C4-modules with the exchange property

DOI10.1080/00927872.2022.2085289OpenAlexW4281740703MaRDI QIDQ5038121

Yasser Ibrahim, Mohamed F. Yousif

Publication date: 29 September 2022

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

Full work available at URL: https://doi.org/10.1080/00927872.2022.2085289

zbMATH Keywords

abelian rings\(C4\)-modules and \(D4\)-modulesexchange and clean rings and modulessummand-square-free and summand-dual-square-free modules

Mathematics Subject Classification ID

Injective modules, self-injective associative rings (16D50) Free, projective, and flat modules and ideals in associative algebras (16D40) Quasi-Frobenius rings (16L60) Noncommutative local and semilocal rings, perfect rings (16L30) Simple and semisimple modules, primitive rings and ideals in associative algebras (16D60) Chain conditions on annihilators and summands: Goldie-type conditions (16P60) Artinian rings and modules (associative rings and algebras) (16P20) Noetherian rings and modules (associative rings and algebras) (16P40)

Cites Work

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• Classes of modules with the exchange property
• Continuous modules are clean.
• Square-free modules with the exchange property.
• Perspectivity and cancellation in regular rings
• Refinements for infinite direct decompositions of algebraic systems
• Automorphism-invariant modules satisfy the exchange property.
• Corner Rings of a Clean Ring Need Not be Clean
• C4-Modules
• Countable Exchange and Full Exchange Rings
• Lifting Idempotents and Exchange Rings
• Exchange rings, units and idempotents
• Utumi modules
• Perspectivity, exchange and summand-dual-square-free modules
• D4-Modules
• Dual-square-free modules
• Perspectivity and von Neumann regularity

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