Unary hyperidentities for varieties of inverse semigroups
type: Item
instance of: scholarly article
title: Unary hyperidentities for varieties of inverse semigroups
zbMATH Open document ID: 0919.20037
DOI: 10.1007/PL00005994
author: K. Appert
published in: Semigroup Forum
publication date: 1999-06-30T00:00:00Z
review text: Hyperidentities of an algebra resemble identities, but contain variables representing operations as well as elements. There has been considerable interest in hyperidentities of varieties of semigroups, which have a rich enough structure to be interesting, but are relatively accessible. Because of the extra operation involved, hyperidentities of inverse semigroups seem somewhat more difficult to handle. Thus the authors of this paper are considering only the case where the operation symbols are unary. They made a start on this endeavour in a previous paper [Semigroup Forum 55, No. 2, 221-231 (1997; Zbl 0885.20034)] where they considered only unary iterative hyperidentities. In this paper they investigate all unary hyperidentities for inverse semigroups and show that they can be associated with varieties defined by the following sets of identities: \(x=y\), \(xx=x\), \(xx^{-1}=yy^{-1}\), \(xx^{-1}=x^{-1}x\), \(x^nx^{-1}=x^{-1}x^n\) (\(n\geq 1\)), \(x^n=x^{n+m}\) (\(n,m\geq 1\)).
Mathematics Subject Classification ID: 20M07
Mathematics Subject Classification ID: 20M18
Mathematics Subject Classification ID: 20M05
zbMATH DE Number: 1251162
zbMATH Keywords: hyperidentities
zbMATH Keywords: varieties of inverse semigroups
reviewed by: Sheila Oates-Williams
MaRDI profile type: Publication
full work available at URL: pl00005994
OpenAlex ID: W1993112979
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description: scientific article; zbMATH DE number 1251162