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Special elements of the lattice of epigroup varieties

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An Erratum to this article was published on 18 June 2016

Abstract

We study special elements of three types (namely, neutral, modular and upper-modular elements) in the lattice of all epigroup varieties. Neutral elements are completely determined (it turns out that only four varieties have this property). We find a strong necessary condition for modular elements that completely reduces the problem of description of corresponding varieties to nilvarieties satisfying identities of some special type. Modular elements are completely classified within the class of commutative varieties, while upper-modular elements are completely determined within the wider class of strongly permutative varieties.

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Authors and Affiliations

  1. Institute of Mathematics and Computer Science, Ural Federal University, Lenina str.51, 620000, Ekaterinburg, Russia

    Vyacheslav Yu. Shaprynskiǐ, Dmitry V. Skokov & Boris M. Vernikov

Authors
  1. Vyacheslav Yu. Shaprynskiǐ
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  2. Dmitry V. Skokov
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  3. Boris M. Vernikov
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Corresponding author

Correspondence to Boris M. Vernikov.

Additional information

Presented by M. Jackson.

The work is supported by Russian Foundation for Basic Research (grant 14-01-00524) and by the Ministry of Education and Science of the Russian Federation (project 2248).

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Shaprynskiǐ, V.Y., Skokov, D.V. & Vernikov, B.M. Special elements of the lattice of epigroup varieties. Algebra Univers. 76, 1–30 (2016). https://doi.org/10.1007/s00012-016-0380-5

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  • DOI: https://doi.org/10.1007/s00012-016-0380-5

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