Ahn, Sun-Shin;Kwon, Seok-Hwan

  • Published : 2008.04.30


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.


BCC-algebra;uniformity;(BCC-)ideal;topological BCC-algebras


  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
  4. J. Hao, Ideal Theory of BCC-algebras, Sci. Math. Japo. 3 (1998), 373-381
  5. K. Iseki and S. Tanaka, An introduction to the theory of BCK-algebras, Math. Japon. 23 (1978), 1-26
  6. Y. B. Jun and H. S. Kim, Uniform structures in positive implication algebras, Intern. Math. J. 2 (2002), no. 2, 215-219
  7. Y. B. Jun and E. H. Roh, On uniformities of BCK-algebras, Commun. Korean Math. Soc. 10 (1995), no. 1, 11-14
  8. J. Meng and Y. B. Jun, BCK-algebras, Kyungmoonsa, Seoul, Korea, 1994
  9. B. T. Sims, Fundamentals of Topology, Macmillan Publishing Co., Inc., New York, 1976
  10. A. Wronski, BCK-algebras do not form a variety, Math. Japon. 28 (1983), 211-213
  11. D. S. Yoon and H. S. Kim, Uniform structures in BCI-algebras, Commun. Korean Math. Soc. 17 (2002), no. 3, 403-407
  12. Y. Imai and K. Iseki, On axiom system of propositional calculi XIV, Proc. Japan Academy 42 (1966), 19-22
  13. Y. Komori, The class of BCC-algebras is not a variety, Math. Japon. 29 (1984), 391-394