id	sid	eid	entity	type
ejpam-6134	1	1	european journal	ORG
ejpam-6134	1	2	2025	DATE
ejpam-6134	1	3	18	CARDINAL
ejpam-6134	1	4	4	CARDINAL
ejpam-6134	1	5	6134	DATE
ejpam-6134	1	6	1307-5543	DATE
ejpam-6134	1	7	new york	GPE
ejpam-6134	1	8	mahmoud m. el-soufi1,2	PERSON
ejpam-6134	1	9	munerah almulhem3,∗	PERSON
ejpam-6134	1	10	m. s. tammam el	PERSON
ejpam-6134	1	11	fayoum university	ORG
ejpam-6134	1	12	fayoum	GPE
ejpam-6134	1	13	egypt 2	ORG
ejpam-6134	1	14	al baha university	ORG
ejpam-6134	1	15	al baha	PERSON
ejpam-6134	1	16	kingdom	GPE
ejpam-6134	1	17	saudi arabia 3	GPE
ejpam-6134	1	18	imam abdulrahman bin faisal university	PERSON
ejpam-6134	1	19	jubail	GPE
ejpam-6134	1	20	35811	DATE
ejpam-6134	1	21	saudi arabia 4	GPE
ejpam-6134	1	22	62111	DATE
ejpam-6134	1	23	egypt	GPE
ejpam-6134	2	1	φ	ORG
ejpam-6134	2	2	ω	ORDINAL
ejpam-6134	5	1	2020	DATE
ejpam-6134	5	2	16n60	CARDINAL
ejpam-6134	5	3	16u80	CARDINAL
ejpam-6134	5	4	16w20	CARDINAL
ejpam-6134	5	5	16w25	CARDINAL
ejpam-6134	5	6	the years	DATE
ejpam-6134	5	7	algebraic	PERSON
ejpam-6134	8	1	1	CARDINAL
ejpam-6134	10	1	mms06@fayoum.edu.eg	PERSON
ejpam-6134	10	2	m. m. el-soufi	PERSON
ejpam-6134	10	3	malmulhim@iau.edu.sa	PERSON
ejpam-6134	10	4	m. almulhem	PERSON
ejpam-6134	11	1	m. s. tammam el-sayiad	PERSON
ejpam-6134	12	1	1	CARDINAL
ejpam-6134	12	2	2025	CARDINAL
ejpam-6134	13	1	m.m. el-soufi	PERSON
ejpam-6134	13	2	m. almulhem	PERSON
ejpam-6134	13	3	m. s. tammam el-sayiad	PERSON
ejpam-6134	14	1	j. pure	PERSON
ejpam-6134	14	2	18	CARDINAL
ejpam-6134	14	3	4	CARDINAL
ejpam-6134	14	4	2025	CARDINAL
ejpam-6134	14	5	6134 2	DATE
ejpam-6134	14	6	12	CARDINAL
ejpam-6134	14	7	ω	ORG
ejpam-6134	15	1	d(s	PERSON
ejpam-6134	16	1	⊆	CARDINAL
ejpam-6134	16	2	s.	PERSON
ejpam-6134	17	1	d(s	PERSON
ejpam-6134	17	2	− d(s	PERSON
ejpam-6134	17	3	− d(u	PERSON
ejpam-6134	17	4	d(su)−d(s)u−	GPE
ejpam-6134	17	5	∈ ζ(ω	ORG
ejpam-6134	18	1	ω	ORG
ejpam-6134	19	1	2	CARDINAL
ejpam-6134	19	2	ω	ORDINAL
ejpam-6134	19	3	ζ(ω	GPE
ejpam-6134	19	4	3	CARDINAL
ejpam-6134	19	5	4	CARDINAL
ejpam-6134	20	1	1998	DATE
ejpam-6134	20	2	filippov	PERSON
ejpam-6134	21	1	∈	ORG
ejpam-6134	22	1	f(su	ORG
ejpam-6134	22	2	sf(u	ORG
ejpam-6134	22	3	filippov	DATE
ejpam-6134	23	1	5	CARDINAL
ejpam-6134	25	1	6	CARDINAL
ejpam-6134	25	2	f(su	ORG
ejpam-6134	27	1	2022	CARDINAL
ejpam-6134	28	1	7	CARDINAL
ejpam-6134	29	1	f(su	ORG
ejpam-6134	30	1	2022	CARDINAL
ejpam-6134	31	1	8	CARDINAL
ejpam-6134	32	1	ω	ORG
ejpam-6134	32	2	f(su	ORG
ejpam-6134	32	3	f(s)φ(u	ORG
