*-MODULES, TILTING, AND ALMOST ABELIAN CATEGORIES

DOI10.1081/AGB-100105023zbMath1115.18004MaRDI QIDQ2746614

Wolfgang Rump

Publication date: 9 April 2002

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

zbMATH Keywords

equivalent categoriesderived functorspretorsion classtilting pairsAbelian closuresadjoint pairs of functorsalmost Abelian categoriespre-equivalencetilting theorem for module categories

Mathematics Subject Classification ID

Module categories in associative algebras (16D90) Abelian categories, Grothendieck categories (18E10) Preadditive, additive categories (18E05)

Related Items (10)

The relationship between homological properties and representation theoretic realization of artin algebras ⋮ Global theory of lattice-finite Noetherian rings. ⋮ \(n\)-quasi-abelian categories vs \(n\)-tilting torsion pairs ⋮ The structure of aisles and co-aisles of t-structures and co-t-structures ⋮ The acyclic closure of an exact category and its triangulation ⋮ The category of lattices over a lattice-finite ring. ⋮ Torsion pairs and quasi-abelian categories ⋮ The Jordan-Hölder property and Grothendieck monoids of exact categories ⋮ Tilting and trivial extensions ⋮ Unnamed Item

Cites Work

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• Tilting modules of finite projective dimension
• Perpendicular categories with applications to representations and sheaves
• Density and equivalence
• On the structure of *-modules
• Every *-module is finitely generated
• Quasi-tilting modules and counter equivalences
• Chain complexes and stable categories
• Tilting modules and tilting torsion theories
• Noncommutative localizations and applications
• Localizations in categories of modules. I
• Localizations in categories of modules. III
• Torsion Theories Induced by Tilting Modules
• Tilting, cotilting, and serially tilted rings
• Some remarks on equivalences between categories of modules
• Torsion Theories and Tilting Modules
• Equivalences between projective and injective modules and morita duality for artinian rings
• Tilting and torsion theory counter equivalences

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