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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Local rings of countable Cohen-Macaulay type


Authors: Craig Huneke and Graham J. Leuschke
Journal: Proc. Amer. Math. Soc. 131 (2003), 3003-3007
MSC (2000): Primary 13C14; Secondary 13H10, 13C05
Published electronically: May 9, 2003
MathSciNet review: 1993205
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Abstract: We prove (the excellent case of) Schreyer's conjecture that a local ring with countable CM type has at most a one-dimensional singular locus. Furthermore, we prove that the localization of a Cohen-Macaulay local ring of countable CM type is again of countable CM type.


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Additional Information

Craig Huneke
Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
Email: huneke@math.ukans.edu

Graham J. Leuschke
Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
Email: gleuschke@math.ukans.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07167-3
PII: S 0002-9939(03)07167-3
Keywords: Maximal Cohen--Macaulay modules, CM representation type, countable CM type
Received by editor(s): May 10, 2002
Published electronically: May 9, 2003
Additional Notes: Both authors were supported by the National Science Foundation
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2003 American Mathematical Society