### 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.

Original language | English (US) |
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Title of host publication | Commutative Algebra |

Subtitle of host publication | Expository Papers Dedicated to David Eisenbud on the Occasion of His 65th Birthday |

Publisher | Springer New York |

Pages | 577-592 |

Number of pages | 16 |

ISBN (Electronic) | 9781461452928 |

ISBN (Print) | 1461452910, 9781461452911 |

DOIs | |

State | Published - Nov 1 2013 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Leuschke, G. J., & Wiegand, R. (2013). Brauer-Thrall theory for maximal Cohen-Macaulay modules. In

*Commutative Algebra: Expository Papers Dedicated to David Eisenbud on the Occasion of His 65th Birthday*(pp. 577-592). Springer New York. https://doi.org/10.1007/978-1-4614-5292-8_18