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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Core and residual intersections of ideals
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by Alberto Corso, Claudia Polini and Bernd Ulrich PDF
Trans. Amer. Math. Soc. 354 (2002), 2579-2594 Request permission

Abstract:

D. Rees and J. Sally defined the core of an $R$-ideal $I$ as the intersection of all (minimal) reductions of $I$. 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
  • MR Author ID: 348795
  • 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
  • MR Author ID: 340709
  • 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
  • MR Author ID: 175910
  • Email: ulrich@math.purdue.edu
  • 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
  • © Copyright 2002 American Mathematical Society
  • 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
  • MathSciNet review: 1895194