Cayley-like representations are for all algebras, not merely groups.
type: Item
instance of: scholarly article
title: Cayley-like representations are for all algebras, not merely groups.
zbMATH Open document ID: 1058.08002
author: Arthur Knoebel
published in: Algebra Universalis
publication date: 2005-04-19T00:00:00Z
review text: Cayley's Theorem represents a group as a set of permutations with the group operation captured by the composition. Other examples with related representations are monoids, Boolean algebras or Menger algebras, where permutations are replaced by functions with one or more variables. The author shows that any finite algebra has such a representation and so any variety generated by one finite subdirectly irreducible algebra. Such algebras are, e.g., semilattices, distributive lattices, median algebras or elementary Abelian \(p\)-groups. The most general result is obtained for a variety \(\mathcal V\) with a finite number of SI-members which all are finite.
reviewed by: Ivan Chajda
Mathematics Subject Classification ID: 08A05
zbMATH DE Number: 2158756
zbMATH Keywords: Cayley representation
zbMATH Keywords: Menger algebras
zbMATH Keywords: finite algebra
MaRDI profile type: Publication
full work available at URL: s00012-001-8168-6
OpenAlex ID: W2078440689
DOI: 10.1007/S00012-001-8168-6
description: scientific article; zbMATH DE number 2158756