Mathematica Bohemica, online first, 11 pp.

Epimorphisms between finite MV-algebras

Aldo V. Figallo, Marina B. Lattanzi

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

Aldo V. Figallo, Instituto de Ciencias Básicas, Universidad Nacional de San Juan, Av. Ignacio de la Roza 230 Oeste, 5400 San Juan, Argentina, e-mail:; Marina B. Lattanzi, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de La Pampa, Av. Uruguay 151, 6300 Santa Rosa, Argentina, e-mail:

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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