On Uniform Diagonalisation of Matrices over Regular Rings and One-Accessible Regular Algebras

DOI10.1081/AGB-120039630zbMath1074.16005OpenAlexW2016562201MaRDI QIDQ3158329

K. C. O'Meara, Kostia I. Beidar, Robert M. Raphael

Publication date: 24 January 2005

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1081/agb-120039630

zbMATH Keywords

idempotentsnilpotent elementsprojective modulesvon Neumann regular ringsunit-regular ringsseparative cancellationdirect sum cancellationuniform diagonalizations of matrices

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Endomorphism rings; matrix rings (16S50) Free, projective, and flat modules and ideals in associative algebras (16D40) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Canonical forms, reductions, classification (15A21) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50)

Related Items (8)

Unit-regularity of regular nilpotent elements ⋮ Connections between unit-regularity, regularity, cleanness, and strong cleanness of elements and rings ⋮ A note on nil-clean rings ⋮ Konstantin Igorevich Beidar (1951-2004) ⋮ A Jordan canonical form for nilpotent elements in an arbitrary ring ⋮ Certain Properties of Square Matrices over Fields with Applications to Rings ⋮ On approximately simultaneously diagonalizable matrices ⋮ A new setting for constructing von Neumann regular rings

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• On strongly pi-regular rings of stable range one
• Comparability, separativity, and exchange rings

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