The wreath product of atoms of the lattice of semigroup varieties

Tishchenko, A.

doi:10.1090/S0077-1554-07-00166-5

The wreath product of atoms of the lattice of semigroup varieties
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by A. V. Tishchenko
Translated by: E. Khukhro

Trans. Moscow Math. Soc. 2007, 93-118

DOI: https://doi.org/10.1090/S0077-1554-07-00166-5

Published electronically: November 21, 2007

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Abstract:

A semigroup variety is called a Cross variety if it is finitely based, is generated by a finite semigroup, and has a finite lattice of subvarieties. It is established in which cases the wreath product of two semigroup varieties each of which is an atom of the lattice of semigroup varieties is a Cross variety. Furthermore, for all the pairs of atoms $\textbf {U}$ and $\textbf {V}$ for which this is possible, either a finite basis of identities for the wreath product $\textbf {UwV}$ is given explicitly, a finite semigroup generating this variety is found and the lattice of subvarieties is described, or it is proved that such a finite characterization is impossible.

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