The structure of solid binary algebras
type: Item
instance of: scholarly article
title: The structure of solid binary algebras
zbMATH Open document ID: 0854.20066
DOI: 10.1007/BF01243592
published in: Algebra Universalis
publication date: 1997-01-22T00:00:00Z
review text: This paper gives an account of the structure of so-called solid binary algebras which are an abstract characterisation of the idempotent structure of a completely regular semigroup (a semigroup which is a union of groups). The main result is a structure theorem for solid binary algebras in terms of semilattices and rectangular bands. It is an analogue of the classical structure theorem for bands due to Petrich. It is shown that any solid binary algebra generated by two elements is a band, but an example shows that this does not hold for three or more generators. Finally it is proved that the free solid binary algebra can be embedded in a free completely regular semigroup, thus allowing the solution of the word problem for free solid binary algebras.
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 20M17
Mathematics Subject Classification ID: 20M05
zbMATH DE Number: 920793
zbMATH Keywords: solid binary algebras
zbMATH Keywords: idempotents
zbMATH Keywords: unions of groups
zbMATH Keywords: semilattices
zbMATH Keywords: rectangular bands
zbMATH Keywords: generators
zbMATH Keywords: free completely regular semigroups
zbMATH Keywords: word problem
zbMATH Keywords: free solid binary algebras
author: Raymond Broeksteeg
reviewed by: Peter M. Higgins
MaRDI profile type: Publication
cites work: The set of idempotents of a completely regular semigroup as a binary algebra
cites work: The free completely regular semigroup on a set
cites work: Free completely regular semigroups. I: Representation.
cites work: Q4126563
cites work: On the word problem for free completely regular semigroups
cites work: Coextensions of Regular Semigroups by Rectangular Bands.I
cites work: Free completely regular semigroups
full work available at URL: https://doi.org/10.1007/bf01243592
OpenAlex ID: W2048115100
description: scientific article; zbMATH DE number 920793