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Brauer-thrall I for orders and its application to orders with loops in their Auslander-Reiten graph

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Representations of Algebras

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References

  • [A] Auslander, M.: “Applications of morphisms determined by modules”; Proc. Conf. on Representation Theory, Philadelphia (1976), Marcel Dekker (1978), 245–327.

    Google Scholar 

  • [AR] Auslander, M.—I. Reiten: “Representation theory of Artin algebras IV”; Comm. Algebra 5 (1977), 443–518.

    Article  MathSciNet  MATH  Google Scholar 

  • [DKR] Drozd, J.A.—V.V. Kirichenko—A.V. Roiter: “On hereditary and Bass-orders”; Izv. Akad. Nauk SSSR 31 (1967), 1415–1436.

    MathSciNet  Google Scholar 

  • [HPR1] Happel, D.—U. Preiser—C.M. Ringel: “A characterization of Dynkin-diagrams using subadditive functions with application to DTr-periodic modules”; to appear in Proc. Ottawa Conf. Representation Theory of Algebras (1979). Springer Lecture Notes.

    Google Scholar 

  • [HPR2] Happel, D.—U. Preiser—C.M. Ringel: “Binary polyhedral groups and Euclidean diagrams”; Preprint.

    Google Scholar 

  • [H] Harada, M.: “Structure of hereditary orders over local rings”; J. of Math., Osaka City Univ. 14 (1963), 1–22.

    MathSciNet  MATH  Google Scholar 

  • [HS] Harada, M.—Y. Sai: “On categories of indecomposable modules I”; Osaka J. Math. 7 (1970), 323–344.

    MathSciNet  MATH  Google Scholar 

  • [M] Maranda, J.-M.: “On p-adic integral representations of finite groups”; Canad. J. Math. 5 (1953), 344–355.

    Article  MathSciNet  MATH  Google Scholar 

  • [Rm] Riedtmann, Chr.: “Algebren, Darstellungsköcher, Überlagerungen und zurück”; Comment. Math. Helvetici 55 (1980), 199–224.

    Article  MathSciNet  MATH  Google Scholar 

  • [Ri] Ringel, C.M.: “Report on the Brauer-Thrall conjectures: Roiters Theorem and the Theorem of Nazarova and Roiter. (On algorithms for solving vector-space problems I)”; to appear in Proc. Second Intern. Conference on Represent. Theory of Algebras, Ottawa 1979.

    Google Scholar 

  • [RR] Ringel, C.M.—K.W. Roggenkamp: “Diagrammatic methods in the representation theory of orders”; J. Algebra 60 (1979), 11–42.

    Article  MathSciNet  MATH  Google Scholar 

  • [RW] Roggenkamp, K.W.—A. Wiedemann: “The lattice type of orders II”; to appear in Proc. Conference on Orders and their Applications, Oberwolfach (1980). Springer Lecture Notes.

    Google Scholar 

  • [Ro] Roggenkamp, K.W.: “Lattices over orders II”; Springer Lecture Notes in Math. 142 (1970).

    Google Scholar 

  • [T] Todorov, G.: “Almost split sequences for TrD-periodic modules”; Proc. Ottawa Conf. Representation Theory of Algebras (1979), Springer Lecture Notes.

    Google Scholar 

  • [W] Wiedemann, A.: “Orders with loops in their Auslander-Reitengraph”; to appear Comm. Algebra (1981).

    Google Scholar 

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Maurice Auslander Emilo Lluis

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© 1981 Springer-Verlag

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Wiedemann, A. (1981). Brauer-thrall I for orders and its application to orders with loops in their Auslander-Reiten graph. In: Auslander, M., Lluis, E. (eds) Representations of Algebras. Lecture Notes in Mathematics, vol 903. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0093004

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  • DOI: https://doi.org/10.1007/BFb0093004

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  • Print ISBN: 978-3-540-11179-5

  • Online ISBN: 978-3-540-38963-7

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