Computing the core of ideals in arbitrary characteristic

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• 作者：Louiza Fouli
• 关键词：Cores ; Reductions ; Reduction numbers
• 刊名：Journal of Algebra
• 出版年：2008
• 出版时间：1 April 2008
• 年：2008
• 卷：319
• 期：7
• 页码：2855-2867
• 全文大小：170 K

文摘

Let R be a local Gorenstein ring with infinite residue field of arbitrary characteristic. Let I be an R-ideal with g=htI>0, analytic spread ℓ, and let J be a minimal reduction of I. We further assume that I satisfies facee1c0c727188c026d1347e741a78e"" title=""Click to view the MathML source"">G_ℓ and depthR/I^jdimR/I−j+1 for 1jℓ−g. The question we are interested in is whether core(I)=Jⁿ⁺¹:∑_bI(J,b)ⁿ for n0. In the case of analytic spread Polini and Ulrich show that this is true with even weaker assumptions [C. Polini, B. Ulrich, A formula for the core of an ideal, Math. Ann. 331 (2005) 487–503, Theorem 3.4]. We give a negative answer to this question for higher analytic spreads and suggest a formula for the core of such ideals.