Forum Mathematicum, ( ISI ), No (20), Year (2008-1) , Pages (265-273)

Title : ( On the finiteness properties of associated primes of generalized local cohomology modules )

Authors: Kazem Khashyarmanesh ,

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Let R be a commutative Noetherian ring, a an ideal of R and N an R-module. We prove that, for every finitely generated R-module of finite projective dimension t, the elements in the support of generalized local cohomology module Hnþt a ðM;NÞ of height n are finite for all nb0. This implies that, if R is a d-dimensional local ring, then Hdþt1 a ðM;NÞ has finite support for arbitrary R, a and N. In addition, for a non-negative integer n, we show that if M and N are arbitrary finitely generated R-modules such that the R-modules Hia ðNÞ and Hia ðM;NÞ have finite support for all i < n, then AssHn a ðM;NÞ is finite.

Keywords

local cohomology
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@article{paperid:1007432,
author = {Khashyarmanesh, Kazem},
title = {On the finiteness properties of associated primes of generalized local cohomology modules},
journal = {Forum Mathematicum},
year = {2008},
number = {20},
month = {January},
issn = {0933-7741},
pages = {265--273},
numpages = {8},
keywords = {local cohomology modules},
}

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%0 Journal Article
%T On the finiteness properties of associated primes of generalized local cohomology modules
%A Khashyarmanesh, Kazem
%J Forum Mathematicum
%@ 0933-7741
%D 2008

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