【摘要】：眾所周知,Noether環(huán)的每個理想是有限生成的背后隱含著一些一致性質。在過去的二十五年里,有關這方面的研究取得了一些重大進展,主要包括:局部環(huán)的一致Artin-Rees定理,既約優(yōu)秀局部環(huán)的Briancon-Skoda定理等,這些結果的重要性在于存在一個對環(huán)的所有理想均成立的整數(shù)。本文主要研究Noether環(huán)的一致局部上同調零化子以及極大理想的一致既約性質。Noether環(huán)R的一致局部上同調零化子是關于所有局部上同調模H_(PR_P)~i(R_P),ihtP的零化子問題,這里P是R的任意素理想。本文的一個研究重點是研究一致局部上同調零化子在多項式擴張和Rees擴張下的性質,我們有如下的結論:1、有限維的Noether環(huán)R有一致局部上同調零化子的充分必要條件為多項式環(huán)R[X]有一致局部上同調零化子。2、如果有限維Noether局部環(huán)(R,m)有一致局部上同調零化子,則Rees環(huán)存在不依賴于參數(shù)理想選取的一致局部上同調零化子。3、如果有限維Noether局部環(huán)(R,m)有一致局部上同調零化子,則Rees環(huán)存在不依賴于m-準素理想選取的一致局部上同調零化子。本文的另一個研究問題是極大理想的一致既約性質,它與環(huán)的一致BrianconSkoda性質密切相關,我們證明了如下的結論:4、一類環(huán)的極大理想具有一致既約性質,特別是優(yōu)秀環(huán)的極大理想具有一致既約性質。
[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.
【學位授予單位】：上海師范大學
【學位級別】：博士
【學位授予年份】：2016
【分類號】：O153.3

【參考文獻】

相關期刊論文 前1條

1 劉剛劍;宋傳寧;;一致局部上同調零化子和多項式擴張[J];上海師范大學學報(自然科學版);2006年01期

，

本文編號：2153284