Some results on top local cohomology modules with respect to a pair of ideals

Saeed Jahandoust; Reza Naghipour

Mathematica Bohemica (2020)

  • Volume: 145, Issue: 4, page 377-386
  • ISSN: 0862-7959

Abstract

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Let I and J be ideals of a Noetherian local ring ( R , 𝔪 ) and let M be a nonzero finitely generated R -module. We study the relation between the vanishing of H I , J dim M ( M ) and the comparison of certain ideal topologies. Also, we characterize when the integral closure of an ideal relative to the Noetherian R -module M / J M is equal to its integral closure relative to the Artinian R -module H I , J dim M ( M ) .

How to cite

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Jahandoust, Saeed, and Naghipour, Reza. "Some results on top local cohomology modules with respect to a pair of ideals." Mathematica Bohemica 145.4 (2020): 377-386. <http://eudml.org/doc/297168>.

@article{Jahandoust2020,
abstract = {Let $I$ and $J$ be ideals of a Noetherian local ring $(R,\mathfrak \{m\})$ and let $M$ be a nonzero finitely generated $R$-module. We study the relation between the vanishing of $H_\{I,J\}^\{\dim M\}(M)$ and the comparison of certain ideal topologies. Also, we characterize when the integral closure of an ideal relative to the Noetherian $R$-module $M/JM$ is equal to its integral closure relative to the Artinian $R$-module $H_\{I,J\}^\{\dim M\}(M)$.},
author = {Jahandoust, Saeed, Naghipour, Reza},
journal = {Mathematica Bohemica},
keywords = {Artinian module; integral closure; local cohomology; quasi-unmixed module},
language = {eng},
number = {4},
pages = {377-386},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some results on top local cohomology modules with respect to a pair of ideals},
url = {http://eudml.org/doc/297168},
volume = {145},
year = {2020},
}

TY - JOUR
AU - Jahandoust, Saeed