id	sid	eid	entity	type
cana-5404	1	1	1074	CARDINAL
cana-5404	1	2	32	CARDINAL
cana-5404	2	1	2025	DATE
cana-5404	2	2	2138	CARDINAL
cana-5404	3	1	multiplicative	ORG
cana-5404	3	2	one	CARDINAL
cana-5404	3	3	ahmed aboubakr1,2	PERSON
cana-5404	3	4	nawal m. noureldeen1,3 1department	PERSON
cana-5404	3	5	medina	GPE
cana-5404	3	6	saudi arabia	GPE
cana-5404	4	1	2department	TIME
cana-5404	4	2	fayoum university	ORG
cana-5404	4	3	63514	CARDINAL
cana-5404	4	4	fayoum	GPE
cana-5404	4	5	egypt	GPE
cana-5404	5	1	aaboubakr@taibahu.edu.sa & afs00@fayoum.edu.eg 3department	ORG
cana-5404	5	2	ain shams university	ORG
cana-5404	5	3	egypt	GPE
cana-5404	6	1	neldeen@taibahu.edu.sa	ORG
cana-5404	6	2	12-01-2025	CARDINAL
cana-5404	6	3	15-02-2025	CARDINAL
cana-5404	6	4	01-03-2025	CARDINAL
cana-5404	7	1	𝑀𝑢𝑙𝑡.	GPE
cana-5404	7	2	γ(𝜈𝜔	ORG
cana-5404	7	3	∈	ORG
cana-5404	8	1	γ	GPE
cana-5404	8	2	𝑀𝑢𝑙𝑡.	GPE
cana-5404	10	1	γ(𝜔	PERSON
cana-5404	10	2	±[𝜈	ORG
cana-5404	11	1	γ(𝜔	PERSON
cana-5404	13	1	ℬ.	PERSON
cana-5404	14	1	16w25	DATE
cana-5404	14	2	16n60	CARDINAL
cana-5404	14	3	16u80	CARDINAL
cana-5404	15	1	multiplicative (generalized)derivation	ORG
cana-5404	16	1	1introduction	CARDINAL
cana-5404	16	2	multiplicative	NORP
cana-5404	16	3	first	ORDINAL
cana-5404	16	4	1991	DATE
cana-5404	16	5	1	CARDINAL
cana-5404	16	6	multiplicative	NORP
cana-5404	17	1	1	CARDINAL
cana-5404	17	2	martindale	ORG
cana-5404	17	3	2	CARDINAL
cana-5404	18	1	3	CARDINAL
cana-5404	19	1	multiplicative	ORG
cana-5404	19	2	4	CARDINAL
cana-5404	19	3	multiplicative	NORP
cana-5404	19	4	multiplicative	NORP
cana-5404	19	5	γ(𝜈𝜔	GPE
cana-5404	19	6	∈ ℬ. later	DATE
cana-5404	19	7	dhara	PERSON
cana-5404	19	8	ali	PERSON
cana-5404	20	1	5	CARDINAL
cana-5404	20	2	multiplicative	ORG
cana-5404	20	3	ℬ.	PERSON
cana-5404	20	4	γ(𝜈𝜔	GPE
cana-5404	20	5	∈	ORG
cana-5404	21	1	𝑀𝑢𝑙𝑡.	GPE
cana-5404	21	2	multiplicative	NORP
cana-5404	22	1	𝑀𝑢𝑙𝑡.	GPE
cana-5404	22	2	0	CARDINAL
cana-5404	22	3	multiplicative	ORG
cana-5404	23	1	mailto:afs00@fayoum.edu.eg	ORG
cana-5404	23	2	1074	CARDINAL
cana-5404	23	3	32	CARDINAL
cana-5404	24	1	2025	CARDINAL
cana-5404	24	2	2139	CARDINAL
cana-5404	25	1	𝑀𝑢𝑙𝑡.	GPE
cana-5404	25	2	ℬ.	PERSON
cana-5404	25	3	1.1	CARDINAL
