Varieties of pseudocomplemented Kleene algebras
Diego Castaño, Valeria Castaño, José Patricio Díaz Varela, Marcela Muñoz Santis
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Source: Crossref
Published: Feb 1, 2021
DOI: 10.1002/malq.202000025
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Abstract In this paper we study the subdirectly irreducible algebras in the variety of pseudocomplemented De Morgan algebras by means of their De Morgan p‐spaces. We introduce the notion of the body of an algebra and determine 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 of , 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 of generated by the simple members of , determine the structure of the free algebra over a finite set in this variety and their finite weakly projective algebras.
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