Commutative Noetherian semigroups are finitely generated
type: Item
instance of: scholarly article
title: Commutative Noetherian semigroups are finitely generated
zbMATH Open document ID: 1017.20052
author: Gary Brookfield
published in: Semigroup Forum
publication date: 2003-03-27T00:00:00Z
review text: A commutative semigroup \(S\) is called Noetherian if the set of congruences of \(S\), \(\text{Cong }S\), -- ordered in the usual way: \(\sim\leq\sim'\) if and only if \(x\sim y\) implies \(x\sim'y\), whenever \(x,y\in S\) -- is so that is every nonempty subset of \(\text{Cong }S\) has a maximal element. The author gives a short proof of the known fact that if \(S\) is Noetherian, then \(S\) is finitely generated.
Mathematics Subject Classification ID: 20M14
Mathematics Subject Classification ID: 20M05
Mathematics Subject Classification ID: 08A30
zbMATH DE Number: 1889245
zbMATH Keywords: Noetherian semigroups
zbMATH Keywords: congruences of semigroups
zbMATH Keywords: commutative semigroups
zbMATH Keywords: finitely generated semigroups
zbMATH Keywords: congruence lattices
reviewed by: Carlos Galindo
MaRDI profile type: Publication
full work available at URL: s002330010137
OpenAlex ID: W2075178720
DOI: 10.1007/S002330010137
description: scientific article; zbMATH DE number 1889245