On bi-topological BCK-algebras

Volume 28, Issue 3, pp 306--315 http://dx.doi.org/10.22436/jmcs.028.03.08

Publication Date: June 26, 2022 Submission Date: April 19, 2022 Revision Date: May 18, 2022 Accteptance Date: May 28, 2022

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 817 Downloads
• 1568 Views

Authors

R. A. Mohammed - Department of Mathematics, College of Basic Education, University of Duhok, Kurdistan Region, Iraq. Gh. H. Rasheed - Department of Mathematics, College of Basic Education, University of Duhok, Kurdistan Region, Iraq. A. B. Khalaf - Department of Mathematics, College of Science, University of Duhok, Kurdistan Region, Iraq.

Abstract

In this paper, we present the concept of bi-topological BCK-algebra. Several characterizations and properties of this concept are obtained. Also, the concept of BCK-ideal of a BCK-algebra is defined and some of its properties are found.

Share and Cite

Keywords

• BCK-algebra
• bi-topological BCK-algebra
• BCK-ideal

MSC

•  06F35
•  54B10
•  54A05

References

• [1] R. A. Alo, E. Y. Deeba, Topologies of BCK-algebras, Math. Japon., 31 (1986), 841--853
  • View Article
  • MathSciNet


• [2] K. E. Belleza, J. P. Vilela, On B-ideals in a topological B-algebra and the uniform B-topological space, Eur. J. Pure Appl. Math., 13 (2020), 830--839
  • View Article
  • MathSciNet


• [3] R. A. Borzooei, M. Bakhshi, The lattice structure of ideals of a BCK-algebra, J. Mult.-Valued Logic Soft Comput., 18 (2012), 387--399
  • View Article
  • MathSciNet


• [4] A. Dvurečenskij, S. Pulmannová, New trends in quantum structures, Kluwer Academic Publishers, Dordrecht (2000)
  • View Article
  • MathSciNet


• [5] R. Engelking, General Topology, PWN-Polish Scientific Publishers, Warszawa (1977)
  • MathSciNet
  • Google Scholar
  • MATH


• [6] N. C. Gonzaga, Analyzing Some Structural Properties of Topological B-Algebras, Int. J. Math. Math. Sci., 2019 (2019), 7 pages
  • View Article
  • MathSciNet


• [7] Y. Imai, K. Iseki, On axiom systems of propositional calculi. XIV, Proc. Japan Acad., 42 (1966), 19--22
  • View Article
  • MathSciNet


• [8] K. Iseki, An algebra related with a propositional calculus, Proc. Japan Acad., 42 (1966), 26--29
  • View Article
  • MathSciNet


• [9] Y. B. Jun, X. L. Xin, D. S. Lee, On Topological BCI-Algebras, Inform. Sci., 116 (1999), 253--261
  • View Article
  • MathSciNet


• [10] J. C. Kelly, Bitopological spaces, Proc. London Math. Soc. (3), 13 (1963), 71--89
  • View Article
  • MathSciNet


• [11] D. S. Lee, D. N. Ryu, Notes on topological BCK-algebras, Sci. Math., 1 (1998), 231--235
  • View Article
  • MathSciNet
  • Google Scholar


• [12] S. Mehrshad, J. Golzarpoor, On topological BE-algebras, Math. Morav., 21 (2017), 1--13
  • View Article
  • MathSciNet
  • Google Scholar


• [13] J. Meng, Y. B. Jun, BCK-algebras, Kyung Moon Sa Co., Seoul (1994)
  • Google Scholar


• [14] A. Satirad, A. Iampan, Topological UP-algebras, Discuss. Math. Gen. Algebra Appl., 39 (2019), 231--250
  • View Article
  • MathSciNet


• [15] Q. Zhang, C. L. Mi, X. C. Wang, Y. H. Cui, Y. L. Zhang, Negative implicative BCK-algebras, Proceedings of Annual Conference of China Institute of Communications, 2010 (2010), 273--276
  • View Article
  • Google Scholar