Krull-Gabriel dimension of 1-domestic string algebras.

DOI10.1007/S10468-006-9028-ZzbMath1187.16012OpenAlexW2364025005MaRDI QIDQ865034

Gena Puninski, M. Y. Prest

Publication date: 13 February 2007

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

Full work available at URL: https://doi.org/10.1007/s10468-006-9028-z

zbMATH Keywords

finite-dimensional algebrascategories of modulesAuslander-Reiten quiversKrull-Gabriel dimensionpure injective modulesdomestic string algebras

Mathematics Subject Classification ID

Injective modules, self-injective associative rings (16D50) Representation type (finite, tame, wild, etc.) of associative algebras (16G60) Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers (16G70) Representations of quivers and partially ordered sets (16G20) Chain conditions on annihilators and summands: Goldie-type conditions (16P60)

Related Items (5)

The Krull-Gabriel dimension of cycle-finite Artin algebras ⋮ How to construct a `concrete' superdecomposable pure-injective module over a string algebra. ⋮ Pure injective indecomposable modules over 1-domestic string algebras. ⋮ Modules with irrational slope over tubular algebras ⋮ Strongly simply connected algebras with super-decomposable pure-injective modules

Cites Work

• The Ziegler and Zariski spectra of some domestic string algebras.
• Model theory of modules
• The Krull-Gabriel dimension of the representation theory of a tame hereditary Artin algebra and applications to the structure of exact sequences
• Representation embeddings and the Ziegler spectrum
• Ziegler spectra of tame hereditary algebras
• Maps between representations of zero-relation algebras
• On the Krull-Gabriel dimension of an algebra
• On the Infinite Radical of a Module Category
• Auslander-reiten sequences with few middle terms and applications to string algebrass
• Ziegler spectra of serial rings with krull dimension
• The Krull–Gabriel Dimension of a Serial Ring
• Superdecomposable pure-injective modules exist over some string algebras
• Modules and Stability Theory
• One-directed indecomposable pure injective modules over string algebras
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