Quasi-valuation maps based on positive implicative ideals in BCK-algebras

Young Bae Jun, Kyoung Ja Lee, Seok Zun Song

Abstract


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.

Keywords


(positive implicative) ideal, S-quasi-valuation map, I-quasi-valuation map, PI-quasi-valuation map

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