Uniform diagonalisation of matrices over regular rings.
type: Item
instance of: scholarly article
title: Uniform diagonalisation of matrices over regular rings.
zbMATH Open document ID: 1058.16009
author: K. C. O'Meara
author: R. Raphael
published in: Algebra Universalis
publication date: 2005-04-19T00:00:00Z
full work available at URL: http://hdl.handle.net/10092/11860
review text: A regular ring \(R\) is separative if \(A\oplus A\simeq A\oplus B\simeq B\oplus B\) imply \(A\simeq B\) for all finitely generated projective \(R\)-modules \(A,B\). \(2\times 2\) matrices over \(R\) are uniformly diagonalised if there exist \(2\times 2\) matrices \(P,Q\) whose elements depend only on a given \(2\times 2\) matrix \(A\) such that \(PAQ\) is a diagonal matrix. It is shown that the separativity problem for von Neumann regular rings is equivalent to the existence of formula for diagonalised matrices over \(R\).
reviewed by: Ivan Chajda
Mathematics Subject Classification ID: 16E50
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 15A21
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 15A09
zbMATH DE Number: 2158722
zbMATH Keywords: uniform diagonalisation formula
zbMATH Keywords: von Neumann regular rings
zbMATH Keywords: separative rings
zbMATH Keywords: generalized inverses
zbMATH Keywords: projective modules
MaRDI profile type: Publication
OpenAlex ID: W2021575697
DOI: 10.1007/S000120050221
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description: scientific article; zbMATH DE number 2158722