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Article overview
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Core and residual intersections of ideals | | Alberto Corso
; Claudia Polini
; Bernd Ulrich
; | | Date: |
4 Oct 2002 | | Journal: | Trans. Amer. Math. Soc. 354 (2002), 2579-2594 | | Subject: | Commutative Algebra | math.AC | | Abstract: | 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. | | Source: | arXiv, math.AC/0210070 | | Services: | Forum | Review | PDF | Favorites | |
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