id	sid	eid	entity	type
m-1141	1	1	koch	GPE
m-1141	1	2	wallace	PERSON
m-1141	1	3	1956	DATE
m-1141	2	1	separativity	ORG
m-1141	2	2	algebraic regularity	PERSON
m-1141	2	3	burmistrovich	ORG
m-1141	3	1	koch	GPE
m-1141	3	2	wallace	PERSON
m-1141	7	1	j. tom∗	ORG
m-1141	8	1	abasi & akwa ibom	ORG
m-1141	10	1	akwa ibom state university	ORG
m-1141	10	2	ijo international journal of mathematics	ORG
m-1141	10	3	2992-4421	DATE
m-1141	10	4	08	CARDINAL
m-1141	11	1	9 | september 2025	TIME
m-1141	12	1	1	CARDINAL
m-1141	12	2	s. udo	PERSON
m-1141	12	3	akwa ibom state university	ORG
m-1141	13	1	otobongawasi@aksu.edu.ng	PERSON
m-1141	13	2	1	CARDINAL
m-1141	13	3	koch	GPE
m-1141	13	4	wallace	PERSON
m-1141	14	1	16	CARDINAL
m-1141	15	1	∈	ORG
m-1141	15	2	⊆	CARDINAL
m-1141	15	3	⊆	CARDINAL
m-1141	17	1	this algebraic de�	PERSON
m-1141	17	2	1	CARDINAL
m-1141	17	3	12	CARDINAL
m-1141	19	1	16	CARDINAL
m-1141	20	1	koch	GPE
m-1141	20	2	wallace	PERSON
m-1141	21	1	anderson	PERSON
m-1141	22	1	11	CARDINAL
m-1141	24	1	12	CARDINAL
m-1141	25	1	22	CARDINAL
m-1141	27	1	9	CARDINAL
m-1141	28	1	hewitt	PERSON
m-1141	29	1	6	CARDINAL
m-1141	30	1	shourijeh	PERSON
m-1141	31	1	2	CARDINAL
m-1141	32	1	burmistrovich	PERSON
m-1141	34	1	13	CARDINAL
m-1141	35	1	burmistrovich	ORG
m-1141	35	2	16	CARDINAL
m-1141	37	1	19	CARDINAL
m-1141	41	1	2	CARDINAL
m-1141	41	2	2.1	CARDINAL
m-1141	44	1	∈	ORG
m-1141	44	2	2.2	CARDINAL
m-1141	45	1	groupoid	ORG
m-1141	45	2	∈	ORG
m-1141	45	3	∗	CARDINAL
m-1141	46	1	2.3	CARDINAL
m-1141	47	1	∈ s	ORG
m-1141	47	2	e. ijo international journal of mathematics	ORG
m-1141	47	3	2992-4421	DATE
m-1141	47	4	08	CARDINAL
m-1141	48	1	9 | september 2025	TIME
m-1141	49	1	2 de�nition	QUANTITY
m-1141	49	2	2.4	CARDINAL
m-1141	50	1	∈	ORG
m-1141	52	1	1,4,5	CARDINAL
m-1141	53	1	3	CARDINAL
m-1141	53	2	3.1	CARDINAL
m-1141	54	1	two	CARDINAL
m-1141	54	2	∈	ORG
m-1141	55	1	15	CARDINAL
m-1141	55	2	3.2	CARDINAL
m-1141	57	1	22	CARDINAL
m-1141	59	1	20	CARDINAL
m-1141	59	2	asa	ORG
m-1141	59	3	bsa	ORG
m-1141	59	4	bsb	ORG
m-1141	59	5	3.1	CARDINAL
m-1141	59	6	1	CARDINAL
m-1141	59	7	12	CARDINAL
m-1141	60	1	∈	ORG
m-1141	62	1	ab)2	NORP
m-1141	64	1	b(ab)a	DATE
m-1141	64	2	b(ba	ORG
m-1141	67	1	b. ijo international journal of mathematics	ORG
m-1141	67	2	2992-4421	DATE
m-1141	67	3	08	CARDINAL
m-1141	68	1	9 | september 2025	TIME
m-1141	68	2	3 4	CARDINAL
m-1141	68	3	4.1	CARDINAL
m-1141	70	1	g ∈	PERSON