ejpam-6134	34	1	ce-φ-homoderivation	ORG
ejpam-6134	35	1	8	CARDINAL
ejpam-6134	35	2	1 6	CARDINAL
ejpam-6134	36	1	ω	CARDINAL
ejpam-6134	37	1	ω	ORG
ejpam-6134	37	2	zero	CARDINAL
ejpam-6134	37	3	1	CARDINAL
ejpam-6134	38	1	m.m. el-soufi	PERSON
ejpam-6134	38	2	m. almulhem	PERSON
ejpam-6134	38	3	m. s. tammam el-sayiad	PERSON
ejpam-6134	39	1	j. pure	PERSON
ejpam-6134	39	2	18	CARDINAL
ejpam-6134	39	3	4	CARDINAL
ejpam-6134	39	4	2025	CARDINAL
ejpam-6134	39	5	6134 3	DATE
ejpam-6134	39	6	ζ(ω	ORG
ejpam-6134	39	7	φ	ORG
ejpam-6134	39	8	2	CARDINAL
ejpam-6134	40	1	ζ(ω	ORG
ejpam-6134	40	2	3	CARDINAL
ejpam-6134	41	1	nonzero nilpotent ce-homoderivation	ORG
ejpam-6134	41	2	4	CARDINAL
ejpam-6134	41	3	zero	CARDINAL
ejpam-6134	41	4	5	CARDINAL
ejpam-6134	41	5	jordan	GPE
ejpam-6134	41	6	6	CARDINAL
ejpam-6134	44	1	1	CARDINAL
ejpam-6134	45	1	φ	ORG
ejpam-6134	45	2	ω	ORDINAL
ejpam-6134	45	3	two	CARDINAL
ejpam-6134	45	4	ω	DATE
ejpam-6134	46	1	f(su	ORG
ejpam-6134	46	2	f(s)φ(u	ORG
ejpam-6134	47	1	∈ ζ(ω	ORG
ejpam-6134	47	2	f(s)φ(u	ORG
ejpam-6134	48	1	φ	ORG
ejpam-6134	48	2	m)homoderivation	ORG
ejpam-6134	49	1	first	ORDINAL
ejpam-6134	49	2	chung	ORG
ejpam-6134	50	1	9	CARDINAL
ejpam-6134	52	1	∈ ω	ORG
ejpam-6134	52	2	0	CARDINAL
ejpam-6134	53	1	r.	NORP
ejpam-6134	53	2	2	CARDINAL
ejpam-6134	54	1	φ	ORG
ejpam-6134	54	2	two	CARDINAL
ejpam-6134	55	1	1	CARDINAL
ejpam-6134	55	2	s. two maps	ORG
ejpam-6134	55	3	φ	ORG
ejpam-6134	56	1	s. m.m. el-soufi	PERSON
ejpam-6134	56	2	m. almulhem	PERSON
ejpam-6134	56	3	m. s. tammam el-sayiad	PERSON
ejpam-6134	57	1	j. pure	PERSON
ejpam-6134	57	2	18	CARDINAL
ejpam-6134	57	3	4	CARDINAL
ejpam-6134	57	4	2025	CARDINAL
ejpam-6134	57	5	6134 4	DATE
ejpam-6134	57	6	12	CARDINAL
ejpam-6134	57	7	1	CARDINAL
ejpam-6134	58	1	1	CARDINAL
ejpam-6134	59	1	2	CARDINAL
ejpam-6134	59	2	ω	ORG
ejpam-6134	59	3	1)-homoderivation	CARDINAL
ejpam-6134	59	4	ω	GPE
ejpam-6134	60	1	3	CARDINAL
ejpam-6134	60	2	1	CARDINAL
ejpam-6134	60	3	φ	ORG
ejpam-6134	60	4	m)homoderivation	ORG
ejpam-6134	62	1	1	CARDINAL
ejpam-6134	63	1	10	CARDINAL
ejpam-6134	63	2	1(b	CARDINAL
ejpam-6134	63	3	one	CARDINAL
ejpam-6134	64	1	ζ(ω	GPE
ejpam-6134	65	1	2	CARDINAL
ejpam-6134	66	1	11	CARDINAL
ejpam-6134	66	2	4	CARDINAL
ejpam-6134	67	1	2	CARDINAL
ejpam-6134	67	2	ce −	ORG
ejpam-6134	69	1	1	CARDINAL
ejpam-6134	70	1	z6 → z6	ORG
ejpam-6134	70	2	4α	CARDINAL
ejpam-6134	71	1	3α	CARDINAL
ejpam-6134	71	2	∈	ORG
ejpam-6134	72	1	φ	ORG
ejpam-6134	72	2	φ	ORG
ejpam-6134	72	3	z6	ORG
ejpam-6134	73	1	2	CARDINAL