cana-5404	25	4	0	CARDINAL
cana-5404	26	1	∀ 𝑓(𝜈)≠0	GPE
cana-5404	26	2	0	CARDINAL
cana-5404	27	1	𝑓(𝜈)(1+𝑙𝑜𝑔|𝑓(𝜈)|	CARDINAL
cana-5404	28	1	multiplicative	NORP
cana-5404	28	2	𝐷.	NORP
cana-5404	28	3	1.2	CARDINAL
cana-5404	29	1	0	CARDINAL
cana-5404	30	1	0	CARDINAL
cana-5404	31	1	0	CARDINAL
cana-5404	32	1	0	CARDINAL
cana-5404	34	1	0	CARDINAL
cana-5404	34	2	0	CARDINAL
cana-5404	34	3	0	CARDINAL
cana-5404	35	1	0	CARDINAL
cana-5404	35	2	0	CARDINAL
cana-5404	36	1	multiplicative	NORP
cana-5404	36	2	𝐷.	NORP
cana-5404	36	3	the last thirty years	DATE
cana-5404	36	4	ℬ.	PERSON
cana-5404	36	5	6	CARDINAL
cana-5404	37	1	8	CARDINAL
cana-5404	37	2	9	CARDINAL
cana-5404	37	3	10	CARDINAL
cana-5404	38	1	11	CARDINAL
cana-5404	39	1	ℬ.	PERSON
cana-5404	39	2	γ(𝜔	PERSON
cana-5404	40	1	0	CARDINAL
cana-5404	42	1	γ(𝜔	PERSON
cana-5404	43	1	12	CARDINAL
cana-5404	43	2	13	CARDINAL
cana-5404	43	3	14	CARDINAL
cana-5404	43	4	15	CARDINAL
cana-5404	43	5	ali	PERSON
cana-5404	43	6	16	CARDINAL
cana-5404	43	7	1074	CARDINAL
cana-5404	43	8	32	CARDINAL
cana-5404	44	1	2025	CARDINAL
cana-5404	44	2	2140	CARDINAL
cana-5404	45	1	algebras	ORG
cana-5404	46	1	𝑀𝑢𝑙𝑡.	GPE
cana-5404	47	1	two	CARDINAL
cana-5404	47	2	first	ORDINAL
cana-5404	47	3	two	CARDINAL
cana-5404	47	4	second	ORDINAL
cana-5404	47	5	𝑀𝑢𝑙𝑡.	GPE
cana-5404	50	1	γ(𝜔	PERSON
cana-5404	51	1	γ(𝜔	PERSON
cana-5404	51	2	γ(𝜔	ORG
cana-5404	52	1	1.3	CARDINAL
cana-5404	53	1	17	CARDINAL
cana-5404	54	1	2	CARDINAL
cana-5404	54	2	ℬ.	PERSON
cana-5404	54	3	∈	ORG
cana-5404	54	4	0	CARDINAL
cana-5404	55	1	1.4	CARDINAL
cana-5404	56	1	11	CARDINAL
cana-5404	56	2	2.1	CARDINAL
cana-5404	57	1	two	CARDINAL
cana-5404	57	2	ℬ.	PERSON
cana-5404	57	3	∈	ORG
cana-5404	57	4	0	CARDINAL
cana-5404	58	1	2scp	CARDINAL
cana-5404	58	2	𝑴𝒖𝒍𝒕.	GPE
cana-5404	58	3	2.1	CARDINAL
cana-5404	58	4	2	CARDINAL
cana-5404	59	1	∈	ORG
cana-5404	59	2	0	CARDINAL
cana-5404	59	3	∀𝜈 ∈ 𝐿. proof	ORG
cana-5404	60	1	γ(𝜔	PERSON
cana-5404	62	1	∈	ORG
cana-5404	62	2	1	CARDINAL
cana-5404	62	3	1	CARDINAL
cana-5404	63	1	𝜔]𝜉(𝜈	ORG
cana-5404	65	1	2	CARDINAL
cana-5404	65	2	1	CARDINAL
cana-5404	67	1	3	CARDINAL
cana-5404	67	2	2	CARDINAL
cana-5404	67	3	3	CARDINAL
cana-5404	68	1	𝜔]𝜉(𝜈	ORG
cana-5404	69	1	4	CARDINAL
cana-5404	69	2	4	CARDINAL
