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Identities and quasiidentities in the lattice of overcommutative semigroup varieties

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Abstract

We describe overcommutative varieties of semigroups whose lattice of overcommutative subvarieties satisfies a non-trivial identity or quasiidentity. These two properties turn out to be equivalent.

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Acknowledgement

The author is grateful to Professor B. Vernikov for helpful discussions.

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Authors and Affiliations

  1. Institute of Mathematics and Computer Science, Ural Federal University, Lenina 51, 620083, Ekaterinburg, Russia

    V. Y. Shaprynski

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  1. V. Y. Shaprynski
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Correspondence to V. Y. Shaprynski.

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Communicated by Lev N. Shevrin.

The article was partially supported by the Russian Foundation for Basic Research (grant No. 10-01-00524) and the Ministry of Education and Science of the Russian Federation (project No. 2.1.1/13995).

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Shaprynski, V.Y. Identities and quasiidentities in the lattice of overcommutative semigroup varieties. Semigroup Forum 86, 202–211 (2013). https://doi.org/10.1007/s00233-012-9403-5

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  • DOI: https://doi.org/10.1007/s00233-012-9403-5

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