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, Volume 57, Issue 1, pp 1–31 | Cite as

Lower bounds for faithful, preinjective modules

  • Luise Unger
Article

Abstract

Let\(k\overrightarrow \Delta \) be the path algebra for some representation-infinite quiver\(\overrightarrow \Delta \) over some field k. There exists a bound\(m(\overrightarrow \Delta )\) such that τmI is faithful for all indecomposable injective\(k\overrightarrow \Delta \)-modules I and all\(m \geqslant m(\overrightarrow {\Delta )} \), and such that there → exists an indecomposable injective\(k\overrightarrow \Delta \)-module J satisfying that\({}_\tau m(\overrightarrow {\Delta )} - I_J \) J is not faithful, τ denotes the Auslander-Reiten-translation. Let m(Δ) be the maximum of the\(m(\overrightarrow {\Delta )} \) taken over all possible orientations of the underlying graph Δ. In this article we determine the bounds m(Δ) for representation-infinite quivers\(\overrightarrow \Delta \) for which Δ is a tree.

Keywords

Number Theory Algebraic Geometry Topological Group Path Algebra Preinjective Module 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Luise Unger
    • 1
  1. 1.Fakultät für MathematikUniversität BielefeldBielefeldFRG

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