On finitely related semigroups.
type: Item
instance of: scholarly article
title: On finitely related semigroups.
zbMATH Open document ID: 1278.20077
author: Peter Mayr
published in: Semigroup Forum
publication date: 2013-06-14T00:00:00Z
review text: Let \(\mathbf A=\langle A,F\rangle\) be an algebra, where \(A\) is a set and \(F\) is a set of finitary operations on \(A\). The algebra \(\mathbf A\) is called finitely related if there exist subalgebras \(R_1,\dots,R_l\) of finitary powers of \(\mathbf A\) such that every operation on \(A\) that preserves every \(R_i\) (\(1\leq i\leq l\)) is a term operation on \(A\). Finitely related algebras were considered by many authors under varied names. It is shown that the following finite semigroups are finitely related: commutative semigroups, 3-nilpotent monoids, regular bands, semigroups with a single idempotent, and Clifford semigroups. Some examples of not finitely related semigroups are presented, particularly, the 6-element Brandt monoid is not finitely related. Some open problems are formulated.
reviewed by: Grigori I. Zhitomirski
Mathematics Subject Classification ID: 20M07
Mathematics Subject Classification ID: 08A40
Mathematics Subject Classification ID: 20M05
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 20M14
Mathematics Subject Classification ID: 20M17
zbMATH DE Number: 6176161
zbMATH Keywords: finite semigroups
zbMATH Keywords: term functions
zbMATH Keywords: clones
zbMATH Keywords: relations
zbMATH Keywords: finitely related algebras
zbMATH Keywords: finitely related semigroups
MaRDI profile type: Publication
full work available at URL: s00233-012-9455-6
OpenAlex ID: W2159045214
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DOI: 10.1007/S00233-012-9455-6
description: scientific article; zbMATH DE number 6176161