On rings whose projective modules have the exchange property

DOI10.1016/0021-8693(86)90145-6zbMath0603.16016OpenAlexW2037735261MaRDI QIDQ1082405

Josef Stock

Publication date: 1986

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

Full work available at URL: https://doi.org/10.1016/0021-8693(86)90145-6

zbMATH Keywords

decompositionsJacobson radicalnilpotent elementexchange propertyfinite exchange propertyvon Neumann regularprojective direct summandleft P-exchange ringstrongly \(\pi \)-regular

Mathematics Subject Classification ID

Free, projective, and flat modules and ideals in associative algebras (16D40) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Other classes of modules and ideals in associative algebras (16D80) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50)

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Cites Work

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• Projective modules
• Classes of modules with the exchange property
• Projective modules over von Neumann regular rings have the finite exchange property
• An example of a ring whose projective modules have the exchange property
• On the von Neumann regularity of rings with regular prime factor rings
• Algebras over zero-dimensional rings
• On perfect rings and the exchange property
• Semi-perfect modules
• Refinements for infinite direct decompositions of algebraic systems
• Decompositions of injective modules
• Rings over which every module has a maximal submodule
• Exchange rings and decompositions of modules
• Modules with decompositions that complement direct summands
• On the nilpotency of nil-algebras
• Semiregular Modules and Rings
• Lifting Idempotents and Exchange Rings
• Observations on group rings
• A Krull-Schmidt Theorem for Infinite Sums of Modules
• Endomorphism Rings of Projective Modules
• Regular Modules
• A Characterization of Exchange Rings
• Topological Representation of Algebras. II