Connection between MV\(_n\) algebras and \(n\)-valued Lukasiewicz-Moisil algebras. I (Q1381855)

This paper is concerned with the MV-algebras of C. C. Chang, the \(\text{MV}_n\)-algebras of Grigolia and their connections with the \(n\)-valued Łukasiewicz-Moisil algebras \(\text{LM}_n\). There are three main results, namely that \(\text{MV}_3\)-algebras are the same as \(\text{LM}_4\)-algebras; that for \(n\geq 5\) every \(\text{MV}_n\)-algebra is an \(\text{LM}_n\)-algebra; and that \(\text{LM}_3\)-algebras \([\text{LM}_4\)-algebras] can be constructed from odd [even] \(\text{LM}_n\)-algebras.