NEW VARIETIES OF BCI ALGEBRAS
Keywords:
Palindromicity, almost palindromicity, hyper-palindromicity, pointwise palindromicity
Abstract
A BCI algebra is said to form a variety if it satisfies certain axioms. New varieties of BCI algebras, namely; palindromic, almost palindromic, hyper-palindromic and point-wise palindromic BCI algebras are introduced in this paper. These algebras are characterized by distinct axiomatic configurations. Their algebraic properties are investigated. The relationships that exist between the varieties are discussed. Necessary and sufficient conditions for the transformation of one variety to another are presented. Moreover, given any arbitrary algebras of type (2,0), we present conditions for such algebras to belong to any of the new varieties of BCI algebras.
References
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[2] S.S. Ahn and K. S. So, On Generalized upper sets in BE-algebras, Bull. Korean Math. Soc. 46(2009), 281–287.
[3] M. Ebrahimi and A. Izadara, The Ideal Entropy of BCI- algebras and its Application in Binary Linear Codes, Soft Computing, 2019, 23:39–57.
[4] Q. P. Hu and X. Li, On BCH algebras, Math. Seminar Notes II, (1983), 313–320.
[5] E. Ilojide, Monics and Krib Maps in Nayo Algebras, Journal of The Nigerian Mathematical Society, 40,(1),(2021), 1–16.
[6] E. Ilojide, On Obic Algebras, International Journal of Mathematical Combinatorics, 4(2019), 80–88.
[7] E. Ilojide, On Isomorphism Theorems of Torian Algebras, International Journal of Mathematical Combinatorics, 1(2021), 56–61.
[8] E. Ilojide, On Ideals of Torian Algebras, International Journal of Mathematical Combinatorics, 2(2020), 101–108.
[9] E. Ilojide, On Lojid Algebras, International Journal of Mathematical Analysis and Modelling, 7(2),(2024), 369–379.
[10] E. Ilojide, Stabilizers of Lojid Algebras, International Journal of Mathematical Analysis and Modelling, 7(2),(2024), 464–473.
[11] E. Ilojide, A Note on Torian Algebras, International Journal of Mathematical Combinatorics, 2(2020), 80–87.
[12] E. Ilojide, On Right Distributive Torian Algebras, International Journal of Mathematical Combinatorics ,4(2020), 100–107.
[13] Ilojide E., On Kreb Algebras, Journal of Algebraic Hyperstructures and Logical Algebras 5(2)(2024), 169–182.
[14] E. Ilojide, Homomorphisms of Q algebras, Analele Universitatii din Oradea Fascicola Matematica, 28,(2),(2021), 5–13.
[15] E. Ilojide, T. G. Jaiyeola and M. O. Olatinwo, On Holomorphy of Fenyves BCI-algebras, Journal of the Nigerian Mathematical Society, 38(2),(2019), 139–155.
[16] Y. Imai and K. Iseki, On Axiom System of Propositional Calculi, Proc. Japan Acad., 42(1996), 19–22.
[17] K. Iseki, An Algebra Related with Propositional calculus, Proc. Japan Acad., 42(1996), 26–29.
[18] T. G. Jaiyeola, E. Ilojide, M. O. Olatinwo and F. S. Smarandache, On the Classification of Bol- Moufang Type of Some Varieties of Quasi Neutrosophic Triplet Loops (Fenyves BCI-algebras), Symmetry 10(2018), 427. https://doi.org/10.3390/sym10100427.
[19] T. G. Jaiyeola, E. Ilojide, A. J. Saka and K. G. Ilori, 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.
[20] Y. B. Jun, Positive Implicative BE-filters of BE-algebras Based on Lukasiewicz Fuzzy Sets, Journal of Algebraic Hyperstructures and Logical Algebras 4(1), (2023), 1–11.
[21] H. S. Kim and Y. H. Kim, On BE-algebras, Sci. Math. Jpn. 66(2007),113–116.
[22] H. S. Kim, J. Neggers and S. S. Ahn, On Pre-Commutative Algebras, Mathematics, 7(2019), 336. doi:10.33390/math7040336.
[23] J. Neggers, S. A. Sun and S. K. Hee, On Q-algebras, International J. of Math. and Math. Sci. 27(2001), 749–757.
[24] J. Neggers and H. S. Kim, On d-algebras, Mathematica Slovaca, 49(1999), 19–26.
[25] A. Razaei, A. Borumand Saeid and Q. Zhan, Fuzzy Congruence Relations on Pseudo BE- algebras, Journal of Algebraic Hyperstructures and Logical Agebras, 1(2), (2020), 31–43.
Published
2025-10-31
How to Cite
ILOJIDE, E. (2025). NEW VARIETIES OF BCI ALGEBRAS. Unilag Journal of Mathematics and Applications, 5(1), 1 - 12. Retrieved from https://lagjma.unilag.edu.ng/article/view/2772
Section
Articles
Copyright (c) 2025 EMMANUEL ILOJIDE
This work is licensed under a Creative Commons Attribution 4.0 International License.
