id	sid	eid	entity	type
m-769	1	1	ijo international journal of mathematics	ORG
m-769	1	2	2992-4421	DATE
m-769	2	1	michael n. john* http://ijojournals.com/	PERSON
m-769	2	2	06	CARDINAL
m-769	2	3	12 ||	QUANTITY
m-769	2	4	2023 ||	QUANTITY
m-769	3	1	algebraic	PERSON
m-769	3	2	michael n. john department	PERSON
m-769	3	3	akwaibom state university, nigeria	ORG
m-769	3	4	udoakaotobong.	ORG
m-769	4	1	akwaibom state university, nigeria	ORG
m-769	5	1	x×x	PERSON
m-769	8	1	algebraic cryptography	PERSON
m-769	9	1	1	CARDINAL
m-769	10	1	bowen	PERSON
m-769	10	2	1	CARDINAL
m-769	10	3	29	CARDINAL
m-769	11	1	3	CARDINAL
m-769	11	2	10.5281	CARDINAL
m-769	11	3	06	CARDINAL
m-769	12	1	12 |	TIME
m-769	12	2	2023	CARDINAL
m-769	13	1	9	CARDINAL
m-769	13	2	ijo international journal of mathematics	ORG
m-769	13	3	2992-4421	DATE
m-769	13	4	michael n. john	PERSON
m-769	14	1	06	CARDINAL
m-769	14	2	12 ||	QUANTITY
m-769	14	3	2023 ||	QUANTITY
m-769	16	1	4	CARDINAL
m-769	17	1	x×x	PERSON
m-769	20	1	26	CARDINAL
m-769	20	2	27	CARDINAL
m-769	20	3	31	CARDINAL
m-769	20	4	2	CARDINAL
m-769	20	5	2.1let	ORG
m-769	21	1	1	CARDINAL
m-769	21	2		CARDINAL
m-769	23	1	2	CARDINAL
m-769	23	2		CARDINAL
m-769	25	1	3	CARDINAL
m-769	25	2		CARDINAL
m-769	25	3	t×x→x	PERSON
m-769	26	1		CARDINAL
m-769	26	2	μ(h	GPE
m-769	26	3	x))=μ(gh	DATE
m-769	27	1	2.2	CARDINAL
m-769	29	1	10.5281	CARDINAL
m-769	29	2	06	CARDINAL
m-769	30	1	12 |	TIME
m-769	30	2	2023	CARDINAL
m-769	31	1	10	CARDINAL
m-769	31	2	ijo international journal of mathematics	ORG
m-769	31	3	2992-4421	DATE
m-769	32	1	michael n. john* http://ijojournals.com/	PERSON
m-769	32	2	06	CARDINAL
m-769	32	3	12 ||	QUANTITY
m-769	32	4	2023 ||	QUANTITY
m-769	34	1	μ	ORG
m-769	36	1	2.3	CARDINAL
m-769	39	1	μ(t	DATE
m-769	43	1	2.2.let	CARDINAL
m-769	43	2	g×x→x	ORG
m-769	44	1	x×x	ORG
m-769	44	2	two	CARDINAL
m-769	45	1	2.3	CARDINAL
m-769	49	1	x×x	PERSON
m-769	49	2	two	CARDINAL
m-769	49	3	hour	TIME
m-769	50	1	the hour	TIME
m-769	50	2	3	CARDINAL
m-769	50	3	4	CARDINAL
m-769	51	1	two	CARDINAL
m-769	52	1	the hour	TIME
m-769	54	1	10.5281	CARDINAL
m-769	54	2	06	CARDINAL
m-769	54	3	12	CARDINAL
m-769	55	1	2023	CARDINAL
m-769	55	2	11	CARDINAL
m-769	55	3	ijo international journal of mathematics	ORG
m-769	55	4	2992-4421	DATE
m-769	56	1	michael n. john* http://ijojournals.com/	PERSON
m-769	56	2	06	CARDINAL
m-769	56	3	12 ||	QUANTITY
m-769	56	4	2023 ||	QUANTITY
m-769	58	1	3	CARDINAL
m-769	59	1	3.1.let	CARDINAL
m-769	59	2	g×x→x	ORG
m-769	60	1	x×x	PRODUCT
m-769	60	2	x∼y	ORG
