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Gorenstein orders of finite representation type and bijective lattices

Part of the Lecture Notes in Mathematics book series (LNM,volume 1178)

Keywords

  • Dynkin Diagram
  • Springer Lecture Note
  • Split Sequence
  • Torsion Free Module
  • Congruent Modulo

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References

  1. Bautista, R.-S. Brenner: "Replication numbers for non-Dynkin sectional subgraphs in finite Auslander-Reiten quivers and some properties of Weyl roots", Proc.London Math.Soc.(3), 47 (1983), 429–462.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. Drozd, Ju.-V.V. Kirichenko-A.V. Roiter: "On hereditary and Bass orders", Izv.Akad.Nauk SSSR, 31 (1967), 1415–1436

    MathSciNet  Google Scholar 

  3. Happel, D.-U. Preiser-C.M. Ringel: "A characterization of Dynkin diagrams using subadditive functions with applications to DTr-periodic modules", Representation Theory II, Springer Lecture Notes 832 (1980), 280–294

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. "Algebren, Darstellungsköcher, Überlagerungen und zurück", Comment.Math.Helv. 55 (1980), 199–224

    Google Scholar 

  5. Ringel, C.M.-K.W. Roggenkamp: "Diagrammatic methods in representation theory of orders", J.Algebra 60 (1979), 11–42

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Roggenkamp, K.W.: "Lattices over orders II", Springer Lecture Notes Nr. 142 (1970), pp.392

    Google Scholar 

  7. Roggenkamp, K.W.: "Integral representations and structure of finite group rings", Presses de l'Université de Montréal 18eSession Séminaire de Mathématiques Supérieures (1980), 1–165 also: "Representation theory of blocks of defect 1", (Ottawa) Proceedings ICRA II, 2001–2024; LN 832 (1980), 521–544

    Google Scholar 

  8. Roggenkamp, K.W.: "The lattice type of orders: A diagrammatic approach I", Proc. of May Conference in Ring Theory 1980, Antwerpen, Lecture Notes Nr. 825 (1980), 104–129

    Google Scholar 

  9. Roggenkamp, K.W.:"The lattice type of orders II: Auslander-Reiten quivers", Springer Lecture Notes 882, Proc.Oberwolfach "Integral representations and applications" (1980), 430–477, (1983)

    Google Scholar 

  10. Roggenkamp, K.W.: "Auslander-Reiten species of Bäckström orders", J.of Algebra Vol.85, Nr.2, (1983), 449–476

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. Roggenkamp, K.W.: "Auslander-Reiten species for socle determined categories of hereditary algebras and for generalized Bäckström orders", Mitteilungen aus dem Math.Seminar Giessen, Heft 159 (1983), 1–98.

    MATH  Google Scholar 

  12. Wiedemann, A.: "Auslander-Reiten-Graphen von Ordnungen und Blöcke mit zyklischem Defekt 2", Dissertation 1980, Stuttgart also "The Auslander-Reiten graph of integral blocks with cyclic defect two and their integral representations", Math.Z.179 (1982), 407–429

    Google Scholar 

  13. Wiedemann, A.: "Orders with loops in their Auslander-Reiten graph", Com.in Algebra 9 (1981), 641–656

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. Wiedemann, A.: "Classification of the Auslander-Reiten guivers of local Gorenstein orders and simple curve singularities", Preprint 1984, Stuttgart

    Google Scholar 

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© 1986 Springer-Verlag

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Roggenkamp, K.W. (1986). Gorenstein orders of finite representation type and bijective lattices. In: Dlab, V., Gabriel, P., Michler, G. (eds) Representation Theory II Groups and Orders. Lecture Notes in Mathematics, vol 1178. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075298

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  • DOI: https://doi.org/10.1007/BFb0075298

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  • Print ISBN: 978-3-540-16433-3

  • Online ISBN: 978-3-540-39777-9

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