Further results in the theory of generalised inflations of semigroups.
type: Item
instance of: scholarly article
title: Further results in the theory of generalised inflations of semigroups.
zbMATH Open document ID: 1152.20047
published in: Semigroup Forum
publication date: 2008-06-04T00:00:00Z
review text: A broad version of generalized inflation of semigroups given by \textit{G. T. Clarke} and \textit{R. A. R. Monzo} [Semigroup Forum 60, No. 2, 172-186 (2000; Zbl 0951.20045)] is defined. The semigroups satisfying the condition \(xyzw\in\{xy,xw,zy,zw\}\) are precisely those whose power semigroup is a generalized inflation of a band. The structure of generalized inflations is determined for the following types of semigroups: the direct product of a group and a band, a completely simple semigroup and a free semigroup \(F(X)\) on a set \(X\). In some cases a generalized inflation coincides with an inflation.
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 20M05
zbMATH DE Number: 5284775
zbMATH Keywords: generalised inflations
zbMATH Keywords: inclusion classes
zbMATH Keywords: power semigroups
zbMATH Keywords: almost commutative bands
zbMATH Keywords: bands of semigroups
author: Robert A. R. Monzo
reviewed by: Grigori I. Zhitomirski
MaRDI profile type: Publication
full work available at URL: s00233-008-9055-7
OpenAlex ID: W2031204084
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DOI: 10.1007/S00233-008-9055-7
description: scientific article; zbMATH DE number 5284775