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Paper IPM / M / 8291  


Abstract:  
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 \frakmprimary 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 Rmodule
H^{d} _{Φ}(R) is equal to \frakb_{\frak}a, the classical
NorthcottRees integral closure of \frakb. This generalizes
the main result of [13] concerning the question raised by D. Rees.
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