Varieties of Regular Pseudocomplemented de Morgan Algebras

M. E. Adams, Hanamantagouda P. Sankappanavar, Júlia Vaz de Carvalho

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1 Citation (Scopus)

Abstract

In this paper, we investigate the varieties Mn and Kn of regular pseudocomplemented de Morgan and Kleene algebras of range n, respectively. Priestley duality as it applies to pseudocomplemented de Morgan algebras is used. We characterise the dual spaces of the simple (equivalently, subdirectly irreducible) algebras in Mn and explicitly describe the dual spaces of the simple algebras in M1 and K1. We show that the variety M1 is locally finite, but this property does not extend to Mn or even Kn for n =?2. We also show that the lattice of subvarieties of K1 is an ? +?1 chain and the cardinality of the lattice of subvarieties of either K2 or M1 is 2?. A description of the lattice of subvarieties of M1 is given.

Original languageEnglish
Pages (from-to)529-557
Number of pages29
JournalOrder
Volume37
Issue number3
DOIs
Publication statusPublished - 1 Oct 2020

Keywords

  • Discriminator variety
  • Lattice of subvarieties
  • Priestley duality
  • Regular pseudocomplented de Morgan algebra (of range n)
  • Simple algebra
  • Subdirectly irreducible algebra
  • Variety of algebras

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