Algebraic functions in Łukasiewicz implication algebras

In this article we study algebraic functions in {→, 1}-subreducts of MV-algebras, also known as Łukasiewicz implication algebras. A function is algebraic on an algebra A if it is definable by a conjunction of equations on A. We fully characterize algebraic functions on every Łukasiewicz implication algebra belonging to a finitely generated variety. The main tool to accomplish this is a factorization result describing algebraic functions in a subproduct in terms of the algebraic functions of the factors. We prove a global representation theorem for finite Łukasiewicz implication algebras which extends a similar one already known for Tarski algebras. This result together with the knowledge of algebraic functions allowed us to give a partial description of the lattice of classes axiomatized by sentences of the form ∀∃!∧ p ≈ q within the variety generated by the 3-element chain.Fil: Campercholi, Miguel Alejandro Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaFil: Castaño, Diego Nicolás. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Díaz Varela, José Patricio. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Sur. Departamento de Matemática; Argentin