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The number of indecomposable sequences over an Artin algebra of finite type

Author: Stephen P. Corwin
Journal: Proc. Amer. Math. Soc. 105 (1989), 301-304
MSC: Primary 16A64; Secondary 16A35, 16A46
MathSciNet review: 948148
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Abstract: Let $ \Lambda $ be an artin algebra of finite representation type. For a finitely generated $ \Lambda $-module $ C$, there are only finitely many f.g. modules $ A$ such that $ 0 \to A \to B \to C \to 0$ is indecomposable as a short exact sequence.

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  • [A] Maurice Auslander, Functors and morphisms determined by objects, Representation theory of algebras (Proc. Conf., Temple Univ., Philadelphia, Pa., 1976) Dekker, New York, 1978, pp. 1–244. Lecture Notes in Pure Appl. Math., Vol. 37. MR 0480688
  • [C] S. P. Corwin, Representation theory of the diagram $ {A_n}$ over the ring $ k[[x]]$, Dissertation, Virginia Tech, Blacksburg, Virginia.
  • [DR] Vlastimil Dlab and Claus Michael Ringel, Indecomposable representations of graphs and algebras, Mem. Amer. Math. Soc. 6 (1976), no. 173, v+57. MR 0447344

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Article copyright: © Copyright 1989 American Mathematical Society