Comparison of Auslander–Reiten Theory and Gabriel–Roiter Measure Approach to the Module Categories of Tame Hereditary Algebras

DOI10.1080/00927870802175113zbMath1178.16013OpenAlexW2006682732MaRDI QIDQ3548582

Publication date: 16 December 2008

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

Full work available at URL: https://doi.org/10.1080/00927870802175113

zbMATH Keywords

Artin algebras preprojective modules tame hereditary algebras Auslander-Reiten theory representation types Gabriel-Roiter measures irreducible monomorphisms categories of finitely generated indecomposable left modules

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) Representations of associative Artinian rings (16G10)

Related Items (9)

The Gabriel-Roiter measure for \(\widetilde{\mathbb A}_n\). II. ⋮ The GR segments for tame hereditary algebras. ⋮ Gabriel-Roiter inclusions and Auslander-Reiten theory. ⋮ 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 Components in the Rhombic Picture ⋮ The Gabriel-Roiter measure for \(\widetilde\mathbb{A}_n\). ⋮ The Gabriel-Roiter submodules of simple homogeneous modules ⋮ Hall polynomials and the Gabriel–Roiter submodules of simple homogeneous modules

Cites Work

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