ejpam-6134	73	2	ω	CARDINAL
ejpam-6134	73	3	⊕ z6	PERSON
ejpam-6134	73	4	∈	ORG
ejpam-6134	73	5	∈	ORG
ejpam-6134	74	1	ω → ω	ORG
ejpam-6134	74	2	σ	ORG
ejpam-6134	74	3	3ρ	CARDINAL
ejpam-6134	74	4	3	CARDINAL
ejpam-6134	74	5	σ	NORP
ejpam-6134	74	6	∈ ω	ORG
ejpam-6134	75	1	σ	NORP
ejpam-6134	75	2	∈ ω	ORG
ejpam-6134	76	1	ρ +	GPE
ejpam-6134	77	1	3ρ + 3µ	DATE
ejpam-6134	80	1	σ	ORG
ejpam-6134	80	2	3ρ	CARDINAL
ejpam-6134	81	1	3µ	DATE
ejpam-6134	81	2	3ρ + 3µ	DATE
ejpam-6134	88	1	σ	ORG
ejpam-6134	88	2	3µ	DATE
ejpam-6134	91	1	0	CARDINAL
ejpam-6134	91	2	3	CARDINAL
ejpam-6134	92	1	0	CARDINAL
ejpam-6134	92	2	2ρµ	ORDINAL
ejpam-6134	92	3	0	CARDINAL
ejpam-6134	92	4	2ρµ ̸= 0	ORG
ejpam-6134	93	1	φ	ORG
ejpam-6134	93	2	3)homoderivation	CARDINAL
ejpam-6134	93	3	φ	ORG
ejpam-6134	94	1	m.m. el-soufi	PERSON
ejpam-6134	94	2	m. almulhem	PERSON
ejpam-6134	94	3	m. s. tammam el-sayiad	PERSON
ejpam-6134	95	1	j. pure	PERSON
ejpam-6134	95	2	18	CARDINAL
ejpam-6134	95	3	4	CARDINAL
ejpam-6134	95	4	2025	CARDINAL
ejpam-6134	95	5	6134 5	DATE
ejpam-6134	95	6	φ	ORG
ejpam-6134	97	1	φ	ORG
ejpam-6134	97	2	φ	ORG
ejpam-6134	97	3	ω	ORG
ejpam-6134	97	4	∈ z. remark 2.	PERSON
ejpam-6134	97	5	s,+	ORG
ejpam-6134	98	1	two	CARDINAL
ejpam-6134	98	2	s ∈ ω	ORG
ejpam-6134	99	1	1	CARDINAL
ejpam-6134	99	2	ω	ORG
ejpam-6134	100	1	zero	CARDINAL
ejpam-6134	100	2	ω	CARDINAL
ejpam-6134	100	3	ζ(ω	GPE
ejpam-6134	102	1	two	CARDINAL
ejpam-6134	103	1	f(s+	GPE
ejpam-6134	104	1	1	CARDINAL
ejpam-6134	104	2	∈ ω	ORG
ejpam-6134	111	1	2	CARDINAL
ejpam-6134	113	1	sv	ORG
ejpam-6134	114	1	sv	ORG
ejpam-6134	116	1	3	CARDINAL
ejpam-6134	116	2	2	CARDINAL
ejpam-6134	116	3	3	CARDINAL
ejpam-6134	117	1	∈ ω	ORG
ejpam-6134	117	2	4	CARDINAL
ejpam-6134	118	1	4	CARDINAL
ejpam-6134	118	2	∈ ω	ORG
ejpam-6134	119	1	5	CARDINAL
ejpam-6134	119	2	φ	ORG
ejpam-6134	119	3	∈ ω	ORG
ejpam-6134	120	1	6	CARDINAL
ejpam-6134	120	2	m.m. el-soufi	PERSON
ejpam-6134	120	3	m. almulhem	PERSON
ejpam-6134	120	4	m. s. tammam el-sayiad	PERSON
ejpam-6134	121	1	j. pure	PERSON
ejpam-6134	121	2	18	CARDINAL
ejpam-6134	121	3	4	CARDINAL
ejpam-6134	121	4	2025	CARDINAL
ejpam-6134	121	5	6134 6	DATE
ejpam-6134	121	6	12	CARDINAL
ejpam-6134	121	7	4	CARDINAL
ejpam-6134	122	1	∈ ω	ORG
ejpam-6134	122	2	7	CARDINAL
ejpam-6134	122	3	6	CARDINAL
ejpam-6134	122	4	φ	ORG
ejpam-6134	122	5	∈ ω	ORG
ejpam-6134	123	1	8)	CARDINAL
ejpam-6134	123	2	f(v)φf	ORG
ejpam-6134	123	3	∈ ω	ORG
ejpam-6134	124	1	9	CARDINAL
ejpam-6134	124	2	4	CARDINAL
ejpam-6134	124	3	9	CARDINAL
