Asymptotic Behavior of Integral Closures in Modules

• 来源期刊: 代数集刊(英文版)
• 关键词: Rees' integral closures Nagata ring torsion-free module associated primes
• 年，卷（期）: 2007,（3）
• 页码范围: 505-514
• 页数: 10页
• 语种: 英文

摘要

Let R be a commutative Noetherian Nagata ring,let M be a non-zero finitely generated R-module,and let I be an ideal of R such that height M I > O.In this paper,there is a definition of the integral closure Na for any submodule N of M extending Rees'definition for the case of a domain.As the main results,it is shown that the operation N →Na on the set of submodules N of M is a semi-prime operation,and for any submodule Nof M,the sequences Ass R M/(InN)a and hssR(InM)a/(InN)a (n=1,2,...) of associated prime ideals are increasing and ultimately constant for large n.