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Chains and anti-chains in the lattice of epigroup varieties

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Abstract

Let ℰ n be the variety of all epigroups of index ≤n. We prove that, for an arbitrary natural number n, the interval [ℰ n ,ℰn+1] of the lattice of epigroup varieties contains a chain isomorphic to the chain of real numbers with the usual order and an anti-chain of the cardinality continuum.

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References

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Authors and Affiliations

  1. Department of Mathematics and Mechanics, Ural State University, Lenina 51, 620083, Ekaterinburg, Russia

    D. V. Skokov & B. M. Vernikov

Authors
  1. D. V. Skokov
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  2. B. M. Vernikov
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Correspondence to B. M. Vernikov.

Additional information

Communicated by Lev N. Shevrin.

The work was partially supported by the Russian Foundation for Basic Research (grant No. 09-01-12142) and the Federal Education Agency of the Russian Federation (project No. 2.1.1/3537).

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Skokov, D.V., Vernikov, B.M. Chains and anti-chains in the lattice of epigroup varieties. Semigroup Forum 80, 341–345 (2010). https://doi.org/10.1007/s00233-009-9196-3

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  • DOI: https://doi.org/10.1007/s00233-009-9196-3

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