F–multipliers and the localization of LMn×m–algebras

Abstract

In this note, we introduce the notion of n × m-ideal on n × m- valued Łukasiewicz-Moisil algebras (or LMn×m-algebras) which allows us to consider a topology on them. Besides, we define the concept of F-multiplier, where F is a topology on an LMn×m-algebra L, which is used to construct the localization LMn×m-algebra LF. Furthermore, we prove that the LMn×m-algebra of fractions LS associated with an ⋀-closed subset S of L is an LMn×m-algebra of localization. Finally, in the finite case we prove that LS is isomorphic to a special subalgebra of L. Since n-valued Łukasiewicz-Moisil algebras are a particular case of LMn×m-algebras, all these results generalize those obtained in [4] (see also [3]).

Keywords

• n-valued lukasiewicz-moisil algebras
• n × m-valued lukasiewicz-moisil algebras
• f-multiplier
• algebra of fractions
• algebra of localization