Exchange rings with stable range one

DOI10.1007/s10587-007-0099-8zbMath1161.16008OpenAlexW2063314738MaRDI QIDQ3617972

Huanyin Chen

Publication date: 31 March 2009

Published in: Czechoslovak Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/31148

zbMATH Keywords

unitsidempotentsexchange ringsstable range one

Mathematics Subject Classification ID

Grothendieck groups, (K)-theory, etc. (16E20) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) 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 (2)

Characterizations of special clean elements and applications ⋮ On regular power-substitution.

Cites Work

• Matrix equivalence and isomorphism of modules
• A note on the group structure of unit regular ring elements
• Separative cancellation for projective modules over exchange rings
• Stable range one for exchange rings
• Clean matrices and unit-regular matrices.
• Full elements in regular rings.
• Completion of diagrams by automorphisms and Bass' first stable range condition
• Regular elements which is a sum of an idempotent and a left cancellable element.
• EXTENSIONS OF CLEAN RINGS
• A CHARACTERIZATION OF UNIT REGULAR RINGS
• Strongly 𝜋-regular rings have stable range one
• Lifting Idempotents and Exchange Rings
• Countable linear transformations are clean
• A CRASH COURSE ON STABLE RANGE, CANCELLATION, SUBSTITUTION AND EXCHANGE
• The exchange property for purely infinite simple rings
• Stable Range One for Rings with many Idempotents

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