Epimorphisms between finite MV-algebras

Abstract

MV-algebras were introduced by Chang to prove the completeness of the infinite-valued Lukasiewicz 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.