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

In this paper we investigate the sequence of subvarieties $ {mathcal {SDH}_n} $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 $ {mathcal {SDH}_1} $ by means of its space of prime filters, and we characterize subdirectly irreducible and simple algebras in $ {mathcal {SDH}_1} $. We extend these results for finite algebras in the general case $ {mathcal {SDH}_n} $. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim