Regularity and unit-regularity of generalized semigroups of linear transformations
type: Item
instance of: scholarly article
title: Regularity and unit-regularity of generalized semigroups of linear transformations
zbMATH Open document ID: 1009.20073
author: Y. Kemprasit
published in: Southeast Asian Bulletin of Mathematics
publication date: 2002-12-01T00:00:00Z
review text: Let \(V\) and \(W\) be vector spaces over a division ring \(D\), denote by \(L_D(V,W)\) the collection of all linear transformations from \(V\) to \(W\), and let \(\theta\) be a linear transformation from \(W\) to \(V\). Define an associative multiplication \(*\) on \(L_D(V,W)\) by \(\alpha*\beta=\alpha\theta\beta\) and denote this semigroup by \((L_D(V,W),\theta)\). The author proves that \((L_D(V,W),\theta)\) is regular if and only if \(V=\{0\}\), \(W=\{0\}\), or \(\theta\) is an isomorphism from \(W\) onto \(V\) and he proves that \((L_D(V,W),\theta)\) has an identity and is regular if and only if \(V=\{0\}\), \(W=\{0\}\), or \(\theta\) is an isomorphism from \(W\) onto \(V\) and \(\dim_DV<\infty\).
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 20M17
Mathematics Subject Classification ID: 15A04
zbMATH DE Number: 1836970
zbMATH Keywords: regular semigroups
zbMATH Keywords: unit-regular semigroups
zbMATH Keywords: generalized transformation semigroups
zbMATH Keywords: linear transformations
reviewed by: jun. Kenneth D. Magill
MaRDI profile type: Publication
full work available at URL: s100120200006
OpenAlex ID: W2040794730
DOI: 10.1007/S100120200006
description: scientific article; zbMATH DE number 1836970