ejpam-6134	124	4	∈ ω	ORG
ejpam-6134	125	1	φ	PERSON
ejpam-6134	125	2	∈ ω	ORG
ejpam-6134	126	1	⊆	CARDINAL
ejpam-6134	128	1	2	CARDINAL
ejpam-6134	128	2	ω	ORG
ejpam-6134	129	1	ann(ω	PERSON
ejpam-6134	129	2	ω	ORG
ejpam-6134	129	3	ζ(ω	GPE
ejpam-6134	131	1	1	CARDINAL
ejpam-6134	132	1	2	CARDINAL
ejpam-6134	133	1	zero	CARDINAL
ejpam-6134	133	2	ω	ORDINAL
ejpam-6134	135	1	1	CARDINAL
ejpam-6134	136	1	∈ ω	ORG
ejpam-6134	136	2	ω	CARDINAL
ejpam-6134	137	1	f(us	ORG
ejpam-6134	137	2	10	CARDINAL
ejpam-6134	140	1	11	CARDINAL
ejpam-6134	142	1	12	CARDINAL
ejpam-6134	144	1	0	CARDINAL
ejpam-6134	145	1	13	CARDINAL
ejpam-6134	145	2	13	CARDINAL
ejpam-6134	147	1	0	CARDINAL
ejpam-6134	148	1	14	CARDINAL
ejpam-6134	148	2	φ	ORG
ejpam-6134	148	3	φ	ORG
ejpam-6134	150	1	0	CARDINAL
ejpam-6134	151	1	15	CARDINAL
ejpam-6134	151	2	13	CARDINAL
ejpam-6134	151	3	15	CARDINAL
ejpam-6134	153	1	0	CARDINAL
ejpam-6134	154	1	16	CARDINAL
ejpam-6134	154	2	.)[f(t),mf(u	ORG
ejpam-6134	156	1	0	CARDINAL
ejpam-6134	156	2	17	CARDINAL
ejpam-6134	156	3	m.m. el-soufi	PERSON
ejpam-6134	156	4	m. almulhem	PERSON
ejpam-6134	156	5	m. s. tammam el-sayiad	PERSON
ejpam-6134	157	1	j. pure	PERSON
ejpam-6134	157	2	18	CARDINAL
ejpam-6134	157	3	4	CARDINAL
ejpam-6134	157	4	2025	CARDINAL
ejpam-6134	157	5	6134 7	DATE
ejpam-6134	157	6	12	DATE
ejpam-6134	157	7	13	CARDINAL
ejpam-6134	157	8	17	CARDINAL
ejpam-6134	158	1	0	CARDINAL
ejpam-6134	159	1	18	CARDINAL
ejpam-6134	159	2	φ	ORG
ejpam-6134	161	1	0	CARDINAL
ejpam-6134	162	1	19	CARDINAL
ejpam-6134	162	2	19	CARDINAL
ejpam-6134	166	1	∈	ORG
ejpam-6134	166	2	ω	CARDINAL
ejpam-6134	167	1	q.	GPE
ejpam-6134	168	1	∈ ω	ORG
ejpam-6134	169	1	∈ ω.	ORG
ejpam-6134	170	1	firstly	ORDINAL
ejpam-6134	170	2	∈ ω	ORG
ejpam-6134	171	1	∈ ω	ORG
ejpam-6134	173	1	∈ ω	ORG
ejpam-6134	175	1	∀ s	ORG
ejpam-6134	175	2	w ∈ ω	ORG
ejpam-6134	176	1	w ∈ ω	ORG
ejpam-6134	177	1	0	CARDINAL
ejpam-6134	177	2	∀ s	ORG
ejpam-6134	177	3	w ∈ ω	ORG
ejpam-6134	179	1	⊆	CARDINAL
ejpam-6134	179	2	∈ ω	ORG
ejpam-6134	181	1	∈ ω	ORG
ejpam-6134	182	1	∈ ω	ORG
ejpam-6134	183	1	∈ ω	ORG
ejpam-6134	184	1	∈ ω	ORG
ejpam-6134	185	1	20	CARDINAL
ejpam-6134	185	2	12	CARDINAL
ejpam-6134	185	3	20	CARDINAL
ejpam-6134	190	1	∈ ω	ORG
ejpam-6134	191	1	21	CARDINAL
ejpam-6134	191	2	13	CARDINAL
ejpam-6134	195	1	∈ ω.	ORG
ejpam-6134	196	1	∈ ω	ORG
ejpam-6134	197	1	∈ ω	ORG
ejpam-6134	199	1	0	CARDINAL
ejpam-6134	199	2	∈ ω	ORG
ejpam-6134	201	1	0	CARDINAL
ejpam-6134	201	2	∀ u	GPE
ejpam-6134	201	3	s ∈ ω	ORG
ejpam-6134	202	1	10	CARDINAL
