Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

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
Retrieve article in: PDF

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:

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 $ \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)

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 13A15, 13D07, 13H10

Retrieve articles in all Journals with MSC (2000): 13A15, 13D07, 13H10

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.

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google