Title : WHEN ARE THE LOCAL COHOMOLOGY MODULES FINITELY GENERATED? ( When Are the Local Cohomology Modules Finitely Generated? )
Authors: Kazem Khashyarmanesh , Fahimeh Khoshahang Ghasr ,
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Abstract
Let R be a commutative Noetherian ring, an ideal of R, and M an R-module. We prove that for a fixed non-negative integer n, the nth local cohomology module Hn M is finitely generated if and only if Hn M is -cofinite and ⊆ 0 R Hn M . This enables us to establish the Noetherian property of local cohomology modules in several cases. Finally, we obtain a new characterization of the cohomological dimensions.
Keywords
Cofinite modules; Cohomological annihilators; Cohomological dimension; Local cohomology modules.
@article{paperid:203789,
author = {Khashyarmanesh, Kazem and Khoshahang Ghasr, Fahimeh},
title = {WHEN ARE THE LOCAL COHOMOLOGY MODULES FINITELY GENERATED?},
journal = {Communications in Algebra},
year = {2007},
volume = {35},
number = {10},
month = {March},
issn = {0092-7872},
pages = {3038--3044},
numpages = {6},
keywords = {Cofinite modules; Cohomological annihilators; Cohomological dimension; Local
cohomology modules.},
}
%0 Journal Article
%T WHEN ARE THE LOCAL COHOMOLOGY MODULES FINITELY GENERATED?
%A Khashyarmanesh, Kazem
%A Khoshahang Ghasr, Fahimeh
%J Communications in Algebra
%@ 0092-7872
%D 2007
