Self-duality and serial rings

DOI10.1016/0021-8693(79)90132-7zbMath0444.16012OpenAlexW2072414630MaRDI QIDQ1144631

Joel K. Haack

Publication date: 1979

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

Full work available at URL: https://doi.org/10.1016/0021-8693(79)90132-7

zbMATH Keywords

finitely generated modulesLoewy lengthsgeneralized uniserial ringsorthogonal primitive idempotentsquasi-Frobenius-ringweakly symmetric self-duality

Mathematics Subject Classification ID

Finite rings and finite-dimensional associative algebras (16P10) Module categories in associative algebras (16D90) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Quasi-Frobenius rings (16L60) Conditions on elements (16U99)

Related Items (19)

Finite subdirect products of rings and morita duality ⋮ Self-duality of serial rings ⋮ Self-duality of quasi-Harada rings and locally distributive rings. ⋮ Self-duality andl-hereditary semidistributive rings ⋮ Duality for semigroup rings ⋮ Towards self-duality of semidistributive artinian rings ⋮ Endomorphism rings, power series rings, and serial modules ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Endomorphism rings of modules and lattices of submodules ⋮ Examples of QF rings without Nakayama automorphism and H-rings without self-duality ⋮ Semidistributive modules ⋮ When do the transpose and dual agree? ⋮ Self-duality and Harada rings ⋮ Distributive modules and rings and their close analogs ⋮ Serial rings and subdirect products ⋮ Einreihig zerlegbare Ringe sind selbstdual ⋮ Modules ⋮ The structure of serial rings and self-duality

Cites Work

• Unzerlegbare Moduln über artinschen Ringen
• Rings with quivers that are trees
• Left generalized uniserial rings
• Generalized uniserial rings and their Kupisch series
• On indecomposable injectives over artinian rings
• Linear compactness and Morita duality
• Serial rings
• Modules with decompositions that complement direct summands
• A Duality Theory for Injective Modules. (Theory of Quasi-Frobenius Modules)
• Beiträge zur Theorie nichthalbeinfacher Ringe mit Minimalbedingungen.
• Coxeter Functors Without Diagrams
• Rings of left invariant module type
• Rings with Duality
• On Morita Duality
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