Core and residual intersections of ideals

Details Core and residual intersections of ideals Core and residual intersections of ideals

2002-10-04

arxiv.org/abs/math/0210070v1

Trans. Amer. Math. Soc. 354 (2002), 2579-2594

Mathematics

Commutative Algebra

17 pages

Scientific paper

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.

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