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Proofs of definability of some varieties and sets of varieties of semigroups

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Abstract

We show that many important varieties and sets of varieties of semigroups may be defined by relatively simple and transparent first-order formulas in the lattice of all semigroup varieties.

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Notes

  1. We note that the paper [8], as well as the articles [6, 9] mentioned in Sect. 5 below have dealt with the lattice of equational theories of semigroups, that is, the dual of SEM rather than the lattice SEM itself. When reproducing results from [6, 8, 9], we adapt them to the terminology of the present note.

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Acknowledgements

The author thanks Dr. Olga Sapir for many stimulating discussions and to the anonymous referee for a number of useful remarks.

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Authors and Affiliations

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

    B. M. Vernikov

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  1. B. M. Vernikov
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Correspondence to B. M. Vernikov.

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Communicated by Lev N. Shevrin.

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

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Vernikov, B.M. Proofs of definability of some varieties and sets of varieties of semigroups. Semigroup Forum 84, 374–392 (2012). https://doi.org/10.1007/s00233-012-9377-3

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