Serre's condition for associated graded rings

Authors:
Mark Johnson and Bernd Ulrich

Journal:
Proc. Amer. Math. Soc. **127** (1999), 2619-2624

MSC (1991):
Primary 13A30; Secondary 13H10

DOI:
https://doi.org/10.1090/S0002-9939-99-04841-8

Published electronically:
April 23, 1999

MathSciNet review:
1600093

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Abstract | References | Similar Articles | Additional Information

Abstract: A criterion is given for when the associated graded ring of an ideal satisfies Serre's condition . As an application, the integrality and quasi-Gorensteinness of such rings is investigated.

**1.**W. Bruns and J. Herzog,*Cohen-Macaulay rings*, Cambridge University Press, Cambridge, 1993. MR**95h:13020****2.**R.C. Cowsik and M.V. Nori, On the fibers of blowing up, J. Indian Math. Soc.**40**(1976), 217-222. MR**58:28011****3.**R. Hartshorne, Complete intersections and connectedness, Amer. J. Math.**84**(1962), 497-508. MR**26:116****4.**J. Herzog, A. Simis, and W.V. Vasconcelos, On the canonical module of the Rees algebra and the associated graded ring of an ideal, J. Algebra**105**(1987), 285-302. MR**87m:13029****5.**J. Herzog, A. Simis, and W.V. Vasconcelos, Arithmetic of normal Rees algebras, J. Algebra**143**(1991), 269-294. MR**93b:13002****6.**M. Hochster, Criteria for the equality of ordinary and symbolic powers of primes, Math. Z.**133**(1973), 53-65. MR**48:2127****7.**C. Huneke, On the associated graded ring of an ideal, Illinois J. Math.**26**(1982), 121-137. MR**83d:13029****8.**C. Huneke, A. Simis, and W.V. Vasconcelos, Reduced normal cones are domains, in*Invariant theory*, Contemporary Mathematics**88**(1989), 95-101. MR**90c:13010****9.**I. Kaplansky,*Commutative rings*, University of Chicago Press, Chicago, 1974. MR**49:10674****10.**H. Matsumura,*Commutative ring theory*, Cambridge University Press, Cambridge, 1986. MR**88h:13001****11.**M. Nagata,*Local rings*, Krieger, New York, 1975. MR**57:301**

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Additional Information

**Mark Johnson**

Affiliation:
Department of Mathematics, University of Arkansas, Fayetteville, Arkansas 72701

Email:
mark@math.uark.edu

**Bernd Ulrich**

Affiliation:
Department of Mathematics, Michigan State University, East Lansing, Michigan 48824

Email:
ulrich@math.msu.edu

DOI:
https://doi.org/10.1090/S0002-9939-99-04841-8

Received by editor(s):
September 15, 1997

Received by editor(s) in revised form:
December 1, 1997

Published electronically:
April 23, 1999

Additional Notes:
The second author was partially supported by the NSF

Communicated by:
Wolmer V. Vasconcelos

Article copyright:
© Copyright 1999
American Mathematical Society