Über das Radikal in potenzverbundenen Halbgruppen
type: Item
instance of: scholarly article
title: Über das Radikal in potenzverbundenen Halbgruppen
zbMATH Open document ID: 0541.20042
author: J. Brinckmann
published in: Beiträge zur Algebra und Geometrie
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/138277
review text: For a semigroup S define an equivalence rad S: (a,b)\(\in rad S\) iff for every \(s\in S\) there exist i,j,k,m with \((as)^ ia=(as)^ jb\) and \((bs)^ ka=(bs)^ mb.\) Let S be a semigroup such that for every pair a,\(b\in S\) there exist m, n with \(a^ m=b^ n\). The paper investigates the equivalence rad S on S. As typical results of this paper we give: rad S is a congruence and it is identical iff S is cancellative. The following conditions on S are equivalent: a) S is right cancellative, b) S is left cancellative, c) S is cancellative, d) S is right separative, e) S is left separative, f) S is separative.
reviewed by: Václav Koubek
Mathematics Subject Classification ID: 20M11
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 20M15
zbMATH DE Number: 3859413
zbMATH Keywords: equivalence
zbMATH Keywords: congruence
zbMATH Keywords: right cancellative
zbMATH Keywords: right separative
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3859413