m-769	60	3	x)=limn→∞μ(gn	ORG
m-769	61	1	two	CARDINAL
m-769	62	1	3.2.consider	CARDINAL
m-769	63	1	two	CARDINAL
m-769	63	2	3.3	CARDINAL
m-769	65	1	two	CARDINAL
m-769	68	1	two	CARDINAL
m-769	69	1	3.4.let	CARDINAL
m-769	69	2	g×x→x	ORG
m-769	70	1	x×x	PRODUCT
m-769	71	1	ϕ(xy)=ϕ(x)ϕ(y	PERSON
m-769	72	1	10.5281	CARDINAL
m-769	72	2	06	CARDINAL
m-769	73	1	12 |	TIME
m-769	73	2	2023	CARDINAL
m-769	74	1	12	CARDINAL
m-769	74	2	ijo international journal of mathematics	ORG
m-769	74	3	2992-4421	DATE
m-769	75	1	michael n. john* http://ijojournals.com/	PERSON
m-769	75	2	06	CARDINAL
m-769	75	3	12 ||	QUANTITY
m-769	75	4	2023 ||	QUANTITY
m-769	77	1	3.5	CARDINAL
m-769	81	1	3.6	CARDINAL
m-769	83	1	integers h	ORG
m-769	86	1	4.	CARDINAL
m-769	86	2	4.1	CARDINAL
m-769	87	1	t×x→x	PERSON
m-769	87	2	1	CARDINAL
m-769	87	3		CARDINAL
m-769	88	1	x×x	PERSON
m-769	88	2	sn)⊆t	PRODUCT
m-769	89	1	μ(tn	CARDINAL
m-769	89	2	x)→f(x	ORG
m-769	89	3	μ(sn	GPE
m-769	89	4	x)→g(x	NORP
m-769	89	5	10.5281	CARDINAL
m-769	89	6	06	CARDINAL
m-769	90	1	12 |	TIME
m-769	90	2	2023	CARDINAL
m-769	91	1	13	CARDINAL
m-769	91	2	ijo international journal of mathematics	ORG
m-769	91	3	2992-4421	DATE
m-769	92	1	michael n. john* http://ijojournals.com/	PERSON
m-769	92	2	06	CARDINAL
m-769	92	3	12 ||	QUANTITY
m-769	92	4	2023 ||	QUANTITY
m-769	93	1		CARDINAL
m-769	94	1	μ(sn	GPE
m-769	94	2		CARDINAL
m-769	95	1	sn	ORG
m-769	96	1		CARDINAL
m-769	97	1	2	CARDINAL
m-769	97	2		CARDINAL
m-769	97	3	e. 3	ORG
m-769	98	1		CARDINAL
m-769	98	2	f∈e	ORG
m-769	99	1	−1	DATE
m-769	99	2	t.	GPE
m-769	99	3	−1	DATE
m-769	99	4		CARDINAL
m-769	100	1		CARDINAL
m-769	100	2	f−1∈e	ORG
m-769	101	1	4	CARDINAL
m-769	101	2		CARDINAL
m-769	104	1	x.	GPE
m-769	104	2	only one	CARDINAL
m-769	105	1	10.5281	CARDINAL
m-769	105	2	06	CARDINAL
m-769	106	1	12 |	TIME
m-769	106	2	2023	CARDINAL
m-769	107	1	14	CARDINAL
m-769	107	2	ijo international journal of mathematics	ORG
m-769	107	3	2992-4421	DATE
m-769	107	4	michael n. john* http://ijojournals.com/	PERSON
m-769	107	5	06	CARDINAL
m-769	107	6	12 ||	QUANTITY
m-769	107	7	2023 ||	QUANTITY
m-769	108	1	1.proximal	CARDINAL
m-769	108	2	x.	GPE
m-769	109	1		CARDINAL
m-769	110	1		CARDINAL
m-769	110	2	x∼y	ORG
m-769	110	3	x)=limn→∞μ(gn	ORG
m-769	112	1		CARDINAL
m-769	112	2	x∼y	ORG
m-769	112	3	x)=limn→∞μ(gn	ORG
m-769	112	4	limn→∞μ(hn	PERSON
m-769	112	5	y)=limn→∞μ(hn	PERSON
m-769	114	1	limn→∞μ(gn⋅hn	ORG
m-769	114	2	x)=limn→∞μ(gn	ORG
m-769	114	3	μ(hn	DATE
m-769	114	4	y)=limn→∞μ(hn	PERSON
m-769	115	1	2	CARDINAL
m-769	116	1	only one	CARDINAL