ejpam-6134	202	2	f(us	ORG
ejpam-6134	202	3	+mf(u)f(s	PERSON
ejpam-6134	203	1	ω	CARDINAL
ejpam-6134	204	1	2	CARDINAL
ejpam-6134	204	2	8	CARDINAL
ejpam-6134	204	3	1	CARDINAL
ejpam-6134	205	1	1	CARDINAL
ejpam-6134	206	1	zero	CARDINAL
ejpam-6134	208	1	m.m. el-soufi	PERSON
ejpam-6134	208	2	m. almulhem	PERSON
ejpam-6134	208	3	m. s. tammam el-sayiad	PERSON
ejpam-6134	209	1	j. pure	PERSON
ejpam-6134	209	2	18	CARDINAL
ejpam-6134	209	3	4	CARDINAL
ejpam-6134	209	4	2025	CARDINAL
ejpam-6134	209	5	6134 8	DATE
ejpam-6134	209	6	12	CARDINAL
ejpam-6134	209	7	3	CARDINAL
ejpam-6134	212	1	∈ ω	ORG
ejpam-6134	213	1	∈ ζ(ω	ORG
ejpam-6134	213	2	22	CARDINAL
ejpam-6134	213	3	∈ ζ(ω	ORG
ejpam-6134	214	1	23	CARDINAL
ejpam-6134	214	2	22	CARDINAL
ejpam-6134	214	3	23	CARDINAL
ejpam-6134	215	1	∈ ω	ORG
ejpam-6134	216	1	24	CARDINAL
ejpam-6134	216	2	24	CARDINAL
ejpam-6134	216	3	φ	ORG
ejpam-6134	216	4	φ	ORG
ejpam-6134	217	1	∈ ω	ORG
ejpam-6134	218	1	25	CARDINAL
ejpam-6134	218	2	24	CARDINAL
ejpam-6134	218	3	25	CARDINAL
ejpam-6134	218	4	φ(fn−2(r	ORG
ejpam-6134	219	1	∈ ω	ORG
ejpam-6134	220	1	φ	ORG
ejpam-6134	220	2	∈ ω	ORG
ejpam-6134	221	1	26	CARDINAL
ejpam-6134	222	1	∈ ω	ORG
ejpam-6134	223	1	27	CARDINAL
ejpam-6134	223	2	24	CARDINAL
ejpam-6134	223	3	27	CARDINAL
ejpam-6134	223	4	∈ ω	ORG
ejpam-6134	224	1	φ	PERSON
ejpam-6134	224	2	∈ ω	ORG
ejpam-6134	225	1	28	CARDINAL
ejpam-6134	225	2	28	CARDINAL
ejpam-6134	227	1	∈ ω	ORG
ejpam-6134	228	1	29	CARDINAL
ejpam-6134	228	2	f(ξ)]f(ξ	GPE
ejpam-6134	228	3	0	CARDINAL
ejpam-6134	229	1	∈ ω	ORG
ejpam-6134	230	1	0	CARDINAL
ejpam-6134	230	2	∈ ω	ORG
ejpam-6134	231	1	30	CARDINAL
ejpam-6134	231	2	zero	CARDINAL
ejpam-6134	232	1	0	CARDINAL
ejpam-6134	232	2	∈ ω	ORG
ejpam-6134	232	3	28	CARDINAL
ejpam-6134	232	4	30	CARDINAL
ejpam-6134	234	1	8	CARDINAL
ejpam-6134	234	2	2	CARDINAL
ejpam-6134	234	3	3	CARDINAL
ejpam-6134	235	1	2	CARDINAL
ejpam-6134	236	1	ζ(ω	ORG
ejpam-6134	237	1	3	CARDINAL
ejpam-6134	238	1	ζ(ω	GPE
ejpam-6134	238	2	ω preserves ζ(ω	ORG
ejpam-6134	239	1	m.m. el-soufi	PERSON
ejpam-6134	239	2	m. almulhem	PERSON
ejpam-6134	239	3	m. s. tammam el-sayiad	PERSON
ejpam-6134	240	1	j. pure	PERSON
ejpam-6134	240	2	18	CARDINAL
ejpam-6134	240	3	4	CARDINAL
ejpam-6134	240	4	2025	CARDINAL
ejpam-6134	240	5	6134 9	DATE
ejpam-6134	241	1	φ	ORG
ejpam-6134	242	1	ω	ORG
ejpam-6134	242	2	ω	CARDINAL
ejpam-6134	242	3	∈ z	ORG
ejpam-6134	242	4	ω → ω	ORG
ejpam-6134	242	5	φ	ORG
ejpam-6134	243	1	4	CARDINAL
ejpam-6134	244	1	ω	CARDINAL
