On the Finiteness Dimension of Local Cohomology Modules  

作　　者：Hero Saremi Amir Marl 

机构地区：[1]Department of Mathematics, Sanandaj Branch Islamic Azad University, Sanandaj, Iran [2]Department of Mathematics, University of Kurdistan Pasdaran St., P.O. Box 416, Sanandaj, Iran

出　　处：《Algebra Colloquium》2014年第3期517-520,共4页代数集刊（英文版）

摘　　要：Let R be a commutative Noetherian ring, α an ideal of R, and M a non-zero finitely generated R-module. Let t be a non-negative integer. In this paper, it is shown that dim Supp Hi a（M） ≤ 1 for all i 〈 t if and only if there exists an ideal b of R such that dimR/b ≤ 1 and Hia（M） ≌ Hi b（M） for all i 〈 t. Moreover, we prove that dimSuppHia（M） 〈≤dim M - i for all i.Let R be a commutative Noetherian ring, α an ideal of R, and M a non-zero finitely generated R-module. Let t be a non-negative integer. In this paper, it is shown that dim Supp Hi a（M） ≤ 1 for all i 〈 t if and only if there exists an ideal b of R such that dimR/b ≤ 1 and Hia（M） ≌ Hi b（M） for all i 〈 t. Moreover, we prove that dimSuppHia（M） 〈≤dim M - i for all i.

关 键 词：local cohomology modules cofinite modules finiteness dimension 

分 类 号：O152.5[理学—数学] TP311.13[理学—基础数学]