Core and residual intersections of ideals

Authors:
Alberto Corso, Claudia Polini and Bernd Ulrich

Journal:
Trans. Amer. Math. Soc. **354** (2002), 2579-2594

MSC (2000):
Primary 13H10; Secondary 13A30, 13B22, 13C40, 13D45

DOI:
https://doi.org/10.1090/S0002-9947-02-02908-2

Published electronically:
February 1, 2002

MathSciNet review:
1895194

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: D. Rees and J. Sally defined the core of an -ideal as the intersection of all (minimal) reductions of . However, it is not easy to give an explicit characterization of it in terms of data attached to the ideal. Until recently, the only case in which a closed formula was known is the one of integrally closed ideals in a two-dimensional regular local ring, due to C. Huneke and I. Swanson. The main result of this paper explicitly describes the core of a broad class of ideals with good residual properties in an arbitrary local Cohen-Macaulay ring. We also find sharp bounds on the number of minimal reductions that one needs to intersect to get the core.

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Additional Information

**Alberto Corso**

Affiliation:
Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506

Email:
corso@ms.uky.edu

**Claudia Polini**

Affiliation:
Department of Mathematics, University of Oregon, Eugene, Oregon 97403

Address at time of publication:
Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556

Email:
cpolini@nd.edu

**Bernd Ulrich**

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

Address at time of publication:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907

Email:
ulrich@math.purdue.edu

DOI:
https://doi.org/10.1090/S0002-9947-02-02908-2

Keywords:
Integral closure,
reductions,
residual intersections of ideals

Received by editor(s):
April 10, 2001

Published electronically:
February 1, 2002

Additional Notes:
The first author was partially supported by the NATO/CNR Advanced Fellowships Programme during an earlier stage of this work. The second and third authors were partially supported by the NSF

Dedicated:
To Professor Craig Huneke on the occasion of his fiftieth birthday

Article copyright:
© Copyright 2002
American Mathematical Society