ejpam-6134	244	2	ω	ORG
ejpam-6134	246	1	ω	ORG
ejpam-6134	246	2	zero	CARDINAL
ejpam-6134	246	3	2	CARDINAL
ejpam-6134	246	4	φ	ORG
ejpam-6134	246	5	m)homoderivation	ORG
ejpam-6134	246	6	ω	ORDINAL
ejpam-6134	247	1	ω	ORG
ejpam-6134	248	1	ω	ORG
ejpam-6134	248	2	1	CARDINAL
ejpam-6134	249	1	5	CARDINAL
ejpam-6134	250	1	f(0	PERSON
ejpam-6134	250	2	ω	ORG
ejpam-6134	252	1	f(0+0)−f(0)−f(0	PERSON
ejpam-6134	253	1	f(0	PERSON
ejpam-6134	254	1	∈ ζ(ω	ORG
ejpam-6134	256	1	∈ ω	ORG
ejpam-6134	257	1	φ	ORG
ejpam-6134	257	2	ω	ORDINAL
ejpam-6134	257	3	φ	ORG
ejpam-6134	258	1	∀ t ∈ ω	ORG
ejpam-6134	259	1	0	CARDINAL
ejpam-6134	259	2	∀ t	ORG
ejpam-6134	259	3	∈ ω	ORG
ejpam-6134	260	1	f(0	PERSON
ejpam-6134	260	2	f(0)[t	DATE
ejpam-6134	260	3	0	CARDINAL
ejpam-6134	260	4	t ∈ ω	ORG
ejpam-6134	261	1	f(0)w[t	ORG
ejpam-6134	261	2	0	CARDINAL
ejpam-6134	261	3	w ∈ ω	ORG
ejpam-6134	262	1	0	CARDINAL
ejpam-6134	262	2	t ∈ ω	ORG
ejpam-6134	263	1	ω	ORG
ejpam-6134	263	2	0	CARDINAL
ejpam-6134	263	3	t ∈ ω	ORG
ejpam-6134	263	4	ω	ORG
ejpam-6134	264	1	6	CARDINAL
ejpam-6134	267	1	f(u ◦ s	GPE
ejpam-6134	267	2	s ∈ ω	ORG
ejpam-6134	267	3	ω	ORG
ejpam-6134	269	1	ω	ORG
ejpam-6134	269	2	zero	CARDINAL
ejpam-6134	269	3	lemma 1,	ORG
ejpam-6134	269	4	ω	ORG
ejpam-6134	270	1	ω	GPE
ejpam-6134	270	2	zero	CARDINAL
ejpam-6134	271	1	1	CARDINAL
ejpam-6134	272	1	firstly	ORDINAL
ejpam-6134	272	2	0	CARDINAL
ejpam-6134	272	3	∀ u	GPE
ejpam-6134	272	4	s ∈ ω	ORG
ejpam-6134	273	1	su	PERSON
ejpam-6134	274	1	ω	DATE
ejpam-6134	276	1	φ	PERSON
ejpam-6134	276	2	f(u)[s	GPE
ejpam-6134	277	1	∀ u	GPE
ejpam-6134	277	2	s ∈ ω	ORG
ejpam-6134	278	1	31	CARDINAL
ejpam-6134	278	2	31	CARDINAL
ejpam-6134	278	3	f(u)[s	GPE
ejpam-6134	278	4	∀ u	GPE
ejpam-6134	278	5	s ∈ ω	ORG
ejpam-6134	279	1	f(u)[s	GPE
ejpam-6134	280	1	0	CARDINAL
ejpam-6134	280	2	∀ u	GPE
ejpam-6134	280	3	∈ ω	ORG
ejpam-6134	280	4	f(u)[s	GPE
ejpam-6134	281	1	0	CARDINAL
ejpam-6134	281	2	∀ u	GPE
ejpam-6134	281	3	∈ ω	ORG
ejpam-6134	282	1	32	CARDINAL
ejpam-6134	282	2	32	CARDINAL
ejpam-6134	282	3	32	CARDINAL
ejpam-6134	282	4	f(u)[s	GPE
ejpam-6134	283	1	0	CARDINAL
ejpam-6134	283	2	∀ u	GPE
ejpam-6134	283	3	w	GPE
ejpam-6134	283	4	t ∈ ω	ORG
ejpam-6134	284	1	33	CARDINAL
ejpam-6134	284	2	ω	CARDINAL
ejpam-6134	284	3	∈ ω	ORG
ejpam-6134	284	4	f(u)[s	GPE
ejpam-6134	285	1	0	CARDINAL
ejpam-6134	285	2	∈ ω	ORG
ejpam-6134	285	3	u ∈ ω	ORG
ejpam-6134	285	4	f(u)[s	GPE
ejpam-6134	286	1	∈ ω	ORG
ejpam-6134	287	1	st	GPE
ejpam-6134	287	2	m.m. el-soufi	PERSON
ejpam-6134	287	3	m. almulhem	PERSON
