Colocalization and localization in Abelian categories

DOI10.1016/0021-8693(79)90320-XzbMath0427.16005MaRDI QIDQ1136825

Hiroyuki Tachikawa, Koichiro Ohtake

Publication date: 1979

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

zbMATH Keywords

bilocalizationstrict Giraud subcategoriesstrongly hereditary torsion theories

Mathematics Subject Classification ID

Category-theoretic methods and results in associative algebras (except as in 16D90) (16B50) Torsion theories; radicals on module categories (associative algebraic aspects) (16S90) Localization and associative Noetherian rings (16P50) Localization of categories, calculus of fractions (18E35)

Related Items (18)

Cotorsion Theories Cogenerated by a Torsionfree Class ⋮ Types of Serre subcategories of Grothendieck categories ⋮ Abelian torsion theories with localization ⋮ Auslander's formula: variations and applications ⋮ Left exact torsion theories ⋮ Localization in Abelian Categories ⋮ A generalization of Kato's theorem on Morita duality ⋮ On the existence of covers by injective modules relative to a torsion theory ⋮ T.T.F. theories in abelian categories ⋮ Equivalence between colocalization and localization in Abelian categories with applications to the theory of modules ⋮ Morita equivalence for idempotent rings ⋮ Idempotent functors and localizations in categories of modules and Abelian groups. ⋮ Commutative rings of which all radicals are left exact ⋮ Recollements of module categories ⋮ Embeddings of Exactly Definable and Finitely Accessible Additive Categories into Freyd Categories ⋮ A representation-theoretic approach to recollements of abelian categories ⋮ Endomorphism rings and category equivalences ⋮ On the localization of a ring at torsion theories

Cites Work

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• Colocalization and localization
• Some aspects of torsion
• Localizations in categories of modules. I
• Torsion theories, additive semantics, and rings of quotients. With an appendix by H. H. Storrer on torsion theories and dominant dimensions
• On an \(n\)-fold torsion theory in the category \(_RM\).
• TTF classes and quasi-generators
• A Torsion Theory for Abelian Categories
• Des catégories abéliennes
• Injective Structures

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