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Brauer–Thrall Theory for Maximal Cohen–Macaulay Modules

  • Graham J. Leuschke
  • Roger WiegandEmail author
Chapter

Abstract

The Brauer-Thrall Conjectures, now theorems, were originally stated for finitely generated modules over a finite-dimensional k-algebra. They say, roughly speaking, that infinite representation type implies the existence of lots of indecomposable modules of arbitrarily large k-dimension. These conjectures have natural interpretations in the context of maximal Cohen-Macaulay modules over Cohen-Macaulay local rings. This is a survey of progress on these transplanted conjectures.

Keywords

Local Ring Indecomposable Module Minimal Prime Ideal Hypersurface Singularity Principal Ideal Ring 
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.

Notes

Acknowledgments

Research for this work was partially supported by NSF grant DMS-0902119 (GJL) and by a Simons Foundation Collaboration Grant (RW).

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsSyracuse UniversitySyracuseUSA
  2. 2.Department of MathematicsUniversity of Nebraska–LincolnLincolnUSA

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