De Morgan Heyting algebras satisfying the identity x n (′*) ≈ x ( n +1)(′*)

Abstract

In this paper we investigate the sequence of subvarieties SDHn of De Morgan Heyting algebras characterized by the identity x^n (´∗) ≈ x^(n+1)(´∗) . We obtain necessary and sufficient conditions for a De Morgan Heyting algebra to be in SDH_1 by means of its space of prime filters, and we characterize subdirectly irreducible and simple algebras in SDH_1 . We extend these results for finite algebras in the general case SDH_n .