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



In this paper we investigate the sequence of subvarieties equation imageof De Morgan Heyting algebras characterized by the identity xn(′*)x(n+1)(′*). We obtain necessary and sufficient conditions for a De Morgan Heyting algebra to be in equation image by means of its space of prime filters, and we characterize subdirectly irreducible and simple algebras in equation image. We extend these results for finite algebras in the general case equation image. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim