The Gabriel-Roiter measure for right pure semisimple rings.

DOI10.1007/s10468-008-9084-7zbMath1243.16010OpenAlexW1990343177MaRDI QIDQ1029573

Nguyen Viet Dung, Daniel Simson

Publication date: 13 July 2009

Published in: Algebras and Representation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10468-008-9084-7

zbMATH Keywords

Auslander-Reiten quiversfinite representation typepreprojective modulespreinjective modulesGabriel-Roiter measuresright pure semisimple rings

Mathematics Subject Classification ID

Module categories in associative algebras (16D90) Representation type (finite, tame, wild, etc.) of associative algebras (16G60) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Representations of associative Artinian rings (16G10) Simple and semisimple modules, primitive rings and ideals in associative algebras (16D60)

Related Items

Indecomposable modules over pure semisimple hereditary rings., The Auslander–Reiten Components in the Rhombic Picture, Splitting torsion pairs over pure semisimple rings.

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Preprojective modules over Artin algebras
• Partial Coxeter functors and right pure semisimple hereditary rings
• Representations of K-species and bimodules
• Pure semisimple categories and rings of finite representation type
• A test for finite representation type
• An Artin problem for division ring extensions and the pure semisimplicity conjecture. II
• On local right pure semisimple rings of length two or three.
• On right pure semisimple hereditary rings and an Artin problem
• An Artin problem for division ring extensions and the pure semisimplicity conjecture. I
• The Gabriel-Roiter measure.
• Purity, algebraic compactness, direct sum decompositions, and representation type
• ON SMALL RIGHT PURE SEMISIMPLE RINGS AND THE STRUCTURE OF THEIR AUSLANDER-REITEN QUIVER
• Quadratic Extensions of Skew Fields
• The Theorem of Bo Chen and Hall Polynomials
• On the Sparsity of Representations of Rings of Pure Global Dimension Zero
• Strong Preinjective Partitions and Representation Type of Artinian Rings
• An axiomatic characterization of the Gabriel-Roiter measure
• Duality and Pure-Semisimple Rings
• On Rings whose Left Modules are Direct Sums of Finitely Generated Modules
• On pure semi-simple Grothendieck categories II
• Preinjective modules and finite representation type of artinian rings
• Note on Rings of Finite Representation Type and Decompositions of Modules
• Representation Theory of Artin Algebras II
• Strong preinjective partitions and almost split morphisms