O’Meara, K. C.; Raphael, R. M. Uniform diagonalisation of matrices over regular rings. (English) Zbl 1058.16009 Algebra Univers. 45, No. 4, 383-405 (2001). 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 \(R\). Reviewer: Ivan Chajda (Olomouc) Cited in 2 ReviewsCited in 3 Documents MSC: 16E50 von Neumann regular rings and generalizations (associative algebraic aspects) 16S50 Endomorphism rings; matrix rings 15A21 Canonical forms, reductions, classification 15A24 Matrix equations and identities 15A09 Theory of matrix inversion and generalized inverses Keywords:uniform diagonalisation formula; von Neumann regular rings; separative rings; generalized inverses; projective modules PDFBibTeX XMLCite \textit{K. C. O'Meara} and \textit{R. M. Raphael}, Algebra Univers. 45, No. 4, 383--405 (2001; Zbl 1058.16009) Full Text: DOI Link