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Codistributive elements of the lattice of semigroup varieties

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Abstract

We prove that if a semigroup variety is a codistributive element of the lattice SEM of all semigroup varieties, then it either coincides with the variety of all semigroups or is a variety of semigroups with completely regular square. We completely classify strongly permutable varieties that are codistributive elements of SEM.We prove that a semigroup variety is a costandard element of the lattice SEMif and only if it is a neutral element of this lattice. In view of results obtained earlier, this gives a complete description of costandard elements of the lattice SEM.

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  1. Ural State University, pr. Lenina 51, Ekaterinburg, 620000, 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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Original Russian Text © B.M. Vernikov, 2011, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2011, No. 7, pp. 13–21.

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Vernikov, B.M. Codistributive elements of the lattice of semigroup varieties. Russ Math. 55, 9–16 (2011). https://doi.org/10.3103/S1066369X11070024

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