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- Title
Varieties of pseudocomplemented Kleene algebras.
- Authors
Castaño, Diego; Castaño, Valeria; Varela, José Patricio Díaz; Santis, Marcela Muñoz
- Abstract
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.
- Subjects
ALGEBRA; ALGEBRAIC varieties; VARIETIES (Universal algebra)
- Publication
Mathematical Logic Quarterly, 2021, Vol 67, Issue 1, p88
- ISSN
0942-5616
- Publication type
Article
- DOI
10.1002/malq.202000025