Diagonalization of matrices over regular rings

P. Ara; K. R. Goodearl; K. C. O'Meara; E. Pardo

doi:10.1016/S0024-3795(96)00596-4

Diagonalization of matrices over regular rings

P. Ara, K. R. Goodearl, K. C. O'Meara, E. Pardo

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

57 Citations (Scopus)

Abstract

Square matrices are shown to be diagonalizable over all known classes of (von Neumann) regular rings. This diagonalizability is equivalent to a cancellation property for finitely generated projective modules which conceivably holds over all regular rings. These results are proved in greater generality, namely for matrices and modules over exchange rings, where attention is restricted to regular matrices. © 1997 Elsevier Science Inc.

Original language	English
Pages (from-to)	147-163
Journal	Linear Algebra and Its Applications
Volume	265
Issue number	1-3
DOIs	https://doi.org/10.1016/S0024-3795(96)00596-4
Publication status	Published - 1 Nov 1997

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title = "Diagonalization of matrices over regular rings",

abstract = "Square matrices are shown to be diagonalizable over all known classes of (von Neumann) regular rings. This diagonalizability is equivalent to a cancellation property for finitely generated projective modules which conceivably holds over all regular rings. These results are proved in greater generality, namely for matrices and modules over exchange rings, where attention is restricted to regular matrices. {\textcopyright} 1997 Elsevier Science Inc.",

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AU - Goodearl, K. R.

AU - O'Meara, K. C.

AU - Pardo, E.

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Y1 - 1997/11/1

N2 - Square matrices are shown to be diagonalizable over all known classes of (von Neumann) regular rings. This diagonalizability is equivalent to a cancellation property for finitely generated projective modules which conceivably holds over all regular rings. These results are proved in greater generality, namely for matrices and modules over exchange rings, where attention is restricted to regular matrices. © 1997 Elsevier Science Inc.

AB - Square matrices are shown to be diagonalizable over all known classes of (von Neumann) regular rings. This diagonalizability is equivalent to a cancellation property for finitely generated projective modules which conceivably holds over all regular rings. These results are proved in greater generality, namely for matrices and modules over exchange rings, where attention is restricted to regular matrices. © 1997 Elsevier Science Inc.

U2 - 10.1016/S0024-3795(96)00596-4

DO - 10.1016/S0024-3795(96)00596-4

M3 - Article

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VL - 265

SP - 147

EP - 163

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 1-3

ER -

Diagonalization of matrices over regular rings

Abstract

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