Proceedings of the Indian Academy of Sciences - Mathematical Sciences, ( ISI ), Volume (120), No (1), Year (2010-2) , Pages (35-43)

Title : ( On the Matlis duals of local cohomology modules and modules of generalized fractions )

Authors: Kazem Khashyarmanesh ,

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Let (R,m) be a commutative Noetherian local ring with non-zero identity, a a proper ideal of R and M a finitely generated R-module with a M\\neq M. Let D(-):=Hom_R(-,E) be the Matlis dual functor, where E:=E(R/m) is the injective hull of the residue field R/m. In this paper, by using a complex which involves modules of generalized fractions, we show that, if x_1, ... ,x_n is a regular sequence on M contained in a, then H^n_(x_1, ... ,x_n)R (D(H^n_a(M))) is a homomorphic image of D(M), where H^i_b(-) is the i-th local cohomology functor with respect to an ideal b of R. By applying this result, we study some conditions on a certain module of generalized fractions under which D(H^n_(x_1,... ,x_n)(D(H^n_a(M))))\\cong D(D(M)).

Keywords

, local cohomology module, Matlis dual functor, module of generalized fractions, filter regular
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@article{paperid:1015209,
author = {Khashyarmanesh, Kazem},
title = {On the Matlis duals of local cohomology modules and modules of generalized fractions},
journal = {Proceedings of the Indian Academy of Sciences - Mathematical Sciences},
year = {2010},
volume = {120},
number = {1},
month = {February},
issn = {0253-4142},
pages = {35--43},
numpages = {8},
keywords = {local cohomology module; Matlis dual functor; module of generalized fractions; filter regular sequence},
}

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%0 Journal Article
%T On the Matlis duals of local cohomology modules and modules of generalized fractions
%A Khashyarmanesh, Kazem
%J Proceedings of the Indian Academy of Sciences - Mathematical Sciences
%@ 0253-4142
%D 2010

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