On Polian Algebras
Keywords:
Polian Algebras, Equipotence, Manifolds, Ideals, Annihilators
Abstract
In this paper, polian algebras are introduced. Their properties are investigated. Left absorbing, right absorbing as well as absorbing polian algebras are studied. Manifolds and equipotence are introduced and studied in polian algebras. Moreover, hyperbolic polian algebras are introduced and their properties are investigated.
References
[1] Ebrahimi M. and Izadara A., The Ideal Entropy of BCI- algebras and its Application in Binary Linear Codes, Soft Computing, 2019, 23:39–57.
[2] Francis M. O., Adeniji A. O., Mogbonju M. M., Workdone by m-Topological Transformation Semigroup, International Journal of Mathematical Sciences and Optimization: Theory and Applications, 9(1) (2023), 33–42.
[3] Hu Q. P. and Li X., On BCH algebras, Math. Seminar Notes II, (1983), 313–320.
[4] Ibrahim A., Akinwunmi S. A. and Mogbonju M. M. and Onyeozili I. A., Combinatorial Model of 3- Dimensional Nildempotency Star-like Classes NcWn∗ Partial One To One Semigroups, International Journal of Mathematical Sciences and Optimization: Theory and Applications, 10(1) (2024), 25–33.
[5] Ilojide E., Monics and Krib Maps in Nayo Algebras, Journal of The Nigerian Mathematical Society, 40,(1),(2021), 1–16.
[6] Ilojide E., On Obic Algebras, International Journal of Mathematical Combinatorics, 4(2019), 80–88.
[7] Ilojide E., A Note on Torian Algebras, International Journal of Mathematical Combinatorics, 2(2020), 80–87.
[8] Ilojide E., On Right Distributive Torian Algebras, International Journal of Mathematical Combinatorics ,4(2020), 100–107.
[9] Ilojide E., On Isomorphism Theorems of Torian Algebras, International Journal of Mathematical Combinatorics, 1(2021), 56–61.
[10] Ilojide E., On Ideals of Torian Algebras, International Journal of Mathematical Combinatorics, 2(2020), 101–108.
[11] Ilojide E., Jaiyeola T.G and Olatinwo M. O., On Holomorphy of Fenyves BCI-algebras, Journal of the Nigerian Mathematical Society, 38(2),(2019), 139–155.
[12] Imai y. and Iseki k., On Axiom System of Propositional Calculi, Proc. Japan Acad., 42(1996), 19–22.
[13] Iseki k., An Algebra Related with Propositional calculus, Proc. Japan Acad., 42(1996), 26–29.
[14] Jaiyeola T. G., Ilojide E., Olatinwo M. O. and Smarandache F. S., On the Classification of BolMoufang Type of Some Varieties of Quasi Neutrosophic Triplet Loops (Fenyves BCI-algebras), Symmetry 10(2018),
427. https://doi.org/10.3390/sym10100427.
[15] Jaiyeola T. G., Ilojide E., Saka A. J. and Ilori K.G., On the Isotopy of Some Varieties of Fenyves Quasi Neutrosophic Triplet Loops(Fenyves BCI-algebras), Neutrosophic Sets and Systems, 31(2020), 200–223. DOI: 105281/zenodo.3640219.
[16] Kim H. S., Neggers J. and Ahn S. S., On Pre-Commutative Algebras, Mathematics, 7(2019), 336. doi:10.33390/math7040336.
[17] Neggers J., Sun S. A. and Hee S. K., On Q-algebras, International J. of Math. and Math. Sci. 27(2001), 749–757.
[18] Neggers J. and Kim H. S., On d-algebras, Mathematica Slovaca, 49(1999), 19–26.
[2] Francis M. O., Adeniji A. O., Mogbonju M. M., Workdone by m-Topological Transformation Semigroup, International Journal of Mathematical Sciences and Optimization: Theory and Applications, 9(1) (2023), 33–42.
[3] Hu Q. P. and Li X., On BCH algebras, Math. Seminar Notes II, (1983), 313–320.
[4] Ibrahim A., Akinwunmi S. A. and Mogbonju M. M. and Onyeozili I. A., Combinatorial Model of 3- Dimensional Nildempotency Star-like Classes NcWn∗ Partial One To One Semigroups, International Journal of Mathematical Sciences and Optimization: Theory and Applications, 10(1) (2024), 25–33.
[5] Ilojide E., Monics and Krib Maps in Nayo Algebras, Journal of The Nigerian Mathematical Society, 40,(1),(2021), 1–16.
[6] Ilojide E., On Obic Algebras, International Journal of Mathematical Combinatorics, 4(2019), 80–88.
[7] Ilojide E., A Note on Torian Algebras, International Journal of Mathematical Combinatorics, 2(2020), 80–87.
[8] Ilojide E., On Right Distributive Torian Algebras, International Journal of Mathematical Combinatorics ,4(2020), 100–107.
[9] Ilojide E., On Isomorphism Theorems of Torian Algebras, International Journal of Mathematical Combinatorics, 1(2021), 56–61.
[10] Ilojide E., On Ideals of Torian Algebras, International Journal of Mathematical Combinatorics, 2(2020), 101–108.
[11] Ilojide E., Jaiyeola T.G and Olatinwo M. O., On Holomorphy of Fenyves BCI-algebras, Journal of the Nigerian Mathematical Society, 38(2),(2019), 139–155.
[12] Imai y. and Iseki k., On Axiom System of Propositional Calculi, Proc. Japan Acad., 42(1996), 19–22.
[13] Iseki k., An Algebra Related with Propositional calculus, Proc. Japan Acad., 42(1996), 26–29.
[14] Jaiyeola T. G., Ilojide E., Olatinwo M. O. and Smarandache F. S., On the Classification of BolMoufang Type of Some Varieties of Quasi Neutrosophic Triplet Loops (Fenyves BCI-algebras), Symmetry 10(2018),
427. https://doi.org/10.3390/sym10100427.
[15] Jaiyeola T. G., Ilojide E., Saka A. J. and Ilori K.G., On the Isotopy of Some Varieties of Fenyves Quasi Neutrosophic Triplet Loops(Fenyves BCI-algebras), Neutrosophic Sets and Systems, 31(2020), 200–223. DOI: 105281/zenodo.3640219.
[16] Kim H. S., Neggers J. and Ahn S. S., On Pre-Commutative Algebras, Mathematics, 7(2019), 336. doi:10.33390/math7040336.
[17] Neggers J., Sun S. A. and Hee S. K., On Q-algebras, International J. of Math. and Math. Sci. 27(2001), 749–757.
[18] Neggers J. and Kim H. S., On d-algebras, Mathematica Slovaca, 49(1999), 19–26.
Published
2024-11-10
How to Cite
Ilojide , E. (2024). On Polian Algebras. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 10(4), 45 - 54. Retrieved from http://ijmso.unilag.edu.ng/article/view/2388
Issue
Section
Articles
Copyright (c) 2024 Authors
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
This is an Open Access article distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, adaptation, and reproduction in any medium, provided that the original work is properly cited.
