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References
V.I. Arnol’d: Critical points of smooth functions. Proc. Int. Cong. Math. Vancouver, Vol. I (1974), 19–39.
M. Auslander: Representation theory of artin algebras II. Comm. Alg. 1 (1974), 269–310.
M. Auslander: Existence theorems for almost split sequences. Ring Theory II, Proc. of the second Oklahoma Conf. (Marcel Dekker, New York, 1975), 1–44.
M. Auslander: Functors and morphisms determined by objects. Proc. Conf. on Repr. Theory, Philadelphia (1976). Marcel Dekker (1978), 1–245.
M. Auslander: Isolated singularities and existence of almost split sequences. Notes by L. Unger. Proc. of the fourth international conference on representations of algebras, Carleton University, Ottawa 1984, Springer Lecture Notes 1178, 194–242.
M. Auslander: Rational singularities and almost split sequences. Transactions of the American Math. Soc., Vol. 293, No. 2 (1986), 511–531.
M. Auslander and I. Reiten: Representation theory of artin algebras III, Comm. Alg. 3 (1975), 239–294; IV, ibid., 5 (1977), 443–518.
R. Buchweitz and G.-M. Greuel and F.-O. Schreyer: Cohen-Macaulay modules on hypersurface singularities II. To appear.
C.W. Curtis and I. Reiner: Methods of Representation Theory I, Pure and applied mathematics (Wiley, London 1981).
E. Dieterich: Classification of the indecomposable representations of the cyclic group of order three in a complete discrete valuation ring of ramification degree four. Preprint, Universität Bielefeld, 1985.
E. Dieterich: Reduction of isolated singularities. Preprint, Brandeis University, 1986.
E. Dieterich and A. Wiedemann: The Auslander-Reiten quiver of a simple curve singularity. Transactions of the American Math. Soc., Vol. 294, No. 2 (1986), 455–475.
D. Eisenbud: Homological algebra on a complete intersection, with an application to group representations. Transactions of the American Math. Soc., Vol. 260, No. 1 (1980), 35–64.
D. Happel and U. Preiser and C.M. Ringel: Vinberg’s characterization of Dynkin diagrams using subadditive functions with application to DTr-periodic modules. Proc. of the third international conf. on repr. of alg., Carleton Univ., Ottawa 1979. Springer Lecture Notes 832, 280–294.
D. Happel and U. Preiser and C.M. Ringel: Binary polyhedral groups and Euclidean diagrams. Manuscripta Mathematica 31 (1980), 317–329.
M. Harada and Y. Sai: On categories of indecomposable modules I. Osaka Journal of Mathematics 7 (1970), 323–344.
J. Herzog and H. Sanders: Indecomposable syzygy modules of high rank over hypersurface rings. To appear in Journal of pure and applied algebra.
H. Knörrer: Cohen-Macaulay modules on hypersurface singularities I. To appear.
Chr. Riedtmann: Algebren, Darstellungsköcher, Überlagerungen und zurūck. Commentarii Mathematici Helvetici 55 (1980), 199–224.
C.M. Ringel: Report on the Brauer-Thrall conjectures. Proceedings of the third international conference on representations of algebras, Carleton University, Ottawa 1979. Springer Lecture Notes 831, 104–136.
C.M. Ringel: Tame algebras and integral quadratic forms. Springer Lecture Notes 1099.
K.W. Roggenkamp and V. Huber-Dyson: Lattices over orders I, Springer Lecture Notes 115; II, ibid., 142.
K.W. Roggenkamp and J.W. Schmidt: Almost split sequences for integral group rings and orders. Communications in Algebra 4 (1976), 893–917.
P. Du Val: On isolated singularities of surfaces that do not affect the conditions of adjunction I, II, III. Proc. Cambridge Phil. Soc. 30 (1934), 483–491.
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Dieterich, E. (1987). The auslander-reiten quiver of an isolated singularity. In: Greuel, GM., Trautmann, G. (eds) Singularities, Representation of Algebras, and Vector Bundles. Lecture Notes in Mathematics, vol 1273. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078848
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DOI: https://doi.org/10.1007/BFb0078848
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