Some New Kinds of BCK-Filters in Bounded BCK-Algebras

Sadegh Khosravi Shoar; Rajab Ali Borzooei

doi:10.18778/0138-0680.2026.12

Authors

Sadegh Khosravi Shoar Fasa University, Department of Mathematics and Computer Science Author https://orcid.org/0000-0003-1167-998X
Rajab Ali Borzooei Shahid Beheshti University, Department of Mathematics Author https://orcid.org/0000-0001-7538-7885

DOI:

https://doi.org/10.18778/0138-0680.2026.12

Keywords:

BCK-filter, implicative BCK-filter, commutative BCK-filter, EQI-filter, EQI-algebras

Abstract

This paper investigates and characterizes some new types of BCK-filters in bounded BCK-algebras. We introduce the notions of EQI-filters, implicative BCK-filters, and commutative BCK-filters. We clarify the relationships among these filters and prove that every implicative BCK-filter is a commutative BCK-filter and every commutative BCK-filter is an EQI-filter, although the converses do not hold in general. We also study these filters in several important subclasses of BCK-algebras. For instance, in involutory BCK-algebras, the notions of EQI-filters, implicative BCK-filters, and commutative BCK-filters coincide, whereas they are distinct in general.

References

C. Bărbăcioru, Positive implicative BCK-algebras, Mathematica Japonica, vol. 38(3) (1993), pp. 513–520.

W. A. Dudek, Y. B. Jun, Poor and crazy filters of BCK-algebras, International Journal of Pure and Applied Mathematical Sciences, vol. 4 (2007), pp. 25–38.

Y. Huang, BCI-Algebra, Science Press, Beijing, China (2006), distributed by Elsevier Science.

Y. Huang, On involutory BCK-algebras, Soochow Journal of Mathematics, vol. 32(1) (2006), pp. 51–57.

Y. Imai, K. Iséki, On Axiom Systems of Propositional Calculi. XIV, Proceedings of the Japan Academy, Series A, Mathematical Sciences, vol. 42(1) (1966), pp. 19–22, DOI: https://doi.org/10.3792/pja/1195522169

K. Iséki, S. Tanaka, An introduction to the theory of BCK-algebras, Mathematica Japonica, vol. 23(1) (1978), pp. 1–26.

J. Meng, On ideals in BCK-algebras, Mathematica Japonica, vol. 40(1) (1994), pp. 143–154.

J. Meng, BCK-filters, Mathematica Japonica, vol. 44(1) (1996), pp. 119–129.

J. Meng, Y. B. Jun, BCK-Algebras, Kyung Moon Sa Co., Seoul, Korea (1994).

S. K. Shoar, EI, involutory and EQI-ideal in bounded BCK-algebras, Afrika Matematika, vol. 27 (2016), pp. 313–324, DOI: https://doi.org/10.1007/s13370-015-0341-8

S. K. Shoar, R. A. Borzooei, R. Moradian, A. Radfar, PC-lattices: A Class of Bounded BCK-algebras, Bulletin of the Section of Logic, vol. 47(1) (2018), pp. 33–44, DOI: https://doi.org/10.18778/0138-0680.47.1.03

S. Tanaka, A New Class of Algebra, Mathematics Seminar Notes, vol. 3 (1975), pp. 37–43, DOI: https://doi.org/10.24546/0100491933