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On representation of finite lattices

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Abstract

In an earlier article, the authors found sufficient conditions for complexity of the lattice of subquasivarieties of a quasivariety. In the present article, we prove that these conditions allow us to represent finite lattices as relative congruence lattices and relative variety lattices in a uniform way. Some applications are presented.

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Acknowledgements

We thank the referee for having thoroughly read the paper, for his comments and suggestions which helped to improve our paper.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch RAS, Acad. Koptyug prosp. 4, 630090, Novosibirsk, Russia

    A. V. Kravchenko & M. V. Schwidefsky

  2. Novosibirsk State University, Pirogova str. 1, 630090, Novosibirsk, Russia

    A. V. Kravchenko & M. V. Schwidefsky

  3. Siberian Institute of Management (Department of the Russian Academy of National Economy and Public Administration under the President of the Russian Federation), Nizhegorodskaya str. 6, 630102, Novosibirsk, Russia

    A. V. Kravchenko

  4. Novosibirsk State Technical University, Karl Marx prosp. 20, 630073, Novosibirsk, Russia

    A. V. Kravchenko & M. V. Schwidefsky

  5. Institute of Mathematics of the National Academy of Sciences, Chui prosp. 265a, Bishkek, 720071, Kyrgyzstan

    A. M. Nurakunov

Authors
  1. A. V. Kravchenko
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  2. A. M. Nurakunov
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  3. M. V. Schwidefsky
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Corresponding author

Correspondence to M. V. Schwidefsky.

Additional information

Dedicated to Ralph Freese, Bill Lampe, and J. B. Nation on occasion of their 70th birthday.

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This article is part of the topical collection “Algebras and Lattices in Hawaii” edited by W. DeMeo.

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Kravchenko, A.V., Nurakunov, A.M. & Schwidefsky, M.V. On representation of finite lattices. Algebra Univers. 80, 15 (2019). https://doi.org/10.1007/s00012-019-0588-2

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  • DOI: https://doi.org/10.1007/s00012-019-0588-2

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