Semi-primary qf-3 quotient rings

DOI10.1080/00927878308822854zbMath0511.16004OpenAlexW2036486301MaRDI QIDQ4749962

Kanzo Masaike

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1080/00927878308822854

zbMATH Keywords

injective hullhereditary torsion theoryleft exact radicalmaximal left quotient ringsclosed left idealsDCC on annihilator idealssemiprimary left and right QF-3 ringtorsionfree injective left module

Mathematics Subject Classification ID

Prime and semiprime associative rings (16N60) Quasi-Frobenius rings (16L60) Torsion theories; radicals on module categories (associative algebraic aspects) (16S90) Other classes of modules and ideals in associative algebras (16D80) Chain conditions on annihilators and summands: Goldie-type conditions (16P60) Localization and associative Noetherian rings (16P50)

Related Items

On Auslander's \(n\)-Gorenstein rings ⋮ QF-3 rings and morita duality ⋮ A characterisation of reflexive modules ⋮ Linear compactness and Morita duality for Grothendieck categories ⋮ Endomorphism rings of cogenerators with finite length ⋮ Torsionfree covers and covers by submodules of flat modules¹ ⋮ Minimal injective resolutions of gorenstein rings ⋮ Localization in abelian categories and double dual functors ⋮ Duality for quotient modules and a characterization of reflexive modules ⋮ Embedding cyclic and torsion-free modules in free modules ⋮ FTF rings and Frobenius extensions ⋮ Morita dualities associated with the \(R\)-dual functors

Cites Work

• Quasi-Frobenius rings and generalizations. QF-3 and QF-1 rings. Notes by Claus Michael Ringel
• Dominant modules and finite localizations
• The descending chain condition relative to a torsion theory
• Duality in QF-3 rings
• Direct-sum representations of injective modules
• Torisonfree injective modules
• Supplement to the paper, 'Orders in \(QF - 3\) rings'
• The ring of endomorphisms of a finite dimensional module
• On embedding torsion free modules into free modules

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