The Gabriel-Roiter measure for representation-finite hereditary algebras.

DOI10.1016/j.jalgebra.2006.08.018zbMath1118.16019OpenAlexW2017246701MaRDI QIDQ875086

Bo Chen

Publication date: 11 April 2007

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2006.08.018

zbMATH Keywords

finite-dimensional algebrasfinitely generated modulesindecomposable modulesBrauer-Thrall conjecturesrepresentation-finite algebrasGabriel-Roiter submodulesalmost split mapsexceptional modulesGabriel-Roiter measure

Mathematics Subject Classification ID

Homological functors on modules (Tor, Ext, etc.) in associative algebras (16E30) 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)

Related Items (12)

The Gabriel-Roiter measure for \(\widetilde{\mathbb A}_n\). II. ⋮ The number of the Gabriel-Roiter measures admitting no direct predecessors over a wild quiver. ⋮ Regular modules with preprojective Gabriel-Roiter submodules over \(n\)-Kronecker quivers. ⋮ THE AUSLANDER–REITEN SEQUENCES ENDING AT GABRIEL–ROITER FACTOR MODULES OVER TAME HEREDITARY ALGEBRAS ⋮ Schofield sequences in the Euclidean case ⋮ Comparison of Auslander–Reiten Theory and Gabriel–Roiter Measure Approach to the Module Categories of Tame Hereditary Algebras ⋮ The Gabriel-Roiter measure for \(\widetilde\mathbb{A}_n\). ⋮ The number of Gabriel-Roiter submodules. ⋮ The Gabriel-Roiter submodules of simple homogeneous modules ⋮ Lie algebras arising from 1-cyclic perfect complexes ⋮ The first Brauer–Thrall conjecture over one-dimensional local rings ⋮ Representation-theoretic properties of balanced big Cohen-Macaulay modules

Cites Work

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• Tame algebras and integral quadratic forms
• On the kernel of an irreducible map.
• The Gabriel-Roiter measure.
• The Theorem of Bo Chen and Hall Polynomials
• Tilted Algebras
• The Kernel of an Irreducible Map

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