Identities in full transformation semigroups
type: Item
instance of: scholarly article
title: Identities in full transformation semigroups
zbMATH Open document ID: 0808.20049
DOI: 10.1007/BF01236507
author: Norbert Sauer
author: M. G. Stone
author: Reinhard Pöschel
author: Mark Sapir
author: M. V. Volkov
published in: Algebra Universalis
publication date: 1994-09-13T00:00:00Z
review text: Let \(L\) be a finite alphabet and let \(L^*\) denote the free monoid over \(L\). The authors show that if two words \(V, W \in L^*\) satisfy certain conditions, then there is an identity involving \(V\) and \(W\), which holds in every proper subsemigroup of \(H_ n\), the semigroup of all selfmaps of the set of \(n\) elements, but not in \(H_ n\) itself. They then go on to provide several constructions of words \(V\) and \(W\) which satisfy the required conditions.
Mathematics Subject Classification ID: 20M05
Mathematics Subject Classification ID: 20M20
zbMATH DE Number: 638598
zbMATH Keywords: semigroup of selfmaps
zbMATH Keywords: free monoid
zbMATH Keywords: words
zbMATH Keywords: identity
reviewed by: jun. Kenneth D. Magill
MaRDI profile type: Publication
cites work: \(k\)-ary monoids of term operations
cites work: Varieties of groups
cites work: Q3981354
cites work: Q3765976
full work available at URL: https://doi.org/10.1007/bf01236507
OpenAlex ID: W1981137089
description: scientific article; zbMATH DE number 638598