Graded annihilators of modules over the Frobenius skew polynomial ring, and tight closure
Graded annihilators of modules over the Frobenius skew polynomial ring, and tight closure
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Frobenius 斜多项式环上的模块的分级歼灭子和紧密闭合
DOI：
10.1090/s0002-9947-07-04247-x
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发表时间：
2006
影响因子：
1.3
通讯作者：
R. Y. Sharp
中科院分区：
文献类型：
--
作者：
R. Y. Sharp
本文研究了素特征为P的交换Noether局部环R中理想[a]的紧闭包。Fedder，K-i.渡边K. E.史密斯，N。Hara和F. Enescu等人在紧闭包的研究中利用了R的上局部上同调模上的自然Frobenius作用，取得了很好的效果，本文也采用了这一方法。本文的主要部分发展了一个理论，这里所谓的“特殊零化子子模”的左模在Frobenius斜多项式环相关的R;这一理论，然后在后面的部分适用于本文的顶部局部上同调模的R和用来表明，如果R是科恩-麦考利，那么它必须有一个弱参数测试元素，即使它不是优秀的。
This paper is concerned with the tight closure of an ideal [a] in a commutative Noetherian local ring R of prime characteristic P. Several authors, including R. Fedder, K-i. Watanabe, K. E. Smith, N. Hara and F. Enescu, have used the natural Frobenius action on the top local cohomology module of such an R to good effect in the study of tight closure, and this paper uses that device. The main part of the paper develops a theory of what are here called `special annihilator submodules' of a left module over the Frobenius skew polynomial ring associated to R; this theory is then applied in the later sections of the paper to the top local cohomology module of R and used to show that, if R is Cohen-Macaulay, then it must have a weak parameter test element, even if it is not excellent.