ejpam-6134	287	4	m. s. tammam el-sayiad	PERSON
ejpam-6134	288	1	j. pure	PERSON
ejpam-6134	288	2	18	CARDINAL
ejpam-6134	288	3	4	CARDINAL
ejpam-6134	288	4	2025	CARDINAL
ejpam-6134	288	5	6134 10	DATE
ejpam-6134	288	6	12	CARDINAL
ejpam-6134	289	1	0	CARDINAL
ejpam-6134	289	2	∀ t	ORG
ejpam-6134	289	3	s ∈ ω	ORG
ejpam-6134	290	1	∈ ω	ORG
ejpam-6134	291	1	0	CARDINAL
ejpam-6134	291	2	u ∈ ω	ORG
ejpam-6134	293	1	ω,+	PRODUCT
ejpam-6134	294	1	ω	ORDINAL
ejpam-6134	294	2	ω	ORG
ejpam-6134	294	3	0	CARDINAL
ejpam-6134	295	1	secondly	ORDINAL
ejpam-6134	295	2	f(u	GPE
ejpam-6134	295	3	0	CARDINAL
ejpam-6134	295	4	ω	CARDINAL
ejpam-6134	296	1	su	PERSON
ejpam-6134	296	2	f(u ◦ s	GPE
ejpam-6134	296	3	0	CARDINAL
ejpam-6134	296	4	f(su	ORG
ejpam-6134	298	1	s ∈ ω	ORG
ejpam-6134	299	1	f(s)φ(u ◦ s	ORG
ejpam-6134	299	2	∀ u	GPE
ejpam-6134	299	3	s ∈ ω	ORG
ejpam-6134	300	1	34	CARDINAL
ejpam-6134	300	2	34	CARDINAL
ejpam-6134	300	3	f(s)φ(u	ORG
ejpam-6134	300	4	∈ ζ(ω	ORG
ejpam-6134	300	5	∀ u	GPE
ejpam-6134	300	6	s ∈ ω	ORG
ejpam-6134	301	1	lemma 2	ORG
ejpam-6134	301	2	s ∈ ω	ORG
ejpam-6134	301	3	u ∈ ω	ORG
ejpam-6134	301	4	φ(s	GPE
ejpam-6134	302	1	s ∈ ω	ORG
ejpam-6134	302	2	f(s)φ(u ◦ s	ORG
ejpam-6134	303	1	u ∈ ω	ORG
ejpam-6134	303	2	35	CARDINAL
ejpam-6134	303	3	su	PERSON
ejpam-6134	303	4	35	CARDINAL
ejpam-6134	303	5	0	CARDINAL
ejpam-6134	304	1	∈ ω	ORG
ejpam-6134	305	1	φ	ORG
ejpam-6134	305	2	φ(s	GPE
ejpam-6134	306	1	0	CARDINAL
ejpam-6134	306	2	∈ ω	ORG
ejpam-6134	307	1	φ(s	GPE
ejpam-6134	308	1	0	CARDINAL
ejpam-6134	308	2	∀ u	GPE
ejpam-6134	308	3	t ∈ ω	ORG
ejpam-6134	309	1	ω	CARDINAL
ejpam-6134	309	2	0 or φ(s) ∈	PERCENT
ejpam-6134	311	1	0	CARDINAL
ejpam-6134	311	2	35	CARDINAL
ejpam-6134	312	1	u ∈ ω	ORG
ejpam-6134	312	2	ω	ORG
ejpam-6134	312	3	φ	ORG
ejpam-6134	312	4	f(s	EVENT
ejpam-6134	312	5	0 or φ(s)	PERCENT
ejpam-6134	314	1	s ∈ ω	ORG
ejpam-6134	314	2	two	CARDINAL
ejpam-6134	314	3	f(s	EVENT
ejpam-6134	314	4	0 or φ(s) ∈	PERCENT
ejpam-6134	315	1	0	CARDINAL
ejpam-6134	315	2	ω	ORG
ejpam-6134	316	1	6	CARDINAL
ejpam-6134	318	1	3	CARDINAL
ejpam-6134	319	1	0	CARDINAL
ejpam-6134	319	2	∈	ORG
ejpam-6134	319	3	2	CARDINAL
ejpam-6134	319	4	r.	NORP
ejpam-6134	319	5	0 1	CARDINAL
ejpam-6134	319	6	∈ ω	ORG
ejpam-6134	320	1	ω → ω	ORG
ejpam-6134	322	1	ω	ORDINAL
ejpam-6134	322	2	∈ z	ORG
ejpam-6134	323	1	ω	ORG
ejpam-6134	324	1	2	CARDINAL
ejpam-6134	324	2	0	CARDINAL
ejpam-6134	324	3	∈ ω	ORG
ejpam-6134	325	1	ω	ORG
ejpam-6134	326	1	theorems 4,	ORG
ejpam-6134	326	2	5	DATE