cana-5404	69	3	4	CARDINAL
cana-5404	69	4	𝜉(𝑧)𝜔[γ(𝜈	DATE
cana-5404	70	1	𝑧]𝜔𝜉(𝜈	ORG
cana-5404	71	1	5	CARDINAL
cana-5404	72	1	∈ 𝐿. lemma 1.3	ORG
cana-5404	73	1	6	CARDINAL
cana-5404	74	1	+ 𝜉(𝜈)𝜈 ∀𝜈	NORP
cana-5404	75	1	∈	ORG
cana-5404	75	2	7	CARDINAL
cana-5404	75	3	1074	CARDINAL
cana-5404	75	4	32	CARDINAL
cana-5404	76	1	2025	CARDINAL
cana-5404	76	2	2141	CARDINAL
cana-5404	76	3	7	CARDINAL
cana-5404	76	4	6	CARDINAL
cana-5404	77	1	𝜈]ℬ𝐿[𝜉(𝜈	TIME
cana-5404	77	2	∈	ORG
cana-5404	77	3	7	CARDINAL
cana-5404	77	4	γ(𝜔	PERSON
cana-5404	79	1	2.2	CARDINAL
cana-5404	80	1	∀𝜈	GPE
cana-5404	80	2	∈	ORG
cana-5404	80	3	2.3	CARDINAL
cana-5404	80	4	2	CARDINAL
cana-5404	80	5	𝑀𝑢𝑙𝑡.	GPE
cana-5404	83	1	ℬ. theorem 2.4	ORG
cana-5404	85	1	∀𝜈	GPE
cana-5404	85	2	∈	ORG
cana-5404	85	3	𝐿[𝛿(𝜈	GPE
cana-5404	85	4	0 and 𝐿[𝜉(𝜈	DATE
cana-5404	85	5	0	CARDINAL
cana-5404	85	6	∀𝜈 ∈ 𝐿. proof	ORG
cana-5404	87	1	∈	ORG
cana-5404	90	1	9	CARDINAL
cana-5404	91	1	10	CARDINAL
cana-5404	91	2	10	CARDINAL
cana-5404	91	3	9	CARDINAL
cana-5404	92	1	∀𝜈	GPE
cana-5404	92	2	11	CARDINAL
cana-5404	92	3	11	CARDINAL
cana-5404	92	4	𝑟[𝜈	ORG
cana-5404	94	1	𝑟𝜈[𝜔	CARDINAL
cana-5404	94	2	∈	ORG
cana-5404	94	3	12	CARDINAL
cana-5404	94	4	11	CARDINAL
cana-5404	94	5	𝑟[𝜈	CARDINAL
cana-5404	95	1	𝑟𝜈[𝜔	CARDINAL
cana-5404	95	2	∈	ORG
cana-5404	95	3	13	CARDINAL
cana-5404	95	4	12	CARDINAL
cana-5404	95	5	13	CARDINAL
cana-5404	97	1	𝛿(𝜔	ORG
cana-5404	98	1	14	CARDINAL
cana-5404	98	2	14	CARDINAL
cana-5404	99	1	0	CARDINAL
cana-5404	100	1	14	CARDINAL
cana-5404	101	1	two	CARDINAL
cana-5404	104	1	∈	ORG
cana-5404	105	1	δ(𝜔)]𝜈	ORG
cana-5404	106	1	𝜔]𝜉(𝜈	ORG
cana-5404	106	2	15	CARDINAL
cana-5404	106	3	8)	CARDINAL
cana-5404	106	4	15	CARDINAL
cana-5404	106	5	𝜔[𝜈	CARDINAL
cana-5404	107	1	𝜔]𝜉(𝜈	ORG
cana-5404	107	2	∈	ORG
cana-5404	107	3	16	CARDINAL
cana-5404	107	4	1074	CARDINAL
cana-5404	107	5	32	CARDINAL
cana-5404	108	1	2142	DATE
cana-5404	109	1	∈ 𝐿.	PERSON
cana-5404	109	2	∀𝜈	GPE
cana-5404	109	3	∈	ORG
cana-5404	110	1	2.5	CARDINAL
cana-5404	110	2	two	CARDINAL
cana-5404	112	1	∈ ℒ	ORG
cana-5404	113	1	2.4	DATE
cana-5404	114	1	0	CARDINAL
cana-5404	115	1	lemma 1.4	ORG
cana-5404	116	1	∈ ℒ	ORG
cana-5404	116	2	2.6	CARDINAL
cana-5404	116	3	2	CARDINAL
