De Morgan algebras with a quasi-Stone operator

T. S. Blyth*, Jie Fang, Lei-bo Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We investigate the class of those algebras (L; A(0), *) in which (L; A(0)) is a de Morgan algebra, (L; *) is a quasi-Stone algebra, and the operations and are linked by the identity x**A(0) = x*A(0)*. We show that such an algebra is subdirectly irreducible if and only if its congruence lattice is either a 2-element chain or a 3-element chain. In particular, there are precisely eight non-isomorphic subdirectly irreducible Stone de Morgan algebras.

Original languageEnglish
Pages (from-to)75-90
Number of pages16
JournalStudia Logica
Volume103
Issue number1
DOIs
Publication statusPublished - Feb 2015

Keywords

  • De Morgan algebra
  • Quasi-Stone algebra
  • QSM-algebra
  • Subdirectly irreducible

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