A topological duality for tense LMn-algebras and applications

Abstract

In 2007, tense n-valued Lukasiewicz-Moisil algebras (or tense LMn-algebras) were introduced by Diaconescu and Georgescu as an algebraic counterpart of the tense n-valued Moisil logic. In this article we continue the study of tense LMn-algebras initiated by Figallo and Pelaitay (2014, Log. J. IGPL, 22, 255-267). More precisely, we determine a topological duality for these algebras. This duality enables us not only to describe the tense LMn-congruences on a tense LMn-algebra, but also to characterize the simple and subdirectly irreducible tense LMn-algebras. Furthermore, by means of the aforementioned duality, a representation theorem for tense LMn-algebras is proved, which was formulated and proved by a different method by Georgescu and Diaconescu.