m-769	117	1		CARDINAL
m-769	118	1		CARDINAL
m-769	118	2	x∼y	ORG
m-769	118	3	x)=limn→∞μ(gn	ORG
m-769	119	1	only one	CARDINAL
m-769	119	2	gn −1	ORG
m-769	120	1	y∼x	DATE
m-769	121	1		CARDINAL
m-769	121	2	x∼y	ORG
m-769	121	3	x)=limn→∞μ(gn	ORG
m-769	121	4	limn→∞μ(hn	PERSON
m-769	121	5	y)=limn→∞μ(hn	PERSON
m-769	123	1	limn→∞μ(gn⋅hn	ORG
m-769	123	2	x)=limn→∞μ(gn	ORG
m-769	123	3	μ(hn	DATE
m-769	123	4	y)=limn→∞μ(hn	PERSON
m-769	124	1	only one	CARDINAL
m-769	124	2	e. ijo	ORG
m-769	124	3	10.5281	CARDINAL
m-769	124	4	06	CARDINAL
m-769	125	1	12 |	TIME
m-769	125	2	2023	CARDINAL
m-769	126	1	15	CARDINAL
m-769	126	2	ijo international journal of mathematics	ORG
m-769	126	3	2992-4421	DATE
m-769	127	1	michael n. john* http://ijojournals.com/	PERSON
m-769	127	2	06	CARDINAL
m-769	127	3	12 ||	QUANTITY
m-769	127	4	2023 ||	QUANTITY
m-769	128	1	t×x→x	PERSON
m-769	129	1	x×x	ORG
m-769	130	1	1	CARDINAL
m-769	130	2	algebraic structure	PERSON
m-769	130	3		CARDINAL
m-769	130	4	x×x	PRODUCT
m-769	131	1	2	CARDINAL
m-769	131	2		CARDINAL
m-769	133	1		CARDINAL
m-769	133	2		CARDINAL
m-769	133	3		CARDINAL
m-769	133	4		CARDINAL
m-769	134	1	10.5281	CARDINAL
m-769	134	2	06	CARDINAL
m-769	135	1	12 |	TIME
m-769	135	2	2023	CARDINAL
m-769	136	1	16	CARDINAL
m-769	136	2	ijo international journal of mathematics	ORG
m-769	136	3	2992-4421	DATE
m-769	136	4	michael n. john* http://ijojournals.com/	PERSON
m-769	136	5	06	CARDINAL
m-769	136	6	12 ||	QUANTITY
m-769	136	7	2023 ||	QUANTITY
m-769	137	1		CARDINAL
m-769	137	2		CARDINAL
m-769	141	1	t×x→x	PERSON
m-769	142	1	x×x	PRODUCT
m-769	143	1	1	CARDINAL
m-769	143	2		CARDINAL
m-769	144	1	ϕ(xy)=ϕ(x)ϕ(y	PERSON
m-769	145	1	2	CARDINAL
m-769	145	2		CARDINAL
m-769	145	3		CARDINAL
m-769	145	4		CARDINAL
m-769	146	1	10.5281	CARDINAL
m-769	146	2	06	CARDINAL
m-769	147	1	12 |	TIME
m-769	147	2	2023	CARDINAL
m-769	148	1	17	CARDINAL
m-769	148	2	ijo international journal of mathematics	ORG
m-769	148	3	2992-4421	DATE
m-769	149	1	michael n. john* http://ijojournals.com/	PERSON
m-769	149	2	06	CARDINAL
m-769	149	3	12 ||	QUANTITY
m-769	149	4	2023 ||	QUANTITY
m-769	150	1		CARDINAL
m-769	150	2		CARDINAL
m-769	150	3	t. homomorphisms	ORG
m-769	151	1		CARDINAL
m-769	151	2		CARDINAL
m-769	151	3	t. homomorphisms	ORG
m-769	152	1		CARDINAL
m-769	152	2	topological	ORG
m-769	152	3		CARDINAL
m-769	154	1	5	CARDINAL
m-769	154	2	x.	GPE
m-769	157	1	10.5281	CARDINAL
m-769	157	2	06	CARDINAL
m-769	158	1	12 |	TIME
m-769	158	2	2023	CARDINAL
m-769	159	1	18	CARDINAL