cana-5404	116	4	∀𝜈	GPE
cana-5404	116	5	∈	ORG
cana-5404	117	1	+ 𝜉(𝜈)𝜔	GPE
cana-5404	121	1	0	CARDINAL
cana-5404	121	2	∀𝜈 ∈ 𝐿. proof	ORG
cana-5404	123	1	γ(𝜔	PERSON
cana-5404	125	1	17	CARDINAL
cana-5404	125	2	17	CARDINAL
cana-5404	125	3	γ(𝜔)]𝜈 + γ(𝜔)[𝜉(𝜈	DATE
cana-5404	126	1	𝜔]𝜉(𝜈	ORG
cana-5404	127	1	18	CARDINAL
cana-5404	127	2	17	CARDINAL
cana-5404	129	1	19	CARDINAL
cana-5404	129	2	18	CARDINAL
cana-5404	129	3	19	CARDINAL
cana-5404	129	4	γ(𝜔)[𝜉(𝜈	ORG
cana-5404	129	5	𝜔]𝜉(𝜈	ORG
cana-5404	129	6	20	CARDINAL
cana-5404	129	7	20	CARDINAL
cana-5404	129	8	𝑧γ(𝜔)[𝜉(𝜈	PRODUCT
cana-5404	130	1	𝜔]𝜉(𝜈	ORG
cana-5404	131	1	𝑧]𝜔𝜉(𝜈	ORG
cana-5404	131	2	21	CARDINAL
cana-5404	131	3	20	CARDINAL
cana-5404	131	4	21	CARDINAL
cana-5404	133	1	22	CARDINAL
cana-5404	133	2	1.3	CARDINAL
cana-5404	133	3	0	CARDINAL
cana-5404	133	4	∀𝜈	GPE
cana-5404	133	5	∈	ORG
cana-5404	133	6	𝜈]ℬ𝐿[𝜉(𝜈	TIME
cana-5404	133	7	0	CARDINAL
cana-5404	133	8	∀𝜈 ∈ 𝐿.	ORG
cana-5404	133	9	0	CARDINAL
cana-5404	133	10	∀𝜈 ∈ 𝐿.	ORG
cana-5404	134	1	∈	ORG
cana-5404	135	1	0	CARDINAL
cana-5404	135	2	∀𝜈 ∈	ORG
cana-5404	135	3	γ(𝜔	PERSON
cana-5404	136	1	∀𝜈	GPE
cana-5404	136	2	∈	ORG
cana-5404	137	1	2.7	CARDINAL
cana-5404	137	2	2	CARDINAL
cana-5404	137	3	𝑀𝑢𝑙𝑡.	GPE
cana-5404	141	1	∈	ORG
cana-5404	141	2	ℬ.	PERSON
cana-5404	141	3	1074	CARDINAL
cana-5404	141	4	32	CARDINAL
cana-5404	142	1	2025	CARDINAL
cana-5404	142	2	2143	CARDINAL
cana-5404	142	3	2.8	CARDINAL
cana-5404	143	1	∈	ORG
cana-5404	143	2	𝐿[𝛿(𝜈	GPE
cana-5404	143	3	0	CARDINAL
cana-5404	143	4	∀𝜈 ∈ 𝐿. proof	ORG
cana-5404	145	1	γ(𝜔	PERSON
cana-5404	145	2	23	CARDINAL
cana-5404	145	3	23	CARDINAL
cana-5404	147	1	𝜔]𝜉(𝜈	ORG
cana-5404	147	2	24	CARDINAL
cana-5404	147	3	23	CARDINAL
cana-5404	148	1	25	CARDINAL
cana-5404	148	2	24	CARDINAL
cana-5404	148	3	25	CARDINAL
cana-5404	149	1	𝜔]𝜉(𝜈	ORG
cana-5404	149	2	26	CARDINAL
cana-5404	149	3	26	CARDINAL
cana-5404	149	4	26	CARDINAL
cana-5404	150	1	27	CARDINAL
cana-5404	150	2	27	CARDINAL
cana-5404	150	3	∈	ORG
cana-5404	151	1	28	CARDINAL
cana-5404	151	2	𝜉(𝜈)𝑧	ORG
cana-5404	151	3	28	CARDINAL
cana-5404	151	4	0	CARDINAL
cana-5404	153	1	∈	ORG
cana-5404	153	2	𝜔]𝜉(𝜈	ORG
cana-5404	154	1	∈	ORG
cana-5404	154	2	∀𝜈	GPE
cana-5404	154	3	∈	ORG
cana-5404	155	1	29	CARDINAL
