Finitely generated projective modules over exchange rings

DOI10.1007/BF02567984zbMath0824.16002MaRDI QIDQ1345752

Tong Wenting, Tong Suo Wu

Publication date: 3 April 1995

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/156044

zbMATH Keywords

finitely generated projective modulescancellationcentral idempotentsGrothendieck groupsrank functionsexchange ringsdirect sum of cyclic modulesspectra of rings

Mathematics Subject Classification ID

Associative rings of functions, subdirect products, sheaves of rings (16S60) Free, projective, and flat modules and ideals in associative algebras (16D40) Grothendieck groups, (K)-theory, etc. (16E20)

Related Items

Further Results on K₀-Groups with Ordered Structure ⋮ Extensions of exchange rings ⋮ Generalized Stable Exchange Rings ⋮ \(K_0\) of Abelian exchange rings with respect to Pierce stalks. ⋮ Endomorphisms of Progenerators over Exchange QB-Rings ⋮ On the stable range condition of exchange rings ⋮ On Exchange QB_∞-Rings ⋮ Extension of refinement rings ⋮ Unnamed Item ⋮ Boolean Algebras, Generalized Abelian Rings, and Grothendieck Groups ⋮ Separative cancellation for projective modules over exchange rings ⋮ The State Space ofK₀of Exchange Rings ⋮ K₀of Exchange Rings with All Idempotents Central ⋮ Further results on finitely generated projective modules

Cites Work

• Classes of modules with the exchange property
• Projective modules over von Neumann regular rings have the finite exchange property
• On rings whose projective modules have the exchange property
• Exchanging torsion modules over Dedekind domains
• Refinements for infinite direct decompositions of algebraic systems
• Lifting Idempotents and Exchange Rings
• Rings all of Whose Pierce Stalks are Local
• A Krull-Schmidt Theorem for Infinite Sums of Modules
• A Characterization of Exchange Rings
• Unnamed Item