Core and residual intersections of ideals

Alberto Corso, Claudia Polini, Bernd Ulrich

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


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.

Original languageEnglish
Pages (from-to)2579-2594
Number of pages16
JournalTransactions of the American Mathematical Society
Issue number7
StatePublished - 2002


  • Integral closure
  • Reductions
  • Residual intersections of ideals

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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