Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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FUZZY QUOTIENT STRUCTURES OF BCK-ALGEBRAS INDUCED BY FUZZY BCK-FILTERS

  • Jun, Young-Bae (Department of Mathematics Education(and RINS) Gyeongsang National University)
  • Published : 2006.01.01
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Abstract

In this paper, we establish a generalization of fundamental homomorphism theorem in BCK-algebras by using fuzzy BCK-filters. We prove that if ${\mu}$. (resp. v) is a fuzzy BCK-filter of abounded BCK-algebra X (resp. Y), then $\frac{X{\times}Y}{{\mu}{\times}v}{\approxeq}X/{\mu}{\times}Y/v;\;and\;if\;{\mu}$ and F is a BCK-filter in a bounded BCK-algebra X such that $F/{\mu}$ is a BCK-filter of $X/{\mu}$, then $\frac{X/{\mu}}{F/{\mu}}{\approxeq}X/F$.

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References

  1. Y. B. Jun, S. S. Ahn and H. S. Kim, On quotient BCK-algberas via fuzzy BCK- filters, J. Fuzzy Math. 7 (1999), no. 2, 465-471
  2. Y. B. Jun, S. M. Hong and J. Meng, Fuzzy BCK-filters, Math. Japonica 47 (1998), no. 1, 45-49
  3. Y. B. Jun and F. L. Zhang, Fuzzy prime and fuzzy irreducible BCK-filters in BCK-algebras, Demonstratio Math. 31 (1998), no. 3, 519-527
  4. J. Meng, BCK-filters, Math. Japonica 44 (1996), no. 1, 119-129

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