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BCK/BCI-ALGEBRAS WITH PSEUDO-VALUATIONS

  • Doh, Myung-Im (Department of Mathematics Gyeongsang National University) ;
  • Kang, Min-Su (Department of Mathematics, Hanyang University)
  • Received : 2010.04.08
  • Accepted : 2010.05.12
  • Published : 2010.06.25

Abstract

Using the Bu$\c{s}$neag's model ([1, 2, 3]), the notion of pseudo-valuations (valuations) on a ${\mathbf{BCK/BCI}}$-algebra is introduced, and a pseudo-metric is induced by a pseudo-valuation on ${\mathbf{BCK/BCI}}$-algebras. Based on the notion of (pseudo) valuation, we show that the binary operation in ${\mathbf{BCK/BCI}}$-algebras is uniformly continuous.

Keywords

(Weak, Positive) pseudo-valuation (Positive) valuation Pseudo-metric induced by pseudo-valuation

References

  1. C. Busneag, Valuations on residuated lattices, An. Univ. Craiova Ser. Mat. Inform. 34 (2007), 21-28.
  2. D. Busneag, Hilbert algebras with valuations, Math. Japon. 44 (1996), 285-289.
  3. D. Busneag, On extensions of pseudo-valuations on Hilbert algebras, Discrete Math. 263 (2003), 11-24. https://doi.org/10.1016/S0012-365X(02)00552-6
  4. Y. S. Huang, BCI-algebra, Science Press, China (2006).
  5. J. Meng, Y. B. Jun, BCK-algebras, Kyungmoon Sa Co., Seoul (1994).

Cited by

  1. Commutative Pseudo Valuations on BCK-Algebras vol.2011, 2011, https://doi.org/10.1155/2011/754047
  2. Commutative pseudo-equality algebras vol.21, pp.16, 2017, https://doi.org/10.1007/s00500-016-2214-y