Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Quasi-Valuation Maps on BCK/BCI-Algebras

  • SONG, SEOK-ZUN (Department of Mathematics, Jeju National University) ;
  • ROH, EUN HWAN (Department of Mathematics Education, Chinju National University of Education) ;
  • JUN, YOUNG BAE (Department of Mathematics Education, Gyeongsang National University)
  • Received : 2014.05.30
  • Accepted : 2015.12.02
  • Published : 2015.12.23
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Abstract

The notion of quasi-valuation maps based on a subalgebra and an ideal in BCK/BCI-algebras is introduced, and then several properties are investigated. Relations between a quasi-valuation map based on a subalgebra and a quasi-valuation map based on an ideal is established. In a BCI-algebra, a condition for a quasi-valuation map based on an ideal to be a quasi-valuation map based on a subalgebra is provided, and conditions for a real-valued function on a BCK/BCI-algebra to be a quasi-valuation map based on an ideal are discussed. Using the notion of a quasi-valuation map based on an ideal, (pseudo) metric spaces are constructed, and we show that the binary operation * in BCK-algebras is uniformly continuous.

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References

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Cited by

  1. Quotient Structures of BCK/BCI-Algebras Induced by Quasi-Valuation Maps vol.7, pp.2, 2018, https://doi.org/10.3390/axioms7020026