An infinite analogue of rings with stable rank one

DOI10.1006/jabr.2000.8330zbMath0963.16008arXivmath/9910131OpenAlexW2086357237MaRDI QIDQ1582245

Francesc Perera, Pere Ara, Gert Kjaergård Pedersen

Publication date: 14 January 2001

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

Full work available at URL: https://arxiv.org/abs/math/9910131

zbMATH Keywords

semiprime ringsexchange ringsvon Neumann regular ringsring extensionsBass stable rankquasi-invertible elements\(QB\)-ringsextremally rich \(C^*\)-algebras

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) 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) (K)-theory and operator algebras (including cyclic theory) (46L80) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50)

Related Items (20)

On ExchangeQB-Rings ⋮ A CLOSURE OPERATION IN RINGS ⋮ The exchange property for purely infinite simple rings ⋮ On the algebraic closure in rings ⋮ Exchange Leavitt path algebras and stable rank ⋮ Quasiunit regularity and \(QB\)-rings. ⋮ Endomorphisms of Progenerators over Exchange QB-Rings ⋮ On JB-rings. ⋮ On Exchange QB_∞-Rings ⋮ The cancellation property of rings ⋮ Quasi-Invertible Regular Elements and Their Applications ⋮ OnQBEndomorphism Rings ⋮ Diagonal reductions of matrices over exchange ideals ⋮ Elements in RegularQB-Rings ⋮ Ideal-comparability over regular rings. ⋮ Generalized Stable Regular Rings ⋮ Generalized Ideal-Stable Regular Rings ⋮ Weakly Stable Modules ⋮ OnQB_∞-Rings ⋮ Extensions of Exchange QB-Rings

Cites Work

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• Bass's first stable range condition
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• On regular rings with stable range 2
• Cancellation of modules and groups and stable range of endomorphism rings
• \(C^*\)-algebras of real rank zero
• Algebras over zero-dimensional rings
• Separative cancellation for projective modules over exchange rings
• Extensions of exchange rings
• Cancellation of projective modules over regular rings with comparability
• Non-stable \(K\)-theory and extremally rich \(C^\ast\)-algebras
• The stable range of \(C^*\)-algebras
• Exchange rings and decompositions of modules
• Ideal Structure of Multiplier Algebras of Simple C^*-algebras With Real Rank Zero
• Dimension and Stable Rank in the K -Theory of C^* -Algebras
• Lifting Idempotents and Exchange Rings
• Exchange rings, related comparability and power-substitution
• Comparability of modules over regular rings
• Approximation and convex decomposition by extremals in a $C^*$-algebra.
• Lifting units modulo exchange ideals and C* -algebras with real rank zero
• Multipliers of von neumann regular rings
• On the geometry of the unit ball of a C*- algebra.

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