n×m−valued Lukasiewicz-Moisil algebras with two modal operators

In 2000, Figallo and Sanza introduced the n×m−valued Lukasiewicz-Moisil algebras, which are a particular case of Matrix Lukasiewicz algebras, and a nontrivial generalization of n−valued Lukasiewicz-Moisil algebras. Here we start a research on the class of n × m−valued Lukasiewicz-Moisil algebras endowed with two modal operators (or 2mLMn×m−algebras). These algebras constitute a common generalization of both weak-tense Boolean algebras and weak-tense nvalued Lukasiewicz-Mosil algebras. Our most important result is a representation theorem for 2mLMn×m−algebras. In addition, as a corollary to the previous theorem, we obtain the representation theorem given by Chiriţă in 2012 for weaktense n−valued Lukasiewicz-Moisil algebras.