-6011	262	1	0	CARDINAL
ejpam-6011	262	2	∈	ORG
ejpam-6011	262	3	arb ⊆	PERSON
ejpam-6011	262	4	nj-abelian	NORP
ejpam-6011	263	1	nj-abelian	NORP
ejpam-6011	264	1	6	CARDINAL
ejpam-6011	265	1	nj-abelian	NORP
ejpam-6011	268	1	10	CARDINAL
ejpam-6011	269	1	3z	CARDINAL
ejpam-6011	269	2	7	CARDINAL
ejpam-6011	270	1	3r	CARDINAL
ejpam-6011	272	1	nj-abelian	NORP
ejpam-6011	273	1	2	CARDINAL
ejpam-6011	274	1	2	CARDINAL
ejpam-6011	275	1	1 1 2 1	QUANTITY
ejpam-6011	275	2	j(r/j(r	EVENT
ejpam-6011	276	1	nj-abelian	NORP
ejpam-6011	277	1	14	DATE
ejpam-6011	278	1	nj-abelian	NORP
ejpam-6011	279	1	nj-abelian	NORP
ejpam-6011	281	1	nj-abelian	NORP
ejpam-6011	281	2	∈	ORG
ejpam-6011	281	3	ae ∈	ORG
ejpam-6011	282	1	ae ∈	ORG
ejpam-6011	282	2	a(r	ORG
ejpam-6011	282	3	⊆	CARDINAL
ejpam-6011	283	1	1− ares ∈ u(r	PRODUCT
ejpam-6011	283	2	r.	NORP
ejpam-6011	283	3	1 −	QUANTITY
ejpam-6011	283	4	1	CARDINAL
ejpam-6011	283	5	∈	ORG
ejpam-6011	283	6	1	CARDINAL
ejpam-6011	283	7	1 − ares	QUANTITY
ejpam-6011	283	8	r.	NORP
ejpam-6011	283	9	⊆	CARDINAL
ejpam-6011	283	10	nj-abelian	NORP
ejpam-6011	284	1	4	CARDINAL
ejpam-6011	284	2	nj-abelian	NORP
ejpam-6011	284	3	nj-abelian	NORP
ejpam-6011	285	1	first	ORDINAL
ejpam-6011	285	2	nj-abelian	NORP
ejpam-6011	285	3	n ≥ 2	ORG
ejpam-6011	285	4	15	CARDINAL
ejpam-6011	286	1	integer n ≥ 2	ORG
ejpam-6011	286	2	nj-abelian	NORP
ejpam-6011	287	1	m. saad	PERSON
ejpam-6011	287	2	s. m. abdelwahab	PERSON
ejpam-6011	288	1	j. pure	PERSON
ejpam-6011	288	2	18	CARDINAL
ejpam-6011	288	3	2	CARDINAL
ejpam-6011	288	4	2025	CARDINAL
ejpam-6011	288	5	6011 9	DATE
ejpam-6011	288	6	13	CARDINAL
ejpam-6011	289	1	example 9	DATE
ejpam-6011	289	2	m2(r	ORG
ejpam-6011	289	3	nj-abelian	NORP
ejpam-6011	289	4	10	CARDINAL
ejpam-6011	289	5	nj-abelian	NORP
ejpam-6011	289	6	nj-abelian	NORP
ejpam-6011	290	1	nj-abelian	NORP
ejpam-6011	290	2	2	CARDINAL
ejpam-6011	290	3	mn+1(r	ORG
ejpam-6011	291	1	nj-abelian	NORP
ejpam-6011	293	1	∈	ORG
ejpam-6011	293	2	∈	ORG
ejpam-6011	293	3	n ∈ n	ORG
ejpam-6011	294	1	abelian	NORP
ejpam-6011	295	1	∈	ORG
ejpam-6011	295	2	n ∈ n	ORG
ejpam-6011	296	1	two	CARDINAL
ejpam-6011	296	2	ψ(n	PERSON
ejpam-6011	296	3	s.	PERSON
ejpam-6011	297	1	∈	ORG
ejpam-6011	297	2	n ∈ n	ORG
ejpam-6011	299	1	2	CARDINAL
ejpam-6011	300	1	15–19	CARDINAL
ejpam-6011	302	1	20	CARDINAL
ejpam-6011	304	1	0	CARDINAL
ejpam-6011	305	1	jacobson	PERSON
ejpam-6011	306	1	1	CARDINAL
ejpam-6011	307	1	two	CARDINAL
