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

 

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
Published electronically: February 6, 2007
MathSciNet review: 2299472
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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.


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Additional Information

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

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08758-8
PII: S 0002-9939(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.