Varieties of pseudocomplemented Kleene algebras

In this paper we study the subdirectly irreducible algebras in the variety PCDM of pseudocomplemented De Morgan algebras by means of their De Morgan p‐spaces. We introduce the notion of the body of an algebra L∈PCDM and determine Body(L) when L is subdirectly irreducible. As a consequence of this, i...

Full description

Saved in:
Bibliographic Details
Published in:Mathematical logic quarterly 2021-02, Vol.67 (1), p.88-104
Main Authors: Castaño, Diego, Castaño, Valeria, Varela, José Patricio Díaz, Santis, Marcela Muñoz
Format: Article
Language:English
Subjects:
Algebra
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper we study the subdirectly irreducible algebras in the variety PCDM of pseudocomplemented De Morgan algebras by means of their De Morgan p‐spaces. We introduce the notion of the body of an algebra L∈PCDM and determine Body(L) when L 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 BPK of PCDM, 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 BPK0 of BPK generated by the simple members of BPK, determine the structure of the free algebra over a finite set in this variety and their finite weakly projective algebras.
ISSN:0942-5616
1521-3870
DOI:10.1002/malq.202000025