Notes on the behavior of the Ratliff-Rush filtration
Notes on the behavior of the Ratliff-Rush filtration
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Ratliff-Rush 过滤行为的注释
DOI：
10.1090/conm/331/05916
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
I. Swanson
中科院分区：
文献类型：
--
作者：
M. Rossi;I. Swanson
我们建立了新的 Ratliff-Rush 闭合理想类别和 Ratliff-Rush 闭合的一些病态行为。特别是，Ratliff-Rush 闭包在模表层元素、理想幂、相关素数、首项理想和最小生成元数下表现不佳。相比之下，Ratliff-Rush 过滤的约简数表现得更好：它保留了有关理想约简数的一些信息。令 I 为诺特环 R 中的理想。从极大值条件可知，对于所有大 n，对于条件 e I n = I n，在 R maximal 中存在理想 e I 。
We establish new classes of Ratliff-Rush closed ideals and some pathological behavior of the Ratliff-Rush closure. In particular, Ratliff-Rush closure does not behave well under passage modulo superficial elements, taking powers of ideals, associated primes, leading term ideals, and the minimal number of generators. In contrast, the reduction number of the Ratliff-Rush filtration behaves better: it preserves some information on the reduction number of the ideal. Let I be an ideal in a Noetherian ring R. From the maximal condition it follows that there exist ideals e I in R maximal with respect to the condition e I n = I n for all large n.