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Quasivarieties with Definable Relative Principal Subcongruences

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Abstract

For quasivarieties of algebras, we consider the property of having definable relative principal subcongruences, a generalization of the concepts of definable relative principal congruences and definable principal subcongruences. We prove that a quasivariety of algebras with definable relative principal subcongruences has a finite quasiequational basis if and only if the class of its relative (finitely) subdirectly irreducible algebras is strictly elementary. Since a finitely generated relatively congruence-distributive quasivariety has definable relative principal subcongruences, we get a new proof of the result due to D. Pigozzi: a finitely generated relatively congruence-distributive quasivariety has a finite quasi-equational basis.

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Authors and Affiliations

  1. Institute of Mathematics, National Academy of Science, Bishkek, Kyrghyz Republic

    A. M. Nurakunov

  2. Faculty of Mathematics and Information Sciences, Warsaw University of Technology, Warsaw, Poland

    M. M. Stronkowski

  3. Eduard Čech Center, Charles University, Prague, Czech Republic

    M. M. Stronkowski

Authors
  1. A. M. Nurakunov
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  2. M. M. Stronkowski
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Correspondence to M. M. Stronkowski.

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Nurakunov, A.M., Stronkowski, M.M. Quasivarieties with Definable Relative Principal Subcongruences. Stud Logica 92, 109–120 (2009). https://doi.org/10.1007/s11225-009-9188-z

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  • DOI: https://doi.org/10.1007/s11225-009-9188-z

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