Filter Depth and Cofiniteness of Local Cohomology Modules Defined by a Pair of Ideals

• 作者: Abolfazl Tehranian Atiyeh Pour Eshmanan Talemi
• 来源期刊: 代数集刊:英文版
• 学科: 数学
• 关键词: 上同调 理想 模块 过滤器 定义 inf文件 局部环 IGT
• 年，卷（期）: 2014,（4）
• 页码范围: 597-604
• 页数: 8页
• 分类号: O152.5
• 语种: 中文

摘要

Let I, J be ideals of a commutative Noetherian local ring (R, m) and let M be a finite R-module. The f-depth of M with respect to I is the least integer r such that H_I(M) is not Artinian. In this paper we show that inf{f-depth(a, M) 丨a ∈ W(I, J)} is the least integer such that the local cohomology module with respect to a pair of ideals I, J is not Artinian. As a consequence, it follows that H_I,J(M) is (I, J)-cofinite for all i 〈 inf{f-depth(a, M) 丨a ∈ W(I, J)}. In addition, we show that for a Serre subcategory S, if H_I,J(M) belongs to S for all i 〉 n and if b is an ideal of R such that H^n_I,J(M/bM) belongs to S, then the module H^n_I,J(M)/bH^n_I,J(M) belongs to S.