Quasi-Valuation Maps on BCK/BCI-Algebras

DOI QR코드

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SONG, SEOK-ZUN;ROH, EUN HWAN;JUN, YOUNG BAE

  • 투고 : 2014.05.30
  • 심사 : 2015.12.02
  • 발행 : 2015.12.23

초록

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.

키워드

BCK/BCI-algerba;subalgebra;ideal;S-quasi-valuation map;I-quasi-valuation map;(pseudo) metric space;uniformly continuous

참고문헌

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과제정보

연구 과제 주관 기관 : Jeju National University