Siberian Mathematical Journal

, Volume 48, Issue 1, pp 156–164 | Cite as

On lattices embeddable into subsemigroup lattices. III: Nilpotent semigroups

  • M. V. Semenova
Article

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.

Keywords

lattice semigroup sublattice variety 

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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • M. V. Semenova
    • 1
  1. 1.Sobolev Institute of MathematicsNovosibirskRussia

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