m-1141	70	2	1	CARDINAL
m-1141	70	3	2	CARDINAL
m-1141	70	4	3	CARDINAL
m-1141	70	5	e ∧ e = e (idempotency	ORG
m-1141	73	1	4.2	CARDINAL
m-1141	74	1	operation ∧.	ORG
m-1141	74	2	⋃	DATE
m-1141	75	1	⊆	CARDINAL
m-1141	78	1	∈	ORG
m-1141	78	2	1	CARDINAL
m-1141	78	3	∈	ORG
m-1141	78	4	∈	ORG
m-1141	79	1	ijo international journal of mathematics	ORG
m-1141	79	2	2992-4421	DATE
m-1141	79	3	08	CARDINAL
m-1141	80	1	9 | september 2025	TIME
m-1141	80	2	4	CARDINAL
m-1141	84	1	4.3	CARDINAL
m-1141	86	1	∈	ORG
m-1141	86	2	al b ⇐⇒ s1a = s1b	ORG
m-1141	88	1	∈	ORG
m-1141	89	1	∈	ORG
m-1141	89	2	two	CARDINAL
m-1141	93	1	∈	ORG
m-1141	93	2	4.4	CARDINAL
m-1141	94	1	∈	ORG
m-1141	94	2	⇐	CARDINAL
m-1141	94	3	⇒ s1a ⊆	ORG
m-1141	94	4	∈	ORG
m-1141	94	5	⊆	CARDINAL
m-1141	95	1	ijo international journal of mathematics	ORG
m-1141	95	2	2992-4421	DATE
m-1141	95	3	08	CARDINAL
m-1141	96	1	9 | september 2025	TIME
m-1141	96	2	5	CARDINAL
m-1141	96	3	∈	ORG
m-1141	96	4	⊆	CARDINAL
m-1141	97	1	3	CARDINAL
m-1141	97	2	8	DATE
m-1141	97	3	10,17,19	CARDINAL
m-1141	97	4	21	CARDINAL
m-1141	97	5	4.1	CARDINAL
m-1141	99	1	∈	ORG
m-1141	99	2	sas = sbs ⇒ ∃x ∈ s	PERSON
m-1141	101	1	sas = sbs	ORG
m-1141	101	2	aj b.	PERSON
m-1141	101	3	∈	ORG
m-1141	101	4	alx	ORG
m-1141	103	1	aj	PERSON
m-1141	103	2	sas = sbs	PERSON
m-1141	104	1	∈	ORG
m-1141	104	2	⊆	CARDINAL
m-1141	104	3	1	CARDINAL
m-1141	105	1	5	CARDINAL
m-1141	105	2	5.1	CARDINAL
m-1141	105	3	koch	PERSON
m-1141	105	4	wallace	PERSON
m-1141	105	5	16	CARDINAL
m-1141	106	1	∈	ORG
m-1141	106	2	1	CARDINAL
m-1141	106	3	⊆	CARDINAL
m-1141	106	4	2	CARDINAL
m-1141	107	1	⊆ sab	QUANTITY
m-1141	109	1	9	CARDINAL
m-1141	110	1	arab	NORP
m-1141	113	1	5.1	CARDINAL
m-1141	114	1	⋃	TIME
m-1141	114	2	⊆	CARDINAL
m-1141	118	1	∈	ORG
m-1141	119	1	∈	ORG
m-1141	119	2	∈	ORG
m-1141	120	1	2	CARDINAL
m-1141	120	2	ab ∈	ORG
m-1141	120	3	2	CARDINAL
m-1141	121	1	∈	ORG
m-1141	121	2	∈	ORG
m-1141	121	3	f ≤ e. hence	PERSON
m-1141	123	1	second	ORDINAL
m-1141	125	1	5.1	CARDINAL
m-1141	126	1	⋃	TIME
m-1141	128	1	∈	ORG
m-1141	128	2	∈	ORG
m-1141	128	3	ab ∈	ORG
m-1141	129	1	∈	ORG
m-1141	129	2	ijo international journal of mathematics	ORG
m-1141	129	3	2992-4421	DATE
m-1141	130	1	08	CARDINAL
m-1141	131	1	9 | september 2025	TIME
m-1141	132	1	6 1	CARDINAL
m-1141	134	1	2	CARDINAL
m-1141	134	2	⊆	CARDINAL
m-1141	137	1	∈	ORG
m-1141	137	2	∈	ORG
m-1141	138	1	1	CARDINAL
m-1141	139	1	∈	ORG
m-1141	140	1	t ∈ sg	ORG
