On Exchange QB∞-Rings

DOI10.1142/S1005386707000569zbMath1143.16007MaRDI QIDQ5386781

Huanyin Chen

Publication date: 14 May 2008

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

zbMATH Keywords

exchange rings\(QB_\infty\)-ringsdiagonal reductionsdirect sum cancellations\(QB\)-ringspseudo-invertible matricespseudo-orthogonal elementsregular square matrices

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Matrices over special rings (quaternions, finite fields, etc.) (15B33) 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) Units, groups of units (associative rings and algebras) (16U60) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50) Stable range conditions (19B10)

Related Items (1)

Quasiunit regularity and \(QB\)-rings.

Cites Work

• \(K_0\) of purely infinite simple regular rings
• Pseudosimilarity and cancellation of modules
• Separative cancellation for projective modules over exchange rings
• Finitely generated projective modules over exchange rings
• Diagonalization of matrices over regular rings
• Pseudo-similarity in semigroups.
• An infinite analogue of rings with stable rank one
• Extensions and pullbacks in QB-rings.
• Completion of diagrams by automorphisms and Bass' first stable range condition
• Comparability of modules over regular rings
• On ExchangeQB-Rings
• The exchange property for purely infinite simple rings
• Comparability, separativity, and exchange rings

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