On the annihilators of local cohomology modules
- Bahmanpour, Kamal
- Aʼzami, Jafar
- Ghasemi, Ghader
Publication date
August 2012
DOI Publisher
Elsevier Inc. ISSN
0021-8693 Citation count (estimate)
10Abstract
AbstractLet (R,m) be a commutative Noetherian complete local ring, M a non-zero finitely generated R-module of dimension d⩾1, and TR(M):=⋃{N:N⩽M and dimN<dimM}. In this paper we calculate the annihilator of the top local cohomology module Hmd(M). More precisely, we show that 0:RHmd(M)=0:RM/TR(M). Moreover, for every positive integer n, we calculate the radical of the annihilator of Hmn(M). More precisely, we prove that if Hmn(M) is not finitely generated then Rad(0:RHmn(M))=⋂p∈Sp, whereS={p∈SpecR:(Hpn−1(M))p≠0 and dimR/p=1}
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