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Paper   IPM / M / 8291
School of Mathematics
  Title:   Integral closures, local cohomology and ideal topologies
  Author(s):  R. Naghipour
  Status:   Published
  Journal: Rocky Mountain J. Math.
  Vol.:  37
  Year:  2007
  Pages:   905-916
  Supported by:  IPM
Let (R, \frakm) be a formally equidimensional local ring of dimension d. Suppose that Φ is a system of nonzero ideals of R such that, for all minimal prime ideals \frakp of R,\fraka+\frakp is \frakm-primary for every \fraka ∈ Φ. In this paper, the main result asserts that for any ideal \frakb of R, the integral closure \frakb*(HdΦ(R)) of \frakb with respect to the Artinian R-module Hd Φ(R) is equal to \frakb\fraka, the classical Northcott-Rees integral closure of \frakb. This generalizes the main result of [13] concerning the question raised by D. Rees.

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