Mathematica Bohemica, Vol. 142, No. 4, pp. 345-355, 2017
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.
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Affiliations: 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: avfigallo@gmail.com; Marina B. Lattanzi, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de La Pampa, Av. Uruguay 151, 6300 Santa Rosa, Argentina, e-mail: mblatt@exactas.unlpam.edu.ar