m-769	159	2	ijo international journal of mathematics	ORG
m-769	159	3	2992-4421	DATE
m-769	160	1	michael n. john* http://ijojournals.com/	PERSON
m-769	160	2	06	CARDINAL
m-769	160	3	12 ||	QUANTITY
m-769	160	4	2023 ||	QUANTITY
m-769	161	1	6	CARDINAL
m-769	161	2	michael nsikan john	PERSON
m-769	161	3	akwaibom state university	ORG
m-769	162	1	michael	PERSON
m-769	162	2	combinatorics	ORG
m-769	162	3	blockchain technology	ORG
m-769	163	1	17]–[31	CARDINAL
m-769	163	2	1	CARDINAL
m-769	163	3	r.	PERSON
m-769	163	4	1971	DATE
m-769	165	1	american	NORP
m-769	165	2	152(1	CARDINAL
m-769	165	3	1-33	DATE
m-769	166	1	2	CARDINAL
m-769	166	2	r., &steprāns	ORG
m-769	166	3	j.	PERSON
m-769	166	4	1976	DATE
m-769	168	1	pacific journal of mathematics	ORG
m-769	168	2	99	CARDINAL
m-769	169	1	3	CARDINAL
m-769	169	2	a. (	PERSON
m-769	169	3	2005	DATE
m-769	171	1	ergodic	ORG
m-769	171	2	25(6	CARDINAL
m-769	171	3	1731-1745	CARDINAL
m-769	172	1	4	CARDINAL
m-769	172	2	n., & strauss	ORG
m-769	172	3	1998	DATE
m-769	174	1	semigroup	PERSON
m-769	174	2	57(3	DATE
m-769	174	3	355	CARDINAL
m-769	175	1	5	CARDINAL
m-769	175	2	michael n. john &udoaka o. g	PERSON
m-769	175	3	2023	CARDINAL
m-769	177	1	international journal of research	ORG
m-769	177	2	4	CARDINAL
m-769	177	3	3312-3315	DATE
m-769	177	4	2023	CARDINAL
m-769	179	1	6	CARDINAL
m-769	179	2	michael n. john	PERSON
m-769	179	3	udoaka o. g.	PERSON
m-769	179	4	2395-1990	DATE
m-769	179	5	10	CARDINAL
m-769	179	6	6,pp	CARDINAL
m-769	180	1	01-10	DATE
m-769	180	2	november-december 2023	DATE
m-769	181	1	7	CARDINAL
m-769	181	2	michael n. john	PERSON
m-769	182	1	g.	PERSON
m-769	182	2	alex musa,"key	PERSON
m-769	182	3	10	CARDINAL
m-769	182	4	6	CARDINAL
m-769	182	5	pp52-56	PRODUCT
m-769	183	1	10.5281	CARDINAL
m-769	183	2	06	CARDINAL
m-769	184	1	12 |	TIME
m-769	184	2	2023	CARDINAL
m-769	185	1	19	CARDINAL
m-769	185	2	2992-4421	DATE
m-769	186	1	michael n. john* http://ijojournals.com/	PERSON
m-769	186	2	06	CARDINAL
m-769	186	3	12 ||	QUANTITY
m-769	186	4	2023 ||	QUANTITY
m-769	187	1	8	CARDINAL
m-769	187	2	michael n. john	PERSON
m-769	188	1	boniface o. nwala	PERSON
m-769	188	2	isar journal of science and technology	ORG
m-769	188	3	1	CARDINAL
m-769	188	4	1	CARDINAL
m-769	188	5	pp21-24	PRODUCT
m-769	189	1	9	CARDINAL
m-769	189	2	michael n john	PERSON
m-769	189	3	udoakaotobong g	PERSON
m-769	189	4	alex musa	PERSON
m-769	190	1	1	CARDINAL
m-769	191	1	2023	CARDINAL
m-769	191	2	4(2	DATE
m-769	191	3	32	CARDINAL
m-769	191	4	10.22271	CARDINAL
m-769	191	5	10	CARDINAL
