The relationship between homological properties and representation theoretic realization of artin algebras

DOI10.1090/S0002-9947-04-03482-8zbMath1058.16012arXivmath/0307392MaRDI QIDQ4825670

Osamu Iyama

Publication date: 28 October 2004

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0307392

zbMATH Keywords

torsion theoriescategories of modulesAuslander-Reiten quiversArtin algebrasAuslander-Reiten sequencesAuslander algebrasalmost Abelian categoriesAuslander-regular rings of global dimension two

Mathematics Subject Classification ID

Module categories in associative algebras (16D90) Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) (16E65) Representation type (finite, tame, wild, etc.) of associative algebras (16G60) Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers (16G70) Representations of associative Artinian rings (16G10) Abelian categories, Grothendieck categories (18E10) Homological dimension in associative algebras (16E10)

Related Items

Classifying exact categories via Wakamatsu tilting ⋮ Simple modules over Auslander regular rings ⋮ Auslander correspondence. ⋮ Classifications of exact structures and Cohen-Macaulay-finite algebras ⋮ Cluster tilting for higher Auslander algebras. ⋮ The Auslander-type condition of triangular matrix rings. ⋮ Auslander–Reiten theory in extriangulated categories ⋮ Symmetry and duality on \(n\)-Gorenstein rings. ⋮ Auslander correspondence for triangulated categories ⋮ Auslander-type conditions and cotorsion pairs. ⋮ \(d\)-representation-finite self-injective algebras ⋮ On relative Auslander algebras ⋮ The Jordan-Hölder property and Grothendieck monoids of exact categories ⋮ Distributive lattices and Auslander regular algebras

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