Regular double p-algebras

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

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

In this paper, we investigate the variety RDP of regular double p-algebras and its subvarieties RDPn, n ≥ 1, of range n. First, we present an explicit description of the subdirectly irreducible algebras (which coincide with the simple algebras) in the variety RDP1 and show that this variety is locally finite. We also show that the lattice of subvarieties of RDP1, LV (RDP1), is isomorphic to the lattice of down sets of the poset {1} ⊕ (N × N). We describe all the subvarieties of RDP1 and conclude that LV (RDP1) is countably infinite. An equational basis for each proper subvariety of RDP1 is given. To study the subvarieties RDPn with n ≥ 2, Priestley duality as it applies to regular double p-algebras is used. We show that each of these subvarieties is not locally finite. In fact, we prove that its 1-generated free algebra is infinite and that the lattice of its subvarieties has cardinality 2ℵ:0. We also use Priestley duality to prove that RDP and each of its subvarieties RDPn are generated by their finite members.

Original languageEnglish
Pages (from-to)15-34
Number of pages20
JournalMATHEMATICA SLOVACA
Volume69
Issue number1
DOIs
Publication statusPublished - 25 Feb 2019

Keywords

  • discriminator variety
  • double Heyting algebra
  • equational basis
  • lattice of subvarieties
  • Priestley duality
  • regular double p-algebra
  • simple algebra
  • subdirectly irreducible algebra

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