m-1141	140	2	∈	ORG
m-1141	140	3	∈	ORG
m-1141	141	1	g ∧ e ∧ f	PERSON
m-1141	141	2	ab ∈	ORG
m-1141	142	1	sh∧ea→	ORG
m-1141	145	1	2	CARDINAL
m-1141	145	2	⊆	CARDINAL
m-1141	146	1	ab ∈	ORG
m-1141	149	1	unions	ORG
m-1141	151	1	5.1	CARDINAL
m-1141	152	1	7→	CARDINAL
m-1141	153	1	16	CARDINAL
m-1141	154	1	5.2	CARDINAL
m-1141	155	1	burmistrovich	ORG
m-1141	155	2	10	CARDINAL
m-1141	158	1	7	CARDINAL
m-1141	158	2	6	CARDINAL
m-1141	159	1	two	CARDINAL
m-1141	159	2	5.2	CARDINAL
m-1141	159	3	second	ORDINAL
m-1141	159	4	5.1	CARDINAL
m-1141	160	1	5.1	CARDINAL
m-1141	160	2	koch	GPE
m-1141	160	3	wallace	PERSON
m-1141	162	1	koch	GPE
m-1141	162	2	wallace	PERSON
m-1141	164	1	1	CARDINAL
m-1141	164	2	2	CARDINAL
m-1141	165	1	3	CARDINAL
m-1141	165	2	4	CARDINAL
m-1141	167	1	ijo international journal of mathematics	ORG
m-1141	167	2	2992-4421	DATE
m-1141	167	3	08	CARDINAL
m-1141	168	1	9 | september 2025	TIME
m-1141	168	2	7	CARDINAL
m-1141	168	3	1	CARDINAL
m-1141	168	4	a. h. cli�	PERSON
m-1141	168	5	g. b. preston	PERSON
m-1141	168	6	american mathematical society	ORG
m-1141	168	7	1961	DATE
m-1141	169	1	2	CARDINAL
m-1141	169	2	b. t. shourijeh	PERSON
m-1141	169	3	j. vol.	PERSON
m-1141	170	1	26	CARDINAL
m-1141	170	2	4	CARDINAL
m-1141	172	1	483	CARDINAL
m-1141	172	2	2004	DATE
m-1141	173	1	3	CARDINAL
m-1141	173	2	soviet	NORP
m-1141	173	3	american mathematical society	ORG
m-1141	173	4	2014	DATE
m-1141	174	1	4	CARDINAL
m-1141	174	2	d. d. miller	NORP
m-1141	174	3	tran	PERSON
m-1141	175	1	amer	PERSON
m-1141	178	1	82, 1956	DATE
m-1141	179	1	5	CARDINAL
m-1141	179	2	d. rees	PERSON
m-1141	179	3	the cambridge philosophical society	ORG
m-1141	180	1	36	CARDINAL
m-1141	180	2	4	CARDINAL
m-1141	181	1	387	CARDINAL
m-1141	181	2	400 1940	DATE
m-1141	182	1	6	CARDINAL
m-1141	182	2	e. hewitt	PERSON
m-1141	182	3	h. s. zuckerman	PERSON
m-1141	183	1	amer	PERSON
m-1141	185	1	83	DATE
m-1141	186	1	70-97	CARDINAL
m-1141	187	1	7	CARDINAL
m-1141	187	2	i. e. burmistrovitch	PERSON
m-1141	188	1	z. vol	PERSON
m-1141	189	1	6	CARDINAL
m-1141	190	1	284	CARDINAL
m-1141	190	2	299, 1965	DATE
m-1141	191	1	8	CARDINAL
m-1141	191	2	ann.	PERSON
m-1141	193	1	172	CARDINAL
m-1141	193	2	1951	DATE
m-1141	194	1	9	CARDINAL
m-1141	194	2	j. east	ORG
m-1141	194	3	m. higgins	PERSON
m-1141	195	1	101	CARDINAL
m-1141	195	2	1	CARDINAL
m-1141	196	1	77	CARDINAL
m-1141	196	2	2020	DATE
m-1141	197	1	10	CARDINAL
m-1141	197	2	10	CARDINAL
