image-algebra of fractions and maximal image-algebra of fractions Original Research Article

The aim of this paper is to define the notions of image-valued Lukasiewicz-Moisil algebra of fractions and maximal algebra of fractions taking as a guide-line the elegant construction of a complete ring of fractions by partial morphisms introduced by [Lambek, 1996. Lectures on Rings and Modules, p. 36]. For some informal explanations of the notion of fraction see [Lambek, 1996. Lectures on Rings and Modules, p. 36] In the last part of this paper we prove the existence of a maximal n-valued Lukasiewicz–Moisil algebra of fractions for an n-valued Lukasiewicz–Moisil algebra (Theorem 3.2) and we give an explicit description of this image-valued Lukasiewicz–Moisil algebra for some classes of image-valued Lukasiewicz–Moisil algebras (finite, chains, Boolean algebras).