Noether环中的一致性质
发布时间：2018-07-29 16:27
【摘要】：众所周知,Noether环的每个理想是有限生成的背后隐含着一些一致性质。在过去的二十五年里,有关这方面的研究取得了一些重大进展,主要包括:局部环的一致Artin-Rees定理,既约优秀局部环的Briancon-Skoda定理等,这些结果的重要性在于存在一个对环的所有理想均成立的整数。本文主要研究Noether环的一致局部上同调零化子以及极大理想的一致既约性质。Noether环R的一致局部上同调零化子是关于所有局部上同调模H_(PR_P)~i(R_P),ihtP的零化子问题,这里P是R的任意素理想。本文的一个研究重点是研究一致局部上同调零化子在多项式扩张和Rees扩张下的性质,我们有如下的结论:1、有限维的Noether环R有一致局部上同调零化子的充分必要条件为多项式环R[X]有一致局部上同调零化子。2、如果有限维Noether局部环(R,m)有一致局部上同调零化子,则Rees环存在不依赖于参数理想选取的一致局部上同调零化子。3、如果有限维Noether局部环(R,m)有一致局部上同调零化子,则Rees环存在不依赖于m-准素理想选取的一致局部上同调零化子。本文的另一个研究问题是极大理想的一致既约性质,它与环的一致BrianconSkoda性质密切相关,我们证明了如下的结论:4、一类环的极大理想具有一致既约性质,特别是优秀环的极大理想具有一致既约性质。
[Abstract]:It is well known that there are some uniform properties behind the finite-generation of every ideal of Noether rings. In the past 25 years, great progress has been made in this field, including the uniform Artin-Rees theorem for local rings, the Briancon-Skoda theorem for local rings, and so on. The importance of these results lies in the existence of an integer for all ideals of a ring. In this paper, we study the uniformly local cohomology annihilators of Noether rings and the uniformly cohombic annihilators of maximal ideal. The uniformly local cohomology annihilators of R are about the annihilators of all locally cohomological modules H _ (PR_P) I (RP) / ihtP, where P is an arbitrary prime ideal of R. One of the key points of this paper is to study the properties of uniformly cohomology annihilators under polynomial extensions and Rees extensions. We have the following conclusion: 1, A sufficient and necessary condition for a finite-dimensional Noether ring R to have a uniform local cohomology annihilator is that the polynomial ring R [X] has a uniform local cohomology annihilator .2if the finite-dimensional Noether local ring (R _ m) has a uniform local cohomology annihilator, Then there is a uniform local cohomology annihilator. 3 in Rees ring. If the finite-dimensional Noether local ring (Rum) has a uniform local cohomology annihilator, then Rees ring has a uniform local cohomology annihilator independent of the selection of m- primary ideals. Another problem of this paper is the uniformly irreducible property of maximal ideal, which is closely related to the uniform BrianconSkoda property of rings. We prove the following conclusion: 4, the maximal ideals of a class of rings have uniformly irreducible properties. In particular, the maximal ideals of excellent rings have uniformly irreducible properties.
【学位授予单位】：上海师范大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O153.3
本文编号：2153284
[Abstract]:It is well known that there are some uniform properties behind the finite-generation of every ideal of Noether rings. In the past 25 years, great progress has been made in this field, including the uniform Artin-Rees theorem for local rings, the Briancon-Skoda theorem for local rings, and so on. The importance of these results lies in the existence of an integer for all ideals of a ring. In this paper, we study the uniformly local cohomology annihilators of Noether rings and the uniformly cohombic annihilators of maximal ideal. The uniformly local cohomology annihilators of R are about the annihilators of all locally cohomological modules H _ (PR_P) I (RP) / ihtP, where P is an arbitrary prime ideal of R. One of the key points of this paper is to study the properties of uniformly cohomology annihilators under polynomial extensions and Rees extensions. We have the following conclusion: 1, A sufficient and necessary condition for a finite-dimensional Noether ring R to have a uniform local cohomology annihilator is that the polynomial ring R [X] has a uniform local cohomology annihilator .2if the finite-dimensional Noether local ring (R _ m) has a uniform local cohomology annihilator, Then there is a uniform local cohomology annihilator. 3 in Rees ring. If the finite-dimensional Noether local ring (Rum) has a uniform local cohomology annihilator, then Rees ring has a uniform local cohomology annihilator independent of the selection of m- primary ideals. Another problem of this paper is the uniformly irreducible property of maximal ideal, which is closely related to the uniform BrianconSkoda property of rings. We prove the following conclusion: 4, the maximal ideals of a class of rings have uniformly irreducible properties. In particular, the maximal ideals of excellent rings have uniformly irreducible properties.
【学位授予单位】：上海师范大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O153.3
【参考文献】
相关期刊论文 前1条
1 刘刚剑;宋传宁;;一致局部上同调零化子和多项式扩张[J];上海师范大学学报(自然科学版);2006年01期
，本文编号：2153284
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