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# On extensions of pseudo-valuations on BCK algebras

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creative_2022_31_1_43_49

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In this paper we define a \textit{pseudo-valuation} on a BCK algebra as a real-valued function satisfying and for every is called a \textit{valuation} if whenever We prove that every pseudo-valuation (valuation) induces a pseudo-metric (metric) on defined by for every where is uniformly continuous in both variables. The aim of this paper is to provide several theorems on extensions of pseudo-valuations (valuations) on BCK algebras.