ejpam-6011	310	1	⊆	CARDINAL
ejpam-6011	311	1	n j(s	PERSON
ejpam-6011	313	1	21	CARDINAL
ejpam-6011	313	2	3.1	CARDINAL
ejpam-6011	314	1	16	CARDINAL
ejpam-6011	316	1	nj-abelian	NORP
ejpam-6011	317	1	nj-abelian	NORP
ejpam-6011	318	1	m. saad	PERSON
ejpam-6011	318	2	s. m. abdelwahab	PERSON
ejpam-6011	319	1	j. pure	PERSON
ejpam-6011	319	2	18	CARDINAL
ejpam-6011	319	3	2	CARDINAL
ejpam-6011	319	4	2025	CARDINAL
ejpam-6011	319	5	6011 10	DATE
ejpam-6011	319	6	13	CARDINAL
ejpam-6011	320	1	10	CARDINAL
ejpam-6011	321	1	nj-abelian	NORP
ejpam-6011	327	1	ea	CARDINAL
ejpam-6011	327	2	∈	ORG
ejpam-6011	328	1	frb	ORG
ejpam-6011	328	2	⊆	CARDINAL
ejpam-6011	328	3	s.	PERSON
ejpam-6011	328	4	⊆	CARDINAL
ejpam-6011	328	5	n j(s	PERSON
ejpam-6011	329	1	= j(t	PERSON
ejpam-6011	329	2	nj-abelian	NORP
ejpam-6011	333	1	s.	PERSON
ejpam-6011	334	1	nj-abelian	NORP
ejpam-6011	335	1	nj-abelian	NORP
ejpam-6011	336	1	22	CARDINAL
ejpam-6011	336	2	abelian	NORP
ejpam-6011	337	1	1	CARDINAL
ejpam-6011	341	1	8	CARDINAL
ejpam-6011	341	2	letm represent	PERSON
ejpam-6011	341	3	nj-abelian	NORP
ejpam-6011	342	1	nj-abelian	NORP
ejpam-6011	343	1	17	CARDINAL
ejpam-6011	345	1	nj-abelian	NORP
ejpam-6011	345	2	nj-abelian	NORP
ejpam-6011	346	1	nj-abelian	NORP
ejpam-6011	347	1	nj-abelian	NORP
ejpam-6011	347	2	2(r	CARDINAL
ejpam-6011	347	3	nj-abelian	NORP
ejpam-6011	347	4	7	CARDINAL
ejpam-6011	348	1	nj-abelian	NORP
ejpam-6011	348	2	nj-abelian	NORP
ejpam-6011	348	3	10	CARDINAL
ejpam-6011	349	1	t n+1(r	GPE
ejpam-6011	349	2	r.	NORP
ejpam-6011	349	3	t n+1(r	GPE
ejpam-6011	349	4	nj-abelian	NORP
ejpam-6011	349	5	m. saad	PERSON
ejpam-6011	349	6	s. m. abdelwahab	PERSON
ejpam-6011	350	1	j. pure	PERSON
ejpam-6011	350	2	18	CARDINAL
ejpam-6011	350	3	2	CARDINAL
ejpam-6011	350	4	2025	CARDINAL
ejpam-6011	350	5	6011 11	DATE
ejpam-6011	350	6	13	CARDINAL
ejpam-6011	351	1	0	CARDINAL
ejpam-6011	351	2	a2n	PERSON
ejpam-6011	354	1	aij ∈	PERSON
ejpam-6011	355	1	  a1 a2 a3	QUANTITY
ejpam-6011	356	1	0 a1 a2 a3	QUANTITY
ejpam-6011	358	1	0	CARDINAL
ejpam-6011	361	1	∈	ORG
ejpam-6011	362	1	nj	ORG
ejpam-6011	362	2	18	CARDINAL
ejpam-6011	364	1	nj-abelian	NORP
ejpam-6011	364	2	nj-abelian	NORP
ejpam-6011	365	1	nj-abelian	NORP
ejpam-6011	365	2	nj-abelian	NORP
ejpam-6011	365	3	nj-abelian	NORP
ejpam-6011	366	1	zero	CARDINAL
ejpam-6011	368	1	nj-abelian	NORP
ejpam-6011	368	2	14	CARDINAL
ejpam-6011	369	1	iii)⇒(i	ORG
