On the cofiniteness of local cohomology modules

被引：59
|
作者：
Bahmanpour, Kamal [1 ,2 ]
Naghipour, Reza [1 ,3 ]
机构：
[1] Univ Tabriz, Dept Math, Tabriz, Iran
[2] Islamic Azad Univ, Dept Math, Ardebil Branch, Ardebil, Iran
[3] Inst Studies Theoret Phys & Math, Sch Math, Tehran, Iran
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2008年 / 136卷 / 07期
关键词：
local cohomology; cofinite module; minimax module; associated primes;
D O I：
10.1090/S0002-9939-08-09260-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this note we show that if I is an ideal of a Noetherian ring R and M is a finitely generated R-module, then for any minimax submodule N of H(I)(t) (M) the R-module Hom(R)(R/I, H(I)(t) (M)/N) is finitely generated, whenever the modules H(I)(0)(M), H(I)(1) (M),..., H(I)(t-1) (M) are minimax. As a consequence, it follows that the associated primes of H(I)(t) (M)/N are finite. This generalizes the main result of Brodmann and Lashgari (2000).
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页码：2359 / 2363
页数：5
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