On a wreath product embedding for regular semigroups
type: Item
instance of: scholarly article
title: On a wreath product embedding for regular semigroups
zbMATH Open document ID: 0770.20025
DOI: 10.1007/BF02573545
author: Bernd Billhardt
published in: Semigroup Forum
publication date: 1993-04-01T00:00:00Z
full work available at URL: https://eudml.org/doc/135211
review text: The problem of wreath product embeddings in the theory of inverse semigroups has been studied in previous papers of the author [Semigroup Forum 44, 320-331 and 364-372 (1992; Zbl 0747.20032 and Zbl 0758.20019)]. On the other hand, \textit{M. B. Szendrei} [ibid. 32, 87-96 (1985; Zbl 0564.20037); and Proc. R. Soc. Edinb., Sect. A 106, 89-102 (1987; Zbl 0628.20052)] proved that every \(E\)-unitary regular semigroup with regular band of idempotents \(E\) can be embedded in a semidirect product of a band \(B\) by a group, where \(B\) belongs to the variety of bands generated by \(E\). In this paper, for a regular semigroup \(S\) a wreath product embedding is given, which depends on a group congruence on \(S\), satisfying a certain condition. As applications, wreath product embeddings for certain \(E\)- unitary regular semigroups are considered, and a short alternative proof of Szendrei's result above is established.
reviewed by: Miyuki Yamada
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 20M17
Mathematics Subject Classification ID: 20M18
zbMATH DE Number: 150432
zbMATH Keywords: wreath product embeddings
zbMATH Keywords: inverse semigroups
zbMATH Keywords: regular band of idempotents
zbMATH Keywords: semidirect product
zbMATH Keywords: variety of bands
zbMATH Keywords: group congruence
zbMATH Keywords: \(E\)- unitary regular semigroups
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 150432