ejpam-6011	369	2	10	CARDINAL
ejpam-6011	371	1	8	CARDINAL
ejpam-6011	371	2	2(r	CARDINAL
ejpam-6011	372	1	9	CARDINAL
ejpam-6011	373	1	nj-abelian	NORP
ejpam-6011	374	1	nj-abelian	NORP
ejpam-6011	374	2	integer n. m. saad	PERSON
ejpam-6011	374	3	s. m. abdelwahab	PERSON
ejpam-6011	375	1	j. pure	PERSON
ejpam-6011	375	2	18	CARDINAL
ejpam-6011	375	3	2	CARDINAL
ejpam-6011	375	4	2025	CARDINAL
ejpam-6011	375	5	6011 12	DATE
ejpam-6011	375	6	13	CARDINAL
ejpam-6011	375	7	nj-abelian	NORP
ejpam-6011	375	8	jacobson	PERSON
ejpam-6011	376	1	abelian	NORP
ejpam-6011	377	1	nj-abelian	NORP
ejpam-6011	377	2	j-abelian	PERSON
ejpam-6011	377	3	nj-abelian	NORP
ejpam-6011	378	1	nj-abelian	NORP
ejpam-6011	379	1	j-abelian	PERSON
ejpam-6011	380	1	nj-abelian	NORP
ejpam-6011	381	1	nj-abelian	NORP
ejpam-6011	383	1	jacobson	PERSON
ejpam-6011	386	1	1	CARDINAL
ejpam-6011	386	2	abdullah harmanci	PERSON
ejpam-6011	386	3	burcu	PERSON
ejpam-6011	387	1	abelian	NORP
ejpam-6011	388	1	bolet́ın de matemáticas	PERSON
ejpam-6011	388	2	25(1):27–37	DATE
ejpam-6011	388	3	2018	DATE
ejpam-6011	389	1	2	CARDINAL
ejpam-6011	390	1	abelian	NORP
ejpam-6011	391	1	2550146	DATE
ejpam-6011	391	2	2023	CARDINAL
ejpam-6011	392	1	3	CARDINAL
ejpam-6011	392	2	l. motais de narbonne	ORG
ejpam-6011	393	1	anneaux semi-commutatifs	PERSON
ejpam-6011	393	2	anneaux	PERSON
ejpam-6011	393	3	aux principaux sont idempotents	ORG
ejpam-6011	394	1	106th	ORDINAL
ejpam-6011	394	2	perpignan	NORP
ejpam-6011	394	3	1981	DATE
ejpam-6011	395	1	nat	DATE
ejpam-6011	395	2	paris	GPE
ejpam-6011	395	3	71–73, 1982	DATE
ejpam-6011	396	1	4	CARDINAL
ejpam-6011	398	1	t. am	PERSON
ejpam-6011	400	1	184:43–60, 1973	DATE
ejpam-6011	401	1	5	CARDINAL
ejpam-6011	401	2	m. habeb	PERSON
ejpam-6011	402	1	zero	CARDINAL
ejpam-6011	403	1	mathematical journal of okayama university	ORG
ejpam-6011	403	2	32:73–76, 1990	DATE
ejpam-6011	404	1	6	CARDINAL
ejpam-6011	404	2	howard e. bell	PERSON
ejpam-6011	406	1	australian	NORP
ejpam-6011	406	2	2:363–368	CARDINAL
ejpam-6011	406	3	1970	DATE
ejpam-6011	407	1	7	CARDINAL
ejpam-6011	407	2	sanjiv subba	PERSON
ejpam-6011	409	1	2023	CARDINAL
ejpam-6011	410	1	m. saad	PERSON
ejpam-6011	410	2	s. m. abdelwahab	PERSON
ejpam-6011	411	1	j. pure	PERSON
ejpam-6011	411	2	18	CARDINAL
ejpam-6011	411	3	2	CARDINAL
ejpam-6011	411	4	2025	CARDINAL
ejpam-6011	411	5	6011 13	DATE
ejpam-6011	411	6	13	CARDINAL
ejpam-6011	412	1	8	CARDINAL
