Proceedings of the Indian Academy of Sciences - Mathematical Sciences, ( ISI ), Volume (118), No (2), Year (2008-6) , Pages (197-206)

Title : ( On the finiteness properties of Matlis duals of local cohomology module )

Authors: Kazem Khashyarmanesh , Fahimeh Khoshahang Ghasr ,

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Let R be a complete semi-local ring with respect to the topology defined by its Jacobson radical, a an ideal of R, and M a finitely generated R-module. Let DR(−) := HomR(−, E), where E is the injective hull of the direct sum of all simple R-modules. If n is a positive integer such that Extj R(R/a,DR(Hta (M))) is finitely generated for all t > n and all j  0, then we show that HomR(R/a,DR(Hn a (M))) is also finitely generated. Specially, the set of prime ideals in CoassR(Hn a (M)) which contains a is finite. Next, assume that (R,m) is a complete local ring. We study the finiteness properties of DR(Hr a (R)) where r is the least integer i such that Hi a(R) is not Artinian. Keywords. Local cohomology modules; cofinite modules; associated primes; coassociated primes; filter regular sequences; Matlis duality functor.

Keywords

Local cohomology modules; cofinite
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@article{paperid:1007431,
author = {Khashyarmanesh, Kazem and Khoshahang Ghasr, Fahimeh},
title = {On the finiteness properties of Matlis duals of local cohomology module},
journal = {Proceedings of the Indian Academy of Sciences - Mathematical Sciences},
year = {2008},
volume = {118},
number = {2},
month = {June},
issn = {0253-4142},
pages = {197--206},
numpages = {9},
keywords = {Local cohomology modules; cofinite modules;},
}

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%0 Journal Article
%T On the finiteness properties of Matlis duals of local cohomology module
%A Khashyarmanesh, Kazem
%A Khoshahang Ghasr, Fahimeh
%J Proceedings of the Indian Academy of Sciences - Mathematical Sciences
%@ 0253-4142
%D 2008

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