The exchange property for row and column-finite matrix rings.

DOI10.1016/S0021-8693(03)00266-7zbMath1046.16012MaRDI QIDQ1415362

K. C. O'Meara

Publication date: 3 December 2003

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

zbMATH Keywords

matrix ringsexchange ringsvon Neumann regular ringsmultiplier ringsnon-unital regular rings

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50)

Related Items (5)

Row and column finite matrices ⋮ When is the \(2\times 2\) matrix ring over a commutative local ring strongly clean? ⋮ Finiteness conditions and infinite matrix rings ⋮ Gromov translation algebras over discrete trees are exchange rings ⋮ Ideal extensions and directly infinite algebras

Cites Work

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• Regular rings with involution
• Algebras over zero-dimensional rings
• Separative cancellation for projective modules over exchange rings
• \(K_ 1\) of separative exchange rings and \(C^ *\)-algebras with real rank zero.
• The structure of countably generated projective modules over regular rings
• Free and residually artinian regular rings
• Exchange rings and decompositions of modules
• Lifting Idempotents and Exchange Rings
• Isomorphisms of row and column finite matrix rings
• Countable linear transformations are clean
• Lifting units modulo exchange ideals and C* -algebras with real rank zero
• Multipliers of von neumann regular rings

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