cana-5404	155	2	29	CARDINAL
cana-5404	156	1	0	CARDINAL
cana-5404	156	2	∀𝜈	GPE
cana-5404	156	3	𝑧]𝜈𝜉(𝜈	ORG
cana-5404	156	4	0	CARDINAL
cana-5404	156	5	∀𝜈	GPE
cana-5404	156	6	two	CARDINAL
cana-5404	156	7	𝑧][𝜉(𝜈	ORG
cana-5404	156	8	0	CARDINAL
cana-5404	156	9	∀𝜈	GPE
cana-5404	156	10	∈	ORG
cana-5404	156	11	𝜉(𝜈)𝑧	ORG
cana-5404	157	1	0	CARDINAL
cana-5404	157	2	∀𝜈	GPE
cana-5404	157	3	∈	ORG
cana-5404	157	4	𝜈]ℬ𝐿[𝜉(𝜈	TIME
cana-5404	157	5	0	CARDINAL
cana-5404	157	6	∀𝜈 ∈	ORG
cana-5404	157	7	0	CARDINAL
cana-5404	157	8	∀𝜈 ∈ 𝐿.	ORG
cana-5404	159	1	0	CARDINAL
cana-5404	159	2	∀𝜈 ∈	ORG
cana-5404	159	3	γ(𝜔	PERSON
cana-5404	159	4	∈	ORG
cana-5404	160	1	2.9	CARDINAL
cana-5404	162	1	∀𝜈	GPE
cana-5404	162	2	ℬ.	ORG
cana-5404	162	3	1074	CARDINAL
cana-5404	162	4	32	CARDINAL
cana-5404	163	1	2025	DATE
cana-5404	163	2	2144	CARDINAL
cana-5404	163	3	3.1	CARDINAL
cana-5404	163	4	0	CARDINAL
cana-5404	163	5	∈ ℤ	ORG
cana-5404	166	1	0	CARDINAL
cana-5404	168	1	0	CARDINAL
cana-5404	169	1	0	CARDINAL
cana-5404	169	2	0	CARDINAL
cana-5404	169	3	0	CARDINAL
cana-5404	171	1	γ(𝜈)𝜔	PERSON
cana-5404	171	2	0	CARDINAL
cana-5404	171	3	∀𝜈	GPE
cana-5404	171	4	𝜉 ≠ 0	PERSON
cana-5404	171	5	γ(𝜈𝜔	GPE
cana-5404	171	6	1	CARDINAL
cana-5404	171	7	m. n. :	PERSON
cana-5404	172	1	j. math	PERSON
cana-5404	173	1	sci.	ORG
cana-5404	173	2	14(3)(1991	CARDINAL
cana-5404	173	3	615618	DATE
cana-5404	174	1	2	CARDINAL
cana-5404	174	2	martindale iii	PERSON
cana-5404	174	3	w. s. :	PERSON
cana-5404	175	1	amer	PERSON
cana-5404	176	1	21(1969	CARDINAL
cana-5404	176	2	695	CARDINAL
cana-5404	177	1	3	CARDINAL
cana-5404	177	2	𝐶(𝑋	PRODUCT
cana-5404	177	3	121(3)(1996	CARDINAL
cana-5404	177	4	189	CARDINAL
cana-5404	178	1	4	CARDINAL
cana-5404	178	2	m. n.	PERSON
cana-5404	178	3	m. s.	PERSON
cana-5404	178	4	multiplicative	NORP
cana-5404	178	5	9(1)(2007	DATE
cana-5404	178	6	31	CARDINAL
cana-5404	179	1	5	CARDINAL
cana-5404	179	2	ali	PERSON
cana-5404	179	3	s.	PERSON
cana-5404	179	4	𝑀𝑢𝑙𝑡.	GPE
cana-5404	181	1	86(2013	DATE
cana-5404	181	2	65	CARDINAL
cana-5404	182	1	6	CARDINAL
cana-5404	182	2	colloq	PERSON
cana-5404	182	3	13(3)(2006	CARDINAL
cana-5404	182	4	371380	DATE
cana-5404	183	1	7	CARDINAL
cana-5404	183	2	ashraf	PERSON
