Young Bae Jun, Kyoung Ja Lee, Seok Zun Song, “Quasi-valuation maps based on positive implicative ideals in BCK-algebras”, Algebra Discrete Math., 2018, Volume 26, Issue 1,Pages <nobr>65

RESEARCH ARTICLE

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

Young Bae Jun^a, Kyoung Ja Lee^b, Seok Zun Song^c

^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

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.

MSC: 06F35, 03G25, 03C05

Received: 22.09.2016

Language: English