The reduction number of an ideal and the local cohomology of the associated graded ring
The reduction number of an ideal and the local cohomology of the associated graded ring
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理想的约简数和相关分级环的局部上同调
DOI：
10.1090/s0002-9939-1993-1112496-7
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发表时间：
1993
期刊：
影响因子：
--
通讯作者：
T. Marley
中科院分区：
文献类型：
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作者：
T. Marley
设（R，m）是局部环，I是m-准素理想. Trung的一个结果表明，如果gr 1（R）的局部上同调满足一定的条件，则I的约化数与所选择的最小约化无关.这些条件由t = dim R级gr 1（R）+不等式组成。我们证明了如果R是Cohen-Macaulay，则其中一个不等式总是满足的，而另一个不等式往往是容易检验的.然后给出了在二维Cohen-Macaulay环中的应用。例如，我们证明，如果对于所有大于1的整数，I的Hilbert函数等于I的Hilbert多项式，那么约简数与最小约简的选择无关。
Let (R, m) be a local ring and I an m-primary ideal. A result of Trung shows that if the local cohomology of gr1(R) satisfies certain conditions, then the reduction number of I is independent of the minimal reduction chosen. These conditions consist of t = dim R grade gr1 (R)+ inequalities. We show that if R is Cohen-Macaulay, then one of these inequalities is always satisied, while another can often be easily checked. Applications are then given in two-dimensional Cohen-Macaulay rings. For instance, we show that if the Hilbert function of I equals the Hilbert polynomial of I for all integers greater than 1, then the reduction number is independent of the choice of minimal reduction.