On commutative Grothendieck categories having a Noetherian cogenerator

DOI10.1007/BF01224954zbMath0444.18007OpenAlexW2049261904MaRDI QIDQ1144640

Toma L.Albu

Publication date: 1980

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01224954

zbMATH Keywords

generatorGabriel topologyHopkins-Levitzki theoremadjoint functor theoremcommutative Grothendieck categoriesNoetherian cogenerator

Mathematics Subject Classification ID

Torsion theories, radicals (18E40) Commutative Noetherian rings and modules (13E05) Projectives and injectives (category-theoretic aspects) (18G05) Torsion theories; radicals on module categories (associative algebraic aspects) (16S90) Commutative Artinian rings and modules, finite-dimensional algebras (13E10) Grothendieck groups, (K)-theory and commutative rings (13D15) Torsion theory for commutative rings (13D30) Torsion modules and ideals in commutative rings (13C12)

Related Items

Relativization, absolutization, and latticization in ring and module theory, The Osofsky-Smith Theorem for Modular Lattices, and Applications (II), V-rings relative to gabriel topologies, An indecomposable nonlocally finitely generated Grothendieck category with simple objects

Cites Work

• Finiteness of the injective hull
• The descending chain condition relative to a torsion theory
• Sommes directes de sous-modules co-irréductibles d'un module
• A generalization of quasi-Frobenius rings
• Homological properties of the ring of differential polynomials
• Some Examples from Infinite Matrix Rings
• Finiteness Conditions for Projective and Injective Modules
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