Abstract

The theory of n × m-valued Łukasiewicz algebras with negation was introduced and studied by the author in [14]. It is worth mentioning that in the particular case m = 2 this new class of algebras coincides with that of n-valued Łukasiewicz algebras. In this work, the research on n × m-valued Łukasiewicz algebras with negation is followed. More precisely, it is proved that this class of algebras is a variety in a different way from that indicated in [14]. Besides, the congruences on these algebras are determined and some of their properties are studied. The main result of this paper is that the principal congurences are equationally definable from which it is inferred that this variety is arithmetical. In addition, it is proved that the congruences on these algebras are regular and that every principal one is a factor congruence.1