ejpam-6011	413	1	jacobson radical	PERSON
ejpam-6011	415	1	univ	NORP
ejpam-6011	416	1	al.	ORG
ejpam-6011	416	2	i. cuza iasi	PERSON
ejpam-6011	418	1	62(2):595–606	DATE
ejpam-6011	418	2	2016	DATE
ejpam-6011	419	1	9	CARDINAL
ejpam-6011	419	2	chang ik lee	PERSON
ejpam-6011	419	3	soo yong park	PERSON
ejpam-6011	420	1	jacobson	PERSON
ejpam-6011	421	1	the korean mathematical society	ORG
ejpam-6011	421	2	55(5):1193–1205	CARDINAL
ejpam-6011	421	3	2018	DATE
ejpam-6011	422	1	10	CARDINAL
ejpam-6011	422	2	weixing chen	PERSON
ejpam-6011	424	1	219(4):1122–1130	CARDINAL
ejpam-6011	424	2	2015	DATE
ejpam-6011	425	1	11	CARDINAL
ejpam-6011	425	2	junchao wei	PERSON
ejpam-6011	427	1	turkish	NORP
ejpam-6011	427	2	32(4):393–408, 2008	DATE
ejpam-6011	428	1	12	CARDINAL
ejpam-6011	430	1	2015	DATE
ejpam-6011	431	1	13	CARDINAL
ejpam-6011	431	2	abdullah harmanci	PERSON
ejpam-6011	433	1	hacettepe journal	PERSON
ejpam-6011	433	2	44(2):375–384	CARDINAL
ejpam-6011	433	3	2015	DATE
ejpam-6011	434	1	14	CARDINAL
ejpam-6011	436	1	2008	DATE
ejpam-6011	437	1	15	CARDINAL
ejpam-6011	437	2	jay shapiro	PERSON
ejpam-6011	438	1	athens	GPE
ejpam-6011	438	2	ohio	GPE
ejpam-6011	438	3	sept. 29–30, 1989	DATE
ejpam-6011	438	4	2006	DATE
ejpam-6011	439	1	16	CARDINAL
ejpam-6011	441	1	tokyo	GPE
ejpam-6011	441	2	daigaku	GPE
ejpam-6011	441	3	6(150):83	CARDINAL
ejpam-6011	441	4	142	CARDINAL
ejpam-6011	441	5	1958	DATE
ejpam-6011	442	1	17	CARDINAL
ejpam-6011	442	2	a. amitsur	PERSON
ejpam-6011	444	1	17(2):273–298	CARDINAL
ejpam-6011	444	2	1971	DATE
ejpam-6011	445	1	18	CARDINAL
ejpam-6011	445	2	piotr krylov	PERSON
ejpam-6011	445	3	askar tuganbaev	PERSON
ejpam-6011	446	1	23	CARDINAL
ejpam-6011	446	2	2017	DATE
ejpam-6011	447	1	19	CARDINAL
ejpam-6011	447	2	muhammad saad	PERSON
ejpam-6011	447	3	usama	PERSON
ejpam-6011	447	4	ahmed ma el-sayed	PERSON
ejpam-6011	447	5	nour nabil	PERSON
ejpam-6011	449	1	2025	DATE
ejpam-6011	450	1	20	CARDINAL
ejpam-6011	450	2	müller marianne	PERSON
ejpam-6011	451	1	1987	DATE
ejpam-6011	452	1	21	CARDINAL
ejpam-6011	452	2	gaohua tang	PERSON
ejpam-6011	452	3	chunna li	PERSON
ejpam-6011	452	4	yiqiang zhou	PERSON
ejpam-6011	454	1	42(4):1668–1681, 2014	DATE
ejpam-6011	455	1	22	CARDINAL
ejpam-6011	455	2	robert m	PERSON
ejpam-6011	455	3	phillip	PERSON
ejpam-6011	455	4	griffith	ORG
ejpam-6011	456	1	abelian	NORP
ejpam-6011	456	2	abelian	NORP
ejpam-6011	456	3	456	CARDINAL
ejpam-6011	457	1	2006	DATE