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On the diagonalisation of von Neumann regular matrices. (English) Zbl 0596.15012

Let R be any ring, associative with unit element, A an \(m\times n\) matrix over R. Then A is said to be von Neumann regular if there exists X over R such that \(AXA=A\). Rings are studied over which von Neumann regular matrices are diagonalizable.
Reviewer: S.Zlobec

MSC:

15B33 Matrices over special rings (quaternions, finite fields, etc.)
15A09 Theory of matrix inversion and generalized inverses
15A21 Canonical forms, reductions, classification
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