Varieties of pseudocomplemented Kleene algebras

Abstract

In this paper we study the subdirectly irreducible algebras in the variety ℳ of pseudocomplemented De Morgan algebras by means of their De Morgan p-spaces. We introduce the notion of the body of an algebra ∈ℳ and determine Body() when is subdirectly irreducible. As a consequence of this, in the case of pseudocomplemented Kleene algebras, two special subvarieties arise naturally, for which we give explicit identities that characterise them. We also introduce a subvariety ℬ of ℳ , namely the variety of bundle pseudocomplemented Kleene algebras, fully describe its subvariety lattice and find explicit equational bases for each subvariety. In addition, we study the subvariety ℬ0 of ℬ generated by the simple members of ℬ , determine the structure of the free algebra over a finite set in this variety and their finite weakly projective algebras.