Quasi-valuation maps based on positive implicative ideals in BCK-algebras
Young Bae Juna, Kyoung Ja Leeb, Seok Zun Songc
a Department of Mathematics Education, Gyeongsang National University,
Jinju 52828, Korea
b Department of Mathematics Education, Hannam University, Daejeon 34430, Korea
c Department of Mathematics, Jeju National University, Jeju 63243, Korea
The notion of PI-quasi-valuation maps of a BCK-algebra is introduced, and related properties are investigated. The relationship between an I-quasi-valuation map and a PI-quasi-valuation map is examined. Conditions for an I-quasi-valuation map to be a PI-quasi-valuation map are provided, and conditions for a real-valued function on a BCK-algebra to be a quasi-valuation map based on a positive implicative ideal are founded. The extension property for a PI-quasi-valuation map is established.
(positive implicative) ideal, S-quasi-valuation map, I-quasi-valuation map, PI-quasi-valuation map.
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MSC: 06F35, 03G25, 03C05
Young Bae Jun, Kyoung Ja Lee, Seok Zun Song, “Quasi-valuation maps based on positive implicative ideals in BCK-algebras”, Algebra Discrete Math., 26:1 (2018), 65–75
Citation in format AMSBIB
\by Young~Bae~Jun, Kyoung~Ja~Lee, Seok~Zun~Song
\paper Quasi-valuation maps based on positive implicative ideals in BCK-algebras
\jour Algebra Discrete Math.
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