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

In this note, we introduce the notion of n × m-ideal on n × m- valued Łukasiewicz-Moisil algebras (or LM_n×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 LM_n×m-algebra L, which is used to construct the localization LM_n×m-algebra L_F. Furthermore, we prove that the LM_n×m-algebra of fractions L_S associated with an ⋀-closed subset S of L is an LM_n×m-algebra of localization. Finally, in the finite case we prove that L_S is isomorphic to a special subalgebra of L. Since n-valued Łukasiewicz-Moisil algebras are a particular case of LM_n×m-algebras, all these results generalize those obtained in [4] (see also [3]).