Pre-compatible almost endomorphisms and semigroups whose cube is a band.
type: Item
instance of: scholarly article
title: Pre-compatible almost endomorphisms and semigroups whose cube is a band.
zbMATH Open document ID: 1059.20055
published in: Semigroup Forum
publication date: 2004-07-07T00:00:00Z
review text: The main result of the paper (Theorem~3) is a construction for an arbitrary semigroup whose cube is a given band \(L\). The (moderately bulky) construction is formulated in terms of certain families of mappings on \(L\). As an application the author presents a diagram of a 33-element lattice and claims that this is the subvariety lattice of the variety defined by the identity \(xyz=xywyz\) (Corollary~6). The proofs of Theorem~3 and Corollary~6 are only outlined. Reviewer's remarks: 1. The diagram is incomplete: it omits several lines between points that represent comparable varieties. 2. The author attributes the description of the lattice of varieties of semigroups whose square is a rectangular band to \textit{M. Petrich} [Semigroup Forum 7, 104-152 (1974; Zbl 0282.20048)] while it was first found by \textit{I. I. Mel'nik} [Izv. Vyssh. Uchebn. Zaved., Mat. 1971, No. 12(115), 103-108 (1971; Zbl 0241.20047)].
Mathematics Subject Classification ID: 20M07
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 20M15
Mathematics Subject Classification ID: 08B15
zbMATH DE Number: 2078226
zbMATH Keywords: rectangular bands
zbMATH Keywords: almost endomorphisms
zbMATH Keywords: subvariety lattices
zbMATH Keywords: lattices of varieties
author: Robert A. R. Monzo
MaRDI profile type: Publication
full work available at URL: s00233-001-0004-y
OpenAlex ID: W1965137595
DOI: 10.1007/S00233-001-0004-Y
description: scientific article; zbMATH DE number 2078226