Affiliations: [a] School of Mathematics and Statistics, Anyang Normal University, Anyang, China
| [b] School of Information and Mathematics, Yangtze University, Jingzhou, China
Correspondence:
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Corresponding author. Kuanyun Zhu, School of Information and Mathematics, Yangtze University, Jingzhou, China. E-mail: kyzhu@whu.edu.cn.
Abstract: The concept of pseudo MV-valuations is proposed in the paper, and some related characterizations of pseudo MV-valuations are investigated. The relationships between the pseudo MV-valuations of homomorphic and isomorphic MV-algebras and the relationships between their kernels are presented. We investigate several properties of pseudo MV-metrics induced by pseudo MV-valuations, and obtain that the product of two pseudo MV-metric spaces is a pseudo MV-metric space. Based on the introduced notion of pseudo continuous functions, we get that if a pseudo MV-valuation is contractive, then the binary operations on MV-algebras are pseudo continuous functions. Finally, we construct a congruence relation by using a pseudo MV-valuation, and study some properties of pseudo MV-valuations on quotient MV-algebras.
Keywords: MV-algebra, pseudo MV-valuation, pseudo MV-metric space, pseudo continuous
function
