Title : ( Some Finiteness Results for Local Cohomology Modules with Respect to a Pair of Ideals )
Authors: BATOUL NAAL , Kazem Khashyarmanesh ,
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Abstract
Suppose that R is a commutative Noetherian ring with identity, I, J are ideals of R, and let M be a finitely generated R-module. Let HiI,J(−) be the ith local cohomology functor with respect to (I,J). In this paper, we show that the R-module HomR(R/I,H1I,J(M)/JH1I,J(M)) is always finitely generated. Moreover, we provide sufficient conditions such that the modules HomR(R/I,HiI,J(M)/JHiI,J(M))orTorRj(R/I,HiI,J(M)/JHiI,J(M)) is finitely generated.
Keywords
, local cohomology with respect to a pair of ideals, associated prime ideals, filter regular element
@article{paperid:1084855,
author = {NAAL, BATOUL and Khashyarmanesh, Kazem},
title = {Some Finiteness Results for Local Cohomology Modules with Respect to a Pair of Ideals},
journal = {Mathematical Notes},
year = {2021},
volume = {109},
number = {3},
month = {March},
issn = {0001-4346},
pages = {335--346},
numpages = {11},
keywords = {local cohomology with respect to a pair of ideals; associated prime ideals; filter
regular element},
}
%0 Journal Article
%T Some Finiteness Results for Local Cohomology Modules with Respect to a Pair of Ideals
%A NAAL, BATOUL
%A Khashyarmanesh, Kazem
%J Mathematical Notes
%@ 0001-4346
%D 2021
