论文标题
模块局部深度的渐近稳定性
Asymptotic stability of depths of localizations of modules
论文作者
论文摘要
令r为一个可交换的noetherian环，我是R的理想，并且是有限生成的R模块。商模块M/I^n m的渐近行为是在交换代数中积极研究的主题。 The main result of this paper asserts that the depth of the localization of M/I^n M at any prime ideal of R is stable for large integers n that do not depend on the prime ideal, if the module M or M/I^n M is Cohen-Macaulay for some n>0, or the ring R is one of the following: a homomorphic image of a Cohen-Macaulay ring, a semi-local ring, an excellent ring, a准excellent和catenary环，以及可接受的环。
Let R be a commutative noetherian ring, I an ideal of R, and M a finitely generated R-module. The asymptotic behavior of the quotient modules M/I^n M of M is an actively studied subject in commutative algebra. The main result of this paper asserts that the depth of the localization of M/I^n M at any prime ideal of R is stable for large integers n that do not depend on the prime ideal, if the module M or M/I^n M is Cohen-Macaulay for some n>0, or the ring R is one of the following: a homomorphic image of a Cohen-Macaulay ring, a semi-local ring, an excellent ring, a quasi-excellent and catenary ring, and an acceptable ring.
