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Ideals defining Gorenstein rings are (almost) never products


Author: Craig Huneke
Journal: Proc. Amer. Math. Soc. 135 (2007), 2003-2005
MSC (2000): Primary 13A15, 13D07, 13H10
DOI: https://doi.org/10.1090/S0002-9939-07-08758-8
Published electronically: February 6, 2007
MathSciNet review: 2299472
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Abstract | References | Similar Articles | Additional Information

Abstract: This note proves that if $ S$ is an unramified regular local ring and $ I,J$ proper ideals of height at least two, then $ S/IJ$ is never Gorenstein.


References [Enhancements On Off] (What's this?)

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  • 2. M. Hochster, Euler characteristics over unramified regular local rings, Illinois J. Math., vol. 28, 1984, 281-285. MR 0740618 (85i:13020)
  • 3. S. Lichtenbaum, On the vanishing of $ \operatorname{Tor{}}$ in regular local rings, Illinois J. Math., vol. 10, 1966, 220-226. MR 0188249 (32:5688)
  • 4. M. Nagata, Local Rings, Kreiger Publishing Co., 1975, New York. MR 0460307 (57:301)

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Additional Information

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

DOI: https://doi.org/10.1090/S0002-9939-07-08758-8
Keywords: Regular ring, Gorenstein ring, unramified
Received by editor(s): December 12, 2005
Received by editor(s) in revised form: April 3, 2006
Published electronically: February 6, 2007
Additional Notes: The author gratefully acknowledges support by the NSF grant DMS-0244405. I also thank Bill Heinzer for correspondence concerning the paper, and in particular for sending me the statement and argument of Proposition 1
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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