m-1141	197	3	1	CARDINAL
m-1141	198	1	102	CARDINAL
m-1141	198	2	111	CARDINAL
m-1141	198	3	2022	CARDINAL
m-1141	199	1	11	CARDINAL
m-1141	199	2	l. w. anderson	PERSON
m-1141	199	3	r. p. hunter	PERSON
m-1141	199	4	r. j. koch	PERSON
m-1141	200	1	ams journal	ORG
m-1141	201	1	521	CARDINAL
m-1141	201	2	1965	DATE
m-1141	202	1	12	CARDINAL
m-1141	202	2	98	CARDINAL
m-1141	202	3	362	CARDINAL
m-1141	202	4	1986	DATE
m-1141	203	1	13	CARDINAL
m-1141	203	2	m. petrich	PERSON
m-1141	203	3	charles babbage	PERSON
m-1141	203	4	1984	DATE
m-1141	204	1	14	CARDINAL
m-1141	204	2	n. kumar	PERSON
m-1141	204	3	b. kumar	PERSON
m-1141	204	4	70	CARDINAL
m-1141	204	5	9	CARDINAL
m-1141	204	6	8�11	TIME
m-1141	204	7	2024	DATE
m-1141	205	1	15	CARDINAL
m-1141	205	2	r. thakur	PERSON
m-1141	205	3	11	CARDINAL
m-1141	205	4	5	CARDINAL
m-1141	205	5	2023	CARDINAL
m-1141	206	1	16	CARDINAL
m-1141	206	2	r. j. koch	PERSON
m-1141	206	3	a. d. wallace	PERSON
m-1141	207	1	j.	PERSON
m-1141	207	2	24	DATE
m-1141	207	3	193	CARDINAL
m-1141	207	4	196, 1957	DATE
m-1141	208	1	17	CARDINAL
m-1141	208	2	r. u. ndubisi	PERSON
m-1141	208	3	o. g. udoaka	PERSON
m-1141	209	1	5no	ORDINAL
m-1141	210	1	1	CARDINAL
m-1141	211	1	59	CARDINAL
m-1141	211	2	66	DATE
m-1141	211	3	2016	DATE
m-1141	212	1	10.20454	CARDINAL
m-1141	212	2	1083	CARDINAL
m-1141	213	1	ijo international journal of mathematics	ORG
m-1141	213	2	2992-4421	DATE
m-1141	213	3	08	CARDINAL
m-1141	214	1	9 | september 2025	TIME
m-1141	215	1	8	CARDINAL
m-1141	215	2	18	CARDINAL
m-1141	216	1	9	CARDINAL
m-1141	216	2	3	CARDINAL
m-1141	217	1	90�100	CARDINAL
m-1141	217	2	2023	CARDINAL
m-1141	220	1	19	CARDINAL
m-1141	220	2	o. tom	PERSON
m-1141	220	3	a. musa	PERSON
m-1141	220	4	8	CARDINAL
m-1141	220	5	11	CARDINAL
m-1141	221	1	2456	CARDINAL
m-1141	221	2	3315	DATE
m-1141	221	3	2023	CARDINAL
m-1141	222	1	20	CARDINAL
m-1141	222	2	w. d. burgess	PERSON
m-1141	222	3	r. raphael	PERSON
m-1141	222	4	conrad	ORG
m-1141	223	1	16	CARDINAL
m-1141	224	1	133	CARDINAL
m-1141	224	2	140, 1978	DATE
m-1141	225	1	21	CARDINAL
m-1141	225	2	x. mary	PERSON
m-1141	226	1	2023	CARDINAL
m-1141	227	1	22	CARDINAL
m-1141	228	1	i. krasilnikova	PERSON
m-1141	229	1	arxiv	PERSON
m-1141	229	2	math/0311414v1	PERSON
m-1141	230	1	2003	DATE
m-1141	231	1	ijo international journal of mathematics	ORG
m-1141	231	2	2992-4421	DATE
m-1141	231	3	08	CARDINAL
m-1141	232	1	9 | september 2025	TIME
m-1141	232	2	9	CARDINAL