Lattices of quasi-equational theories as congruence lattices of semilattices with operators, part II

Kira Adaricheva, J. B. Nation

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

Part I proved that for every quasivariety of structures (which may have both operations and relations) there is a semilattice S with operators such that the lattice of quasi-equational theories of (the dual of the lattice of sub-quasivarieties of ) is isomorphic to Con(S, +, 0, ). It is known that if S is a join semilattice with 0 (and no operators), then there is a quasivariety such that the lattice of theories of is isomorphic to Con(S, +, 0). We prove that if S is a semilattice having both 0 and 1 with a group of operators acting on S, and each operator in fixes both 0 and 1, then there is a quasivariety such that the lattice of theories of is isomorphic to Con(S, +, 0, ).

Original languageEnglish
Article number1250066
JournalInternational Journal of Algebra and Computation
Volume22
Issue number7
DOIs
Publication statusPublished - Nov 2012

Keywords

  • Quasivariety
  • congruence lattice
  • representation
  • semilattice

ASJC Scopus subject areas

  • Mathematics(all)

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