Ideals defining Gorenstein rings are (almost) never products
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- by Craig Huneke PDF
- Proc. Amer. Math. Soc. 135 (2007), 2003-2005 Request permission
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
- M. Auslander, Modules over unramified regular local rings, Illinois J. Math. 5 (1961), 631–647. MR 179211, DOI 10.1215/ijm/1255631585
- Melvin Hochster, Euler characteristics over unramified regular local rings, Illinois J. Math. 28 (1984), no. 2, 281–285. MR 740618
- Stephen Lichtenbaum, On the vanishing of $\textrm {Tor}$ in regular local rings, Illinois J. Math. 10 (1966), 220–226. MR 188249
- Masayoshi Nagata, Local rings, Robert E. Krieger Publishing Co., Huntington, N.Y., 1975. Corrected reprint. MR 0460307
Additional Information
- Craig Huneke
- Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
- MR Author ID: 89875
- Email: huneke@math.ku.edu
- 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
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2299472