Brauer–Thrall Theory for Maximal Cohen–Macaulay Modules

Graham J. Leuschke () and Roger Wiegand ()
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Graham J. Leuschke: Syracuse University, Department of Mathematics
Roger Wiegand: University of Nebraska–Lincoln, Department of Mathematics

A chapter in Commutative Algebra, 2013, pp 577-592 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-5292-8_18

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DOI: 10.1007/978-1-4614-5292-8_18

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