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The wreath product of atoms of the lattice of semigroup varieties


Author: A. V. Tishchenko
Translated by: E. Khukhro
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 68 (2007).
Journal: Trans. Moscow Math. Soc. 2007, 93-118
MSC (2000): Primary 20M07; Secondary 20E22
DOI: https://doi.org/10.1090/S0077-1554-07-00166-5
Published electronically: November 21, 2007
MathSciNet review: 2429268
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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 $ {\bf U}$ and $ {\bf V}$ for which this is possible, either a finite basis of identities for the wreath product $ {\bf 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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Additional Information

A. V. Tishchenko
Affiliation: Finance Academy at the Government of the Russian Federation and Moscow State Humanitarian Boarding Institute, Moscow, Russia

DOI: https://doi.org/10.1090/S0077-1554-07-00166-5
Keywords: Semigroup, atom, lattice of subvarieties, semigroup variety, wreath product, basis of identities, Cross variety
Published electronically: November 21, 2007
Article copyright: © Copyright 2007 American Mathematical Society

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