Auslander-reiten quivers of orders as auslander-reiten quivers of module categories over artinian rings

DOI10.1080/00927878708823415zbMath0608.16012OpenAlexW2001093653MaRDI QIDQ3748430

Klaus W. Roggenkamp

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1080/00927878708823415

zbMATH Keywords

coveringalmost split sequencesArtin algebrasGalois coveringAuslander-Reiten quivertriangular matrix algebraAuslander-Reiten speciesBäckström orderrepresentation-finitecategory of \(\Lambda \)-latticesirreducible \(\Gamma \)-lattices

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Module categories in associative algebras (16D90) Category-theoretic methods and results in associative algebras (except as in 16D90) (16B50) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Artinian rings and modules (associative rings and algebras) (16P20) Representation theory of associative rings and algebras (16Gxx)

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Cites Work

• Diagrammatic methods in the representation theory of orders
• Covering spaces in representation-theory
• The Auslander-Reiten graph of integral blocks with cyclic defect two and their integral representations
• Integral representations and diagrams
• Auslander-reiten quivers of schurian orders
• Systems of lattices in vector spaces and their invariants¹