ejpam-6134	326	3	6	CARDINAL
ejpam-6134	326	4	8	CARDINAL
ejpam-6134	326	5	4	CARDINAL
ejpam-6134	326	6	5	DATE
ejpam-6134	326	7	6	CARDINAL
ejpam-6134	327	1	m.m. el-soufi	PERSON
ejpam-6134	327	2	m. almulhem	PERSON
ejpam-6134	327	3	m. s. tammam el-sayiad	PERSON
ejpam-6134	328	1	j. pure	PERSON
ejpam-6134	328	2	18	CARDINAL
ejpam-6134	328	3	4	CARDINAL
ejpam-6134	328	4	2025	CARDINAL
ejpam-6134	328	5	6134 11	DATE
ejpam-6134	328	6	12	CARDINAL
ejpam-6134	328	7	4	CARDINAL
ejpam-6134	329	1	ω	ORG
ejpam-6134	330	1	f(0	PERSON
ejpam-6134	331	1	∈ ω	ORG
ejpam-6134	332	1	5	CARDINAL
ejpam-6134	334	1	generalized homoderivations	PERSON
ejpam-6134	336	1	1	CARDINAL
ejpam-6134	339	1	57(1):129–136	CARDINAL
ejpam-6134	339	2	2016	DATE
ejpam-6134	341	1	2	CARDINAL
ejpam-6134	343	1	east-west	LOC
ejpam-6134	343	2	18(1):47–51	DATE
ejpam-6134	343	3	2016	DATE
ejpam-6134	344	1	3	CARDINAL
ejpam-6134	344	2	munerah	PRODUCT
ejpam-6134	346	1	9(11):33254–33262	CARDINAL
ejpam-6134	346	2	2024	DATE
ejpam-6134	348	1	4	CARDINAL
ejpam-6134	348	2	munerah	PRODUCT
ejpam-6134	350	1	10(3):7191–7205	CARDINAL
ejpam-6134	350	2	2025	DATE
ejpam-6134	352	1	5	CARDINAL
ejpam-6134	353	1	algebras	ORG
ejpam-6134	353	2	sib	CARDINAL
ejpam-6134	354	1	j.	PERSON
ejpam-6134	354	2	39(3):1218–1230	CARDINAL
ejpam-6134	354	3	1998	DATE
ejpam-6134	355	1	6	CARDINAL
ejpam-6134	355	2	mahmoud	PERSON
ejpam-6134	357	1	cairo university	ORG
ejpam-6134	357	2	fayoum	GPE
ejpam-6134	357	3	cairo	GPE
ejpam-6134	357	4	egypt	GPE
ejpam-6134	357	5	2000	DATE
ejpam-6134	360	1	8	CARDINAL
ejpam-6134	360	2	2022	CARDINAL
ejpam-6134	361	1	https://doi.org/10.1155/2022/1112183	ORG
ejpam-6134	362	1	m.m. el-soufi	PERSON
ejpam-6134	362	2	m. almulhem	PERSON
ejpam-6134	362	3	m. s. tammam el-sayiad	PERSON
ejpam-6134	363	1	j. pure	PERSON
ejpam-6134	363	2	18	CARDINAL
ejpam-6134	363	3	4	CARDINAL
ejpam-6134	363	4	2025	CARDINAL
ejpam-6134	363	5	6134 12	DATE
ejpam-6134	363	6	12	CARDINAL
ejpam-6134	364	1	8	CARDINAL
ejpam-6134	364	2	mahmoud	PERSON
ejpam-6134	366	1	2022	CARDINAL
ejpam-6134	366	2	article id 2584177	LAW
ejpam-6134	366	3	5	CARDINAL
ejpam-6134	366	4	2022	CARDINAL
ejpam-6134	368	1	9	CARDINAL
ejpam-6134	370	1	j. algebra	PERSON
ejpam-6134	370	2	1985	DATE
ejpam-6134	372	1	10	CARDINAL
ejpam-6134	374	1	canad	ORG
ejpam-6134	376	1	bull	PERSON
ejpam-6134	377	1	37(4):443–447	CARDINAL
ejpam-6134	377	2	1994	DATE
ejpam-6134	379	1	11	CARDINAL
ejpam-6134	381	1	canad	ORG
ejpam-6134	383	1	bull.	PERSON
ejpam-6134	383	2	26(1):122–126, 1984	DATE