Varieties of pseudocomplemented Kleene algebras

CASTAÑO, VALERIA; VARELA, JOSÉ PATRICIO DÍAZ; CASTAÑO, DIEGO; SANTIS, MARCELA MUÑOZ

MATHEMATICAL LOGIC QUARTERLY

WILEY-V C H VERLAG GMBH

Año: 2021 vol. 67 p. 88 - 104

0942-5616

In this paper we study the subdirectly irreducible algebras in the variety (Formula presented.) of pseudocomplemented De Morgan algebras by means of their De Morgan p-spaces. We introduce the notion of the body of an algebra (Formula presented.) and determine (Formula presented.) when (Formula presented.) 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 (Formula presented.) of (Formula presented.), 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 (Formula presented.) of (Formula presented.) generated by the simple members of (Formula presented.), determine the structure of the free algebra over a finite set in this variety and their finite weakly projective algebras.