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, Volume 95, Issue 1, pp 331–347 | Cite as

On the integral closure of ideals

  • Alberto Corso
  • Craig Huneke
  • Wolmer V. Vasconcelos
Article
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Abstract

Among the several types of closures of an idealI that have been defined and studied in the past decades, the integral closureĪ has a central place being one of the earliest and most relevant. Despite this role, it is often a difficult challenge to describe it concretely once the generators ofI are known. Our aim in this note is to show that in a broad class of ideals their radicals play a fundamental role in testing for integral closedness, and in caseI ≠Ī, ✓I is still helpful in finding some fresh new elements inĪ/I. Among the classes of ideals under consideration are: complete intersection ideals of codimension two, generic complete intersection ideals, and generically Gorenstein ideals.

Mathematics Subject Classification (1991)

Primary: 13H10 Secondary: 13D40, 13D45, 13H15 
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Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • Alberto Corso
    • 1
  • Craig Huneke
    • 1
  • Wolmer V. Vasconcelos
    • 2
  1. 1.Department of MathematicsPurdue UniversityWest LafayetteUSA
  2. 2.Department of MathematicsRutgers UniversityNew BrunswickUSA

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