### 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.

Language | English (US) |
---|---|

Title of host publication | Commutative Algebra: 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 (Print) | 9781461452928, 1461452910, 9781461452911 |

DOIs | |

State | Published - Nov 1 2013 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*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

**Brauer-Thrall theory for maximal Cohen-Macaulay modules.** / Leuschke, Graham J; Wiegand, Roger.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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

}

TY - CHAP

T1 - Brauer-Thrall theory for maximal Cohen-Macaulay modules

AU - Leuschke, Graham J

AU - Wiegand, Roger

PY - 2013/11/1

Y1 - 2013/11/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84929567416&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84929567416&partnerID=8YFLogxK

U2 - 10.1007/978-1-4614-5292-8_18

DO - 10.1007/978-1-4614-5292-8_18

M3 - Chapter

SN - 9781461452928

SN - 1461452910

SN - 9781461452911

SP - 577

EP - 592

BT - Commutative Algebra: Expository Papers Dedicated to David Eisenbud on the Occasion of His 65th Birthday

PB - Springer New York

ER -