Spectral gabriel topologies and relative singular functors

DOI10.1080/00927878508823147zbMath0552.16009OpenAlexW1969435943MaRDI QIDQ3344099

José L. Gómez Pardo

Publication date: 1985

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

Full work available at URL: https://doi.org/10.1080/00927878508823147

zbMATH Keywords

quotient categoryring of quotientspreradicalsspectral categoryFiniteness conditionsGabriel filter of left idealsrelative Goldie topologyrelative singular functor

Mathematics Subject Classification ID

Category-theoretic methods and results in associative algebras (except as in 16D90) (16B50) Torsion theories, radicals (18E40) Torsion theories; radicals on module categories (associative algebraic aspects) (16S90) Localization and associative Noetherian rings (16P50) Radicals and radical properties of associative rings (16Nxx)

Related Items (16)

Semiperfect modules relative to a torsion theory ⋮ A generalization of purely extending modules relative to a torsion theory ⋮ Gabriel dimension and spectral torsion theories ⋮ On \(\tau\)-extending modules. ⋮ On regular selfinjective localizations ⋮ Relative splitting properties with applications to endomorphism rings ⋮ Spectral torsion theories in module categories ⋮ Endomorphism rings of quotient modules for spectral torsion theories ⋮ Boolean perspectives of idioms and the Boyle derivative ⋮ Relative injectivity and chain conditions ⋮ The Osofsky-Smith Theorem for Modular Lattices, and Applications (II) ⋮ V-rings relative to gabriel topologies ⋮ On relative coherence and applications^∗ ⋮ An indecomposable nonlocally finitely generated Grothendieck category with simple objects ⋮ Singular and nonsingular modules relative to a torsion theory ⋮ Comultiplication modules relative to a hereditary torsion theory

Cites Work

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• The kernels of completion maps and a relative form of Nakayama's lemma
• The descending chain condition relative to a torsion theory
• Fully bounded Grothendieck categories: Addendum
• Spektralkategorien und reguläre Ringe im von-Neumannschen Sinn
• A generalization of quasi-Frobenius rings
• Some aspects of Goldie's torsion theory
• Torsion-free covers
• Coherence relative to an hereditary torsion theory
• Singular submodule relative to a kernel functor
• Semisimple rings of quotients
• On regular self-injective rings

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