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

Kira Adaricheva, J. B. Nation

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We show that for every quasivariety of structures (where both functions and relations are allowed) 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, . As a consequence, new restrictions on the natural quasi-interior operator on lattices of quasi-equational theories are found.

Original languageEnglish
Article number1250065
JournalInternational Journal of Algebra and Computation
Issue number7
Publication statusPublished - Nov 1 2012



  • Quasivariety
  • congruence lattice
  • quasi-equational theory
  • semilattice

ASJC Scopus subject areas

  • Mathematics(all)

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