Regular \(\mathcal J\)-classes of subspace semigroups
type: Item
instance of: scholarly article
title: Regular \(\mathcal J\)-classes of subspace semigroups
zbMATH Open document ID: 1012.20061
published in: Semigroup Forum
publication date: 2002-12-01T00:00:00Z
review text: For a finite-dimensional algebra \(A\) over an infinite field \(K\), the subspace semigroup \({\mathcal S}(A)\) consists of all subspaces of \(A\) with operation \(V*W=\text{lin}_KVW\), the linear span of \(VW\) over \(K\). \({\mathcal S}(A)\) is strongly \(\pi\)-regular. It was first studied by the author and \textit{M. S. Putcha} [J. Algebra 233, No. 1, 87-104 (2000; Zbl 0983.20062)]. The author studies the completely \(0\)-simple principal factors of \({\mathcal S}(M_n(K))\). Idempotents and regular \(\mathcal J\)-classes are characterized and some symmetries of \({\mathcal S}(M_n(K))\) are established.
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 16P10
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 20M10
zbMATH DE Number: 1837344
zbMATH Keywords: basic algebras
zbMATH Keywords: chains of ideals
zbMATH Keywords: completely \(0\)-simple principal factors
zbMATH Keywords: full matrix algebras
zbMATH Keywords: Green's relations
zbMATH Keywords: idempotents
zbMATH Keywords: linear algebraic semigroups
zbMATH Keywords: linear spans
zbMATH Keywords: regular \(\mathcal J\)-classes
zbMATH Keywords: strongly \(\pi\)-regular semigroups
zbMATH Keywords: subspace semigroups
zbMATH Keywords: symmetries
author: Jan Okniński
reviewed by: Huang Wenxue
MaRDI profile type: Publication
full work available at URL: s002330010125
OpenAlex ID: W2026712608
DOI: 10.1007/S002330010125
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description: scientific article; zbMATH DE number 1837344