A key module over pure-semisimple hereditary rings.

DOI10.1016/j.jalgebra.2006.06.025zbMath1151.16016OpenAlexW1987828518MaRDI QIDQ863368

Lidia Angeleri Hügel

Publication date: 26 January 2007

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2006.06.025

zbMATH Keywords

tilting theoryinfinite representation typecotorsion pairsrings of finite representation typepreinjective componentsendofinite modulesindecomposable left pure semisimple ringsleft almost split mapsperfect cotorsion pairs

Mathematics Subject Classification ID

Module categories in associative algebras (16D90) Representation type (finite, tame, wild, etc.) of associative algebras (16G60) Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers (16G70)

Related Items

Small potential counterexamples to the pure semisimplicity conjecture ⋮ Approximations and Mittag-Leffler conditions the applications ⋮ TTF triples in functor categories. ⋮ Indecomposable modules over pure semisimple hereditary rings. ⋮ Endoproperties of modules and local duality. ⋮ DEFINABLE SUBCATEGORIES OVER PURE SEMISIMPLE RINGS ⋮ Preinjective modules over pure semisimple rings. ⋮ On the endofiniteness of a key module over pure semisimple rings ⋮ Splitting torsion pairs over pure semisimple rings. ⋮ Large tilting modules and representation type. ⋮ Auslander-Reiten components over pure-semisimple hereditary rings. ⋮ Pure semisimplicity conjecture and Artin problem for dimension sequences ⋮ Tilting cotorsion pairs and pure semisimple rings

Cites Work

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• Existenz von Auslander-Reiten-Folgen
• Preprojective modules over Artin algebras
• Partial Coxeter functors and right pure semisimple hereditary rings
• A test for finite representation type
• Almost split sequences arising from the preprojective partition
• An Artin problem for division ring extensions and the pure semisimplicity conjecture. II
• Covers induced by Ext
• Endocoherent modules.
• Tilting modules and tilting torsion theories
• An Artin problem for division ring extensions and the pure semisimplicity conjecture. I
• Relative homological algebra
• Endofinite modules and pure semisimple rings.
• On the telescope conjecture for module categories.
• One dimensional tilting modules are of finite type.
• Purity, algebraic compactness, direct sum decompositions, and representation type
• Infinitely generated tilting modules of finite projective dimension
• The spectrum of a module category
• How To Make Ext Vanish
• On the Sparsity of Representations of Rings of Pure Global Dimension Zero
• Strong Preinjective Partitions and Representation Type of Artinian Rings
• Rein injektive direkte summen von moduln
• A duality result for almost split sequences
• Locally finitely presented additive categories
• Existence criteria and construction methods for certain classes of tilting modules
• A dichotomy for finite length modules induced by local duality
• Covers and Envelopes via Endoproperties of Modules
• DIRECT SUM DECOMPOSITION OF THE PRODUCT OF PREINJECTIVE MODULES OVER RIGHT PURE SEMISIMPLE HEREDITARY RINGS
• Representation Theory of Artin Algebras II
• Finitely Presented Right Modules Over a Left Pure-Semisimple Ring
• Infinite Dimensional Representations of Canonical Algebras
• Tilting modules and Gorenstein rings
• A Krull-Schmidt Theorem for Infinite Sums of Modules
• Tilting Cotorsion Pairs
• Strong preinjective partitions and almost split morphisms
• Tilting preenvelopes and cotilting precovers

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