The structure of the core of ideals |
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Authors: | Alberto Corso Claudia Polini Bernd Ulrich |
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Institution: | (1) Department of Mathematics, University of Kentucky, Lexington, KY 40506, USA (e-mail: corso@ms.uky.edu) , US;(2) Department of Mathematics, University of Oregon, Eugene, OR 97403, USA (e-mail: polini@math.uoregon.edu) , US;(3) Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA (e-mail: ulrich@math.msu.edu) , US |
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Abstract: | The core of an R-ideal I is the intersection of all reductions of I. This object was introduced by D. Rees and J. Sally and later studied by C. Huneke and I. Swanson, who showed in particular
its connection to J. Lipman's notion of adjoint of an ideal. Being an a priori infinite intersection of ideals, the core is
difficult to describe explicitly. We prove in a broad setting that: core(I) is a finite intersection of minimal reductions; core(I) is a finite intersection of general minimal reductions; core(I) is the contraction to R of a ‘universal’ ideal; core(I) behaves well under flat extensions. The proofs are based on general multiplicity estimates for certain modules.
Received: 16 May 2000 / Revised version: 11 December 2000 / Published online: 17 August 2001 |
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Keywords: | Mathematics Subject Classification (2000): 13A30 13B21 13H15 13C40 13H10 |
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