cana-5404	183	3	m., ali, a.	PERSON
cana-5404	183	4	rani	PERSON
cana-5404	183	5	r.	NORP
cana-5404	183	6	southeast asian	NORP
cana-5404	183	7	29(2005	CARDINAL
cana-5404	183	8	669-675	CARDINAL
cana-5404	184	1	8	CARDINAL
cana-5404	184	2	m.	PERSON
cana-5404	184	3	n., ali	PERSON
cana-5404	184	4	s.	PERSON
cana-5404	184	5	m.	PERSON
cana-5404	187	1	28(2)(2010	CARDINAL
cana-5404	187	2	25	CARDINAL
cana-5404	188	1	9	CARDINAL
cana-5404	188	2	m.	PERSON
cana-5404	188	3	two	CARDINAL
cana-5404	188	4	glasg	PERSON
cana-5404	190	1	j.	PERSON
cana-5404	190	2	33(1991	DATE
cana-5404	190	3	89	CARDINAL
cana-5404	191	1	1074	CARDINAL
cana-5404	191	2	32	CARDINAL
cana-5404	192	1	2025	CARDINAL
cana-5404	192	2	2145	CARDINAL
cana-5404	193	1	10	CARDINAL
cana-5404	194	1	j. okayama univ.	PERSON
cana-5404	194	2	44(2002	CARDINAL
cana-5404	194	3	43	CARDINAL
cana-5404	195	1	11	CARDINAL
cana-5404	195	2	m. s.	PERSON
cana-5404	195	3	a. b. :	PERSON
cana-5404	196	1	j.	PERSON
cana-5404	196	2	5(4)(2003	CARDINAL
cana-5404	196	3	465	CARDINAL
cana-5404	197	1	12	CARDINAL
cana-5404	197	2	bell,	ORG
cana-5404	197	3	h. e.	PERSON
cana-5404	197	4	m. n. :	PERSON
cana-5404	197	5	canad	ORG
cana-5404	199	1	bull	PERSON
cana-5404	199	2	37(4)(1994	CARDINAL
cana-5404	199	3	443	CARDINAL
cana-5404	200	1	13	CARDINAL
cana-5404	200	2	m. :	PERSON
cana-5404	200	3	amer	PERSON
cana-5404	201	1	335(2)(1993	DATE
cana-5404	201	2	525	CARDINAL
cana-5404	202	1	14	CARDINAL
cana-5404	202	2	j.	PERSON
cana-5404	202	3	xu	PERSON
cana-5404	202	4	x. w.	PERSON
cana-5404	203	1	sinica	ORG
cana-5404	203	2	english	LANGUAGE
cana-5404	203	3	1835-1842	DATE
cana-5404	204	1	15	CARDINAL
cana-5404	204	2	yasen	PERSON
cana-5404	204	3	m. and anwar	PERSON
cana-5404	205	1	korean	NORP
cana-5404	206	1	4(43)(2006	CARDINAL
cana-5404	206	2	711	CARDINAL
cana-5404	207	1	16	CARDINAL
cana-5404	207	2	m. s.	PERSON
cana-5404	207	3	internat j. math	PERSON
cana-5404	209	1	sci.	ORG
cana-5404	209	2	6(2005	CARDINAL
cana-5404	209	3	917	CARDINAL
cana-5404	210	1	17	CARDINAL
cana-5404	210	2	h. e.	PERSON
cana-5404	211	1	s.t rizvi	PERSON
cana-5404	211	2	s.m.a.zaidi	ORG
cana-5404	211	3	new delhi	GPE
cana-5404	211	4	india	GPE
cana-5404	211	5	2005	DATE
cana-5404	211	6	1116	DATE