Tameness and Artinianness of Graded Generalized Local Cohomology Modules

作     者：M. Jahangiri N. Shirmohammadi Sh. Tahamtan 

作者机构：Faculty of Mathematical sciences and Computer Kharazmi University rlbhran Iran School of Mathematics Institute for Research in Fundamental Sciences (IPM) P.O. Box 19395-5749 Tehran Iran School of Mathematics Institute for Research in Fundamental Sciences (IPM) P.O. Box 19395-5749 rlbhran Iran Department of Mathematics University of Tabriz Tabriz Iran Islamic Azad University Borujerd Branch Boroujerd Iran 

出 版 物：《Algebra Colloquium》 (代数集刊（英文版）)

年 卷 期：2015年第22卷第1期

页      面：131-146页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by a grant from IPM supported by a grant from IPM, Iran 

主　　题：graded rings and modules generalized local cohomology Artinian modules,tameness 

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）.