Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

TOPOLOGICAL PROPERTIES IN BCC-ALGEBRAS

  • Ahn, Sun-Shin (Department of Mathematics Education Dongguk University) ;
  • Kwon, Seok-Hwan (Department of Mathematics Education Dongguk University)
  • Published : 2008.04.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we show how to associate certain topologies with special ideals of BCC-algebras on these BCC-algebras. We show that it is natural for BCC-algebras to be topological BCC-algebras with respect to theses topologies. Furthermore, we show how certain standard properties may arise. In addition we demonstrate that it is natural for these topologies to have many clopen sets and thus to be highly connected via the ideal theory of BCC-algebras.

Keywords

References

  1. W. A. Dudek, The number of subalgebras of finite BCC-algebras, Bull. Inst. Math. Academia Sinica 20 (1992), 129-136
  2. W. A. Dudek, On proper BCC-algebras, Bull. Inst. Math. Academia Sinica 20 (1992), 137-150
  3. W. A. Dudeck and X. Zhang, On ideals and congruences in BCC-algebras, Czecho Math. J. 48(123) (1998), 21-29 https://doi.org/10.1023/A:1022407325810
  4. J. Hao, Ideal Theory of BCC-algebras, Sci. Math. Japo. 3 (1998), 373-381
  5. Y. Imai and K. Iseki, On axiom system of propositional calculi XIV, Proc. Japan Academy 42 (1966), 19-22 https://doi.org/10.3792/pja/1195522169
  6. K. Iseki and S. Tanaka, An introduction to the theory of BCK-algebras, Math. Japon. 23 (1978), 1-26
  7. Y. B. Jun and H. S. Kim, Uniform structures in positive implication algebras, Intern. Math. J. 2 (2002), no. 2, 215-219
  8. Y. B. Jun and E. H. Roh, On uniformities of BCK-algebras, Commun. Korean Math. Soc. 10 (1995), no. 1, 11-14
  9. Y. Komori, The class of BCC-algebras is not a variety, Math. Japon. 29 (1984), 391-394
  10. J. Meng and Y. B. Jun, BCK-algebras, Kyungmoonsa, Seoul, Korea, 1994
  11. B. T. Sims, Fundamentals of Topology, Macmillan Publishing Co., Inc., New York, 1976
  12. A. Wronski, BCK-algebras do not form a variety, Math. Japon. 28 (1983), 211-213
  13. D. S. Yoon and H. S. Kim, Uniform structures in BCI-algebras, Commun. Korean Math. Soc. 17 (2002), no. 3, 403-407 https://doi.org/10.4134/CKMS.2002.17.3.403