Comparability, separativity, and exchange rings

DOI10.1080/00927879608825721zbMath0859.16001OpenAlexW2124599666MaRDI QIDQ4890691

Enrique Pardo Espino

Publication date: 10 April 1997

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

Full work available at URL: http://hdl.handle.net/10498/16079

zbMATH Keywords

finitely generated projective modulesstable rankdirect summandscentral idempotentsoperator algebrasexchange rings\(s\)-comparabilityseparative cancellationweak comparabilitydirectly finite von Neumann regular ringssimple regular ringsconical refinement monoidsfull cancellation

Mathematics Subject Classification ID

Free, projective, and flat modules and ideals in associative algebras (16D40) 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) General theory of (C^*)-algebras (46L05) Ordered semigroups and monoids (06F05) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50)

Related Items (27)

Power-substitution,exchange rings and unit II-regularity ⋮ On regular rings with s-comparability ⋮ Comparability, Stability, and Completions of Ideals ⋮ On Uniform Diagonalisation of Matrices over Regular Rings and One-Accessible Regular Algebras ⋮ Related comparability over exchange rings ⋮ Separativity of Regular Rings in Which 2 Is Invertible ⋮ Convexity of Torsion Subgroups inK₀Groups and Dimension Group Properties ofK₀of Pullbacks ⋮ On Exchange QB_∞-Rings ⋮ The structure of countably generated projective modules over regular rings ⋮ Unnamed Item ⋮ EXCHANGE RINGS WITH GENERAL ALEPH-NOUGHT-COMPARABILITY ⋮ Comparability and \(s\)-comparability of modules over exchange rings ⋮ On Regular Rings Satisfying Almost Comparability ⋮ Ideal-comparability over regular rings. ⋮ On generalized stable rings ⋮ Extensions of GM-rings ⋮ Onm-fold stable exchange rings ⋮ Strong separativity over exchange rings ⋮ Exchange rings in which all regular elements are one-sided unit-regular ⋮ Separative cancellation for projective modules over exchange rings ⋮ Regular Rings Satisfying Generalized Almost Comparability ⋮ The State Space ofK₀of Exchange Rings ⋮ Separative Cancellation over Regular Rings ⋮ Exchange rings, related comparability and power-substitution ⋮ Separativity of modules with finite exchange property ⋮ The comparable structure of exchange rings ⋮ REGULAR RINGS WITH COMPARABILITY AND SOME RELATED PROPERTIES

Cites Work

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• On rings whose projective modules have the exchange property
• On regular rings with stable range 2
• Cancellation of modules and groups and stable range of endomorphism rings
• Injective positively ordered monoids. I
• \(K\)-theoretically simple von Neumann regular rings
• Refinements for infinite direct decompositions of algebraic systems
• Simple self-injective rings
• Restricted injectivity, transfer property and decompositions of separative positively ordered monoids.

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