Tameness and Artinianness of Graded Generalized Local Cohomology Modules

• 作者: M. Jahangiri N. Shirmohammadi Sh. Tahamtan
• 来源期刊: 代数集刊:英文版
• 学科: 数学
• 关键词: 子模块 上同调 广义 充分条件 有限生成 IGT SUP 有限性
• 年，卷（期）: 2015,（1）
• 页码范围: 131-146
• 页数: 16页
• 分类号: O152.5
• 语种: 中文

摘要

Let R = ⊙n〉0 Rn be a standard graded ring, a ∩ ⊙n〉0 Rn an ideal of R, and M, N two finitely generated graded R-modules. This paper studies the homogeneous components of graded generalized local cohomology modules. We show that for any i 〉 0, the n-th graded component Hiα(M, N)n of the i-th generalized local cohomology module of M and N with respect to a vanishes for all n 〉〉 0. Some sufficient conditions are pro- posed to satisfy the equality sup{end(Hiα (M, N)) [ i _〉 0} = sup{end(HiR+ (M, N)) | i 〉 0}. Also, some sufficient conditions are proposed for the tameness of Hiα(M, N) such that i = fRα+(M,N) or i = cdα(M,g), where fRα+(M,N) and cdα(M,g) denote the R+- finiteness dimension and the cohomological dimension of M and N with respect to a, respectively. Finally, we consider the Artinian property of some submodules and quotient modules of Hjα(M, N), where j is the first or last non-minimax level of Hiα(M, N).