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Ideals defining Gorenstein rings are (almost) never products
Author(s):
Craig
Huneke
Journal:
Proc. Amer. Math. Soc.
135
(2007),
2003-2005.
MSC (2000):
Primary 13A15, 13D07, 13H10
Posted:
February 6, 2007
MathSciNet review:
2299472
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Abstract:
This note proves that if  is an unramified regular local ring and  proper ideals of height at least two, then  is never Gorenstein.
References:
-
- 1.
- M. Auslander, Modules over unramified regular local rings, Illinois J. Math., vol. 5, 1961, 631-647. MR 0179211 (31:3460)
- 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
 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:
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
Posted:
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
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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