Identities on free products of bands
type: Item
instance of: scholarly article
title: Identities on free products of bands
zbMATH Open document ID: 0669.20046
DOI: 10.1007/BF01236869
published in: Algebra Universalis
publication date: 1989-01-01T00:00:00Z
review text: The author considers the question whether for any normal bands \(U\) and \(V\), the free product \(U*_{{\mathcal B}}V\) of \(U\) and \(V\) within the variety \({\mathcal B}\) of bands belongs to a proper subvariety of \(\mathcal B\). It is shown that, if \(U\) and \(V\) are rectangular bands, then \(U*_{{\mathcal B}}V\) belongs to the variety which in the notation of \textit{C. F. Fennemore} [Math. Nachr. 48, 237-252, 253-262 (1971; Zbl 0194.02703 and Zbl 0194.02801)] is denoted by \([R_ 3d\bar R_ 3=Q_ 3d\bar Q_ 3]\). An example with \(U\) normal and \(V\) trivial shows that \(U*_{{\mathcal B}}V\) need not be contained in any proper subvariety of \(\mathcal B\). The main result states that if \(U\) is right normal and \(V\) a rectangular band, then \(U*_{{\mathcal B}}V\) is in the variety \([R_ 4=S_ 4]\).
reviewed by: Francis Pastijn
Mathematics Subject Classification ID: 20M07
Mathematics Subject Classification ID: 08B15
zbMATH DE Number: 4095780
zbMATH Keywords: normal bands
zbMATH Keywords: free product
zbMATH Keywords: variety
zbMATH Keywords: rectangular bands
author: Colleen A. Vachuska
MaRDI profile type: Publication
cites work: All Varieties of Bands I
cites work: Q4126563
cites work: A band generated by two semilattices is regular
cites work: Normal forms for band free products
cites work: Commutative semigroups
description: scientific article; zbMATH DE number 4095780