Moscow Mathematical Society

Author(s): 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
Posted: 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 ${\bf U}$ 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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Retrieve articles in Transactions of the Moscow Mathematical Society with MSC (2000): 20M07, 20E22

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

DOI: 10.1090/S0077-1554-07-00166-5
PII: S 0077-1554(07)00166-5
Keywords: Semigroup, atom, lattice of subvarieties, semigroup variety, wreath product, basis of identities, Cross variety
Posted: November 21, 2007
Copyright of article: Copyright 2007, American Mathematical Society

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ISSN: 1547-738X(e) ISSN: 0077-1554(p)

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