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On lattices embeddable into subsemigroup lattices. III: Nilpotent semigroups

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Abstract

We prove that the class of the lattices embeddable into subsemigroup lattices of n-nilpotent semigroups is a finitely based variety for all n < ω. Repnitskiĭ showed that each lattice embeds into the subsemigroup lattice of a commutative nilsemigroup of index 2. In this proof he used a result of Bredikhin and Schein which states that each lattice embeds into the suborder lattices of an appropriate order. We give a direct proof of the Repnitskiĭ result not appealing to the Bredikhin-Schein theorem, so answering a question in a book by Shevrin and Ovsyannikov.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    M. V. Semenova

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  1. M. V. Semenova
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Original Russian Text Copyright © 2007 Semenova M. V.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 1, pp. 192–204, January–February, 2007.

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Semenova, M.V. On lattices embeddable into subsemigroup lattices. III: Nilpotent semigroups. Sib Math J 48, 156–164 (2007). https://doi.org/10.1007/s11202-007-0016-2

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  • DOI: https://doi.org/10.1007/s11202-007-0016-2

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