Brauer-Thrall theory for maximal Cohen-Macaulay modules

Graham J. Leuschke, Roger Wiegand

Research output: Chapter in Book/Report/Conference proceedingChapter

3 Scopus citations

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 languageEnglish (US)
Title of host publicationCommutative Algebra
Subtitle of host publicationExpository Papers Dedicated to David Eisenbud on the Occasion of His 65th Birthday
PublisherSpringer New York
Pages577-592
Number of pages16
ISBN (Electronic)9781461452928
ISBN (Print)1461452910, 9781461452911
DOIs
StatePublished - Nov 1 2013

ASJC Scopus subject areas

  • Mathematics(all)

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    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