Simplicity of wreath product of semigroups with fixed passive semigroup
type: Item
instance of: scholarly article
title: Simplicity of wreath product of semigroups with fixed passive semigroup
zbMATH Open document ID: 0813.20076
DOI: 10.1007/BF02573491
author: A. V. Tishchenko
published in: Semigroup Forum
publication date: 1995-05-23T00:00:00Z
full work available at URL: https://eudml.org/doc/135354
review text: The wreath product \(T = (S \text{ wr } R\mid A_ R)\) of semigroups \(S\) and \(R\) by a right \(R\)-act \(A\), i.e., \(R\)-operand or \(R\)-system in other terminology, is defined as the set \(F(A,S) \times R\), where \(F(A,S)\) is the set of all mappings from \(A\) into \(S\), and the multiplication on \(T\) is given by the rule \((f,p)(g,q) = (f^ p g,pq)\) with \((f^ pg)(x) = f(x)g(xp)\) for all \(x \in A\). Main Theorem: The wreath product \((S \text{ wr }R \mid A_ R)\) is a simple semigroup for each simple semigroup \(R\) and each of its right acts \(A_ R\) iff the passive semigroup \(S\) is left simple.
Mathematics Subject Classification ID: 20M50
Mathematics Subject Classification ID: 20M10
zbMATH DE Number: 682634
zbMATH Keywords: wreath product
zbMATH Keywords: simple semigroups
zbMATH Keywords: right acts
reviewed by: Ulrich Knauer
MaRDI profile type: Publication
cites work: Q5564342
cites work: Q5510798
cites work: The kernel of the wreath product of semigroups
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cites work: Embedding of regular semigroups in wreath products
description: scientific article; zbMATH DE number 682634