m-769	191	6	michael nsikan john	PERSON
m-769	191	7	udoakaotobong.	PERSON
m-769	192	1	alex musa	PERSON
m-769	193	1	2023	CARDINAL
m-769	195	1	gph international journal of mathematics	ORG
m-769	197	1	11	CARDINAL
m-769	197	2	john	PERSON
m-769	197	3	michael n.	PERSON
m-769	197	4	h. e., &udoaka	PERSON
m-769	197	5	o. g.	PERSON
m-769	197	6	2023	CARDINAL
m-769	199	1	international journal of research	ORG
m-769	199	2	4(11	CARDINAL
m-769	200	1	https://doi.org/10.5281/zenodo.10207210	PERSON
m-769	201	1	12	CARDINAL
m-769	201	2	michael n. john	PERSON
m-769	202	1	boniface o. nwala	PERSON
m-769	202	2	perpetua ngozi	PERSON
m-769	203	1	2023	CARDINAL
m-769	205	1	gph international journal of mathematics	ORG
m-769	206	1	https://doi.org/10.5281/zenodo.10207316	PERSON
m-769	207	1	13	CARDINAL
m-769	207	2	michael n. john	PERSON
m-769	207	3	obukohwo, victor, & henry etarogheneegbogho	ORG
m-769	208	1	2023	CARDINAL
m-769	209	1	rsa	ORG
m-769	210	1	gph international journal of mathematics	ORG
m-769	210	2	06(11	CARDINAL
m-769	212	1	14	CARDINAL
m-769	212	2	john michael	PERSON
m-769	213	1	n.	PERSON
m-769	213	2	bassey e. e.	PERSON
m-769	213	3	udoaka o.g.	PERSON
m-769	213	4	2023	CARDINAL
m-769	213	5	q8	GPE
m-769	213	6	11	CARDINAL
m-769	213	7	4	CARDINAL
m-769	213	8	20-26	CARDINAL
m-769	215	1	15	CARDINAL
m-769	215	2	michael n. john	PERSON
m-769	215	3	otobong g. udoaka	PERSON
m-769	216	1	2023	CARDINAL
m-769	218	1	11(4	DATE
m-769	218	2	111–125	CARDINAL
m-769	220	1	16	CARDINAL
m-769	220	2	michael n. john	PERSON
m-769	220	3	i. u	PERSON
m-769	220	4	2023	CARDINAL
m-769	220	5	11	CARDINAL
m-769	220	6	4	CARDINAL
m-769	220	7	2731	CARDINAL
m-769	221	1	ijo	ORG
m-769	221	2	10.5281	CARDINAL
m-769	221	3	06	CARDINAL
m-769	222	1	12 |	TIME
m-769	222	2	2023	CARDINAL
m-769	222	3	20	CARDINAL
m-769	223	1	ijo international journal of mathematics	ORG
m-769	223	2	2992-4421	DATE
m-769	223	3	michael n. john*	PERSON
m-769	224	1	06	CARDINAL
m-769	224	2	12 ||	QUANTITY
m-769	224	3	2023 ||	QUANTITY
m-769	225	1	17	CARDINAL
m-769	225	2	michael n. john	PERSON
m-769	225	3	effiong, &	ORG
m-769	226	1	2023	CARDINAL
m-769	227	1	2321	CARDINAL
m-769	227	2	4767	CARDINAL
m-769	227	3	2321 4759	DATE
m-769	227	4	11	CARDINAL
m-769	227	5	6 || nov	QUANTITY
m-769	227	6	dec.	GPE
m-769	227	7	2023 ||	QUANTITY
m-769	228	1	01-04	CARDINAL
m-769	229	1	18	CARDINAL
m-769	229	2	michael n. j.	PERSON
m-769	229	3	ochonogor n.	PERSON
m-769	229	4	2023	CARDINAL
m-769	229	5	11	CARDINAL
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