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An Uncountably Infinite Number of Indecomposable Totally Reflexive Modules

Published online by Cambridge University Press:  11 January 2016

Ryo Takahashi
Ryo Takahashi*
Affiliation:
Department of Mathematics, School of Science and Technology, Meiji University, Kawasaki 214-8571, Japan, takahasi@math.meiji.ac.jp
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Abstract

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Several years ago, Huneke and Leuschke proved a theorem solving a conjecture of Schreyer. It asserts that an excellent Cohen-Macaulay local ring of countable Cohen-Macaulay type which is complete or has uncountable residue field has at most a one-dimensional singular locus. In this paper, it is verified that the assumption of the excellent property can be removed, and the theorem is considered over an arbitrary local ring. The main purpose of this paper is to prove that the existence of a certain prime ideal and a certain totally reflexive module implies the existence of an uncountably infinite number of isomorphism classes of indecomposable totally reflexive modules.

Keywords

13C1416G60
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 187 , September 2007 , pp. 35 - 48
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2007

References

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