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| Paper IPM / M / 8291 |
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| Abstract: | |
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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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