A finiteness condition for semigroups generalizing a theorem of Coudrain and Schützenberger
type: Item
instance of: scholarly article
title: A finiteness condition for semigroups generalizing a theorem of Coudrain and Schützenberger
zbMATH Open document ID: 0848.20050
published in: Advances in Mathematics
publication date: 1995-01-23T00:00:00Z
review text: Let \(T'\) be a subsemigroup of a semigroup \(T\). If a) \(T\) satisfies the minimum condition for bi-ideals \((\min_B)\) and b) every subgroup of \(T\) generated by some finite subset of \(T'\) is finite then \(T'\) is locally finite. The case \(T' =T\) yields a generalization of a theorem of \textit{M. Coudrain} and \textit{M. P. Schützenberger} [C. R. Acad. Sci., Paris, Sér. A 262, 1149-1151 (1966; Zbl 0141.01801)]. Also, a new proof of the theorem of \textit{R. McNaughton} and \textit{Y. Zalcstein} [J. Algebra 34, 292-299 (1975; Zbl 0302.20054)] based on this result is given.
Mathematics Subject Classification ID: 20M05
zbMATH DE Number: 706487
zbMATH Keywords: finiteness condition for semigroups
zbMATH Keywords: locally finite groups
zbMATH Keywords: minimum condition for bi-ideals
author: Aldo De Luca
author: Stefano Varricchio
MaRDI profile type: Publication
full work available at URL: aima.1994.1067
OpenAlex ID: W2029955828
DOI: 10.1006/AIMA.1994.1067
description: scientific article; zbMATH DE number 706487