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Epimorphisms between finite MV-algebras

Aldo V. Figallo, Marina B. Lattanzi

Received December 5, 2014.   First published February 1, 2017.

Abstract: MV-algebras were introduced by Chang to prove the completeness of the infinite-valued Łukasiewicz propositional calculus. Recently, algebraic theory of MV-algebras has been intensively studied. Wajsberg algebras are just a reformulation of Chang MV-algebras where implication is used instead of disjunction. Using these equivalence, in this paper we provide conditions for the existence of an epimorphism between two finite MV-algebras $A$ and $B$. Specifically, we define the mv-functions with domain in the ordered set of prime elements of $B$ and with range in the ordered set of prime elements of $A$, and prove that every epimorphism from $A$ to $B$ can be uniquely constructed from an mv-function.

Keywords: MV-algebras; mv-function; epimorphism

Classification (MSC 2010): 06D35, 08A35

DOI: 10.21136/MB.2017.0077-14

Full text available as PDF.

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