Representation of congruences on regular semigroups with inverse transversals
type: Item
instance of: scholarly article
title: Representation of congruences on regular semigroups with inverse transversals
zbMATH Open document ID: 0943.20063
DOI: 10.1007/BF02650729
author: Xilin Tang
author: Limin Wang
publication date: 2000-02-17T00:00:00Z
review text: Let \(S\) be a regular semigroup. An inverse subsemigroup \(S^0\) of \(S\) containing a unique inverse of each element of \(S\) is called an inverse transversal of \(S\) (this concept was introduced by \textit{T. S. Blyth} and \textit{R. McFadden} [Proc. R. Soc. Edinb., Sect. A 92, 253-270 (1982; Zbl 0507.20026)]). Based on a representation theorem of regular semigroups having an inverse transversal due to \textit{T. Saito} [Proc. Edinb. Math. Soc., II. Ser. 32, No. 1, 41-51 (1989; Zbl 0647.20063)] all congruences on \(S\) are described by means of congruences on the structural components of this representation. This process is simplified by a modification of the above representation provided by \textit{X. Tang} [Semigroup Forum 55, No. 1, 24-32 (1997; Zbl 0897.20040)]. Since any homomorphic image \(T\) of a regular semigroup \(S\) with inverse transversal also has an inverse transversal, the structure of \(T\) is described in terms of the components in the representation of \(S\).
Mathematics Subject Classification ID: 20M17
Mathematics Subject Classification ID: 08A30
Mathematics Subject Classification ID: 20M10
zbMATH DE Number: 1356524
zbMATH Keywords: inverse transversals
zbMATH Keywords: regular semigroups
zbMATH Keywords: congruences
reviewed by: H. Mitsch
MaRDI profile type: Publication
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cites work: Regular semigroups with inverse transversals
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cites work: Congruence lattices of regular semigroups with inverse transversals1
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full work available at URL: https://doi.org/10.1007/bf02650729
OpenAlex ID: W2063168439
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 1356524