A representation theorem for tense $n\times m$-valued Łukasiewicz-Moisil algebras

Figallo, Aldo Victorio ; Pelaitay, Gustavo

Mathematica Bohemica, Tome 140 (2015) no. 3, pp. 345-360.

Résumé

In 2000, Figallo and Sanza introduced $n\times m$-valued Łukasiewicz-Moisil algebras which are both particular cases of matrix Łukasiewicz algebras and a generalization of $n$-valued Łukasiewicz-Moisil algebras. Here we initiate an investigation into the class {\bf tLM}$_{n\times m}$ of tense $n\times m$-valued Łukasiewicz-Moisil algebras (or tense LM$_{n\times m}$-algebras), namely $n\times m$-valued Łukasiewicz-Moisil algebras endowed with two unary operations called tense operators. These algebras constitute a generalization of tense Łukasiewicz-Moisil algebras (or tense LM$_{n}$-algebras). Our most important result is a representation theorem for tense LM$_{n\times m}$-algebras. Also, as a corollary of this theorem, we obtain the representation theorem given by Georgescu and Diaconescu in 2007, for tense LM$_{n}$-algebras.

Détail

DOI : 10.21136/MB.2015.144400

Classification : 03G20, 06D30
Keywords: $n$-valued Łukasiewicz-Moisil algebra; tense $n$-valued Łukasiewicz-Moisil algebra; $n\times m$-valued Łukasiewicz-Moisil algebra