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Algebra and Discrete Mathematics, 2018, Volume 26, Issue 1, Pages 65–75 (Mi adm670)  
RESEARCH ARTICLE

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
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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.
Received: 22.09.2016
Document Type: Article
MSC: 06F35, 03G25, 03C05
Language: English
Citation: 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
\Bibitem{JunLeeSon18}
\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.
\yr 2018
\vol 26
\issue 1
\pages 65--75
\mathnet{http://mi.mathnet.ru/adm670}
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