When Some Complement of a Submodule Is a Summand

DOI10.1080/00927870601074830zbMath1118.16004OpenAlexW2148372034MaRDI QIDQ3429305

Adnan Tercan, Gary F. Birkenmeier

Publication date: 30 March 2007

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

Full work available at URL: https://doi.org/10.1080/00927870601074830

zbMATH Keywords

idempotentsendomorphism ringsdirect summandsrings of matricescomplementsinjective hullsessential extensions\(C_{11}\)-modulesrational hulls\(C_{11}\)-rings

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Injective modules, self-injective associative rings (16D50) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70)

Related Items (12)

Two Open Questions On Goldie Extending Modules ⋮ Modules whose certain submodules are essentially embedded in direct summands ⋮ Unnamed Item ⋮ The Extending Condition Relative to Sets of Submodules ⋮ A variation of coretractable modules ⋮ Modules Whose Submodules are Essentially Embedded in Direct Summands ⋮ Goldie Extending Modules ⋮ Generalized SSP-modules ⋮ Generalized extending modules via exchange and clean properties ⋮ Modules Whoset-Closed Submodules Have a Summand as a Complement ⋮ Unnamed Item ⋮ On Generalized FI-extending Modules

Cites Work

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• Unnamed Item
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• THE FULLY INVARIANT EXTENDING PROPERTY FOR ABELIAN GROUPS
• Self-injective rings and the minimal direct summand containing the nilpotents
• Does Every Right Ideal of a Matrix Ring Contain a Nilpotent Element?
• When is the cs condition hereditary?
• On certain CS-rings
• Idempotents and completely semiprime ideals
• Generalizations of CS-modules
• A Non-Trivial Ring with Non-Rational Injective Hull

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