Canadian Mathematical Bulletin, ( ISI ), Volume (53), No (4), Year (2010-7) , Pages (667-673)

Title : ( On the endomorphism rings of Local cohomology modules )

Authors: Kazem Khashyarmanesh ,

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Abstract. Let R be a commutative Noetherian ring and a a proper ideal of R. We show that if n := gradeR a, then EndR(Hn a (R)) ∼ = Ext n R(Hn a (R), R). We also prove that, for a nonnegative integer n such that Hi a(R) = 0 for every i 6= n, if Ext i R(Rz , R) = 0 for all i > 0 and z ∈ a, then EndR(Hn a (R)) is a homomorphic image of R, where Rz is the ring of fractions of R with respect to a multiplicatively closed subset {z j | j > 0} of R. Moreover, if HomR(Rz , R) = 0 for all z ∈ a, then ¹Hn a (R) is an isomorphism, where ¹Hn a (R) is the canonical ring homomorphism R → EndR(Hn a (R))

Keywords

, Local cohomology module, Endomorphism ring, Matlis dual functor, filter
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@article{paperid:1018353,
author = {Khashyarmanesh, Kazem},
title = {On the endomorphism rings of Local cohomology modules},
journal = {Canadian Mathematical Bulletin},
year = {2010},
volume = {53},
number = {4},
month = {July},
issn = {0008-4395},
pages = {667--673},
numpages = {6},
keywords = {Local cohomology module; Endomorphism ring; Matlis dual functor; filter regular sequence},
}

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%0 Journal Article
%T On the endomorphism rings of Local cohomology modules
%A Khashyarmanesh, Kazem
%J Canadian Mathematical Bulletin
%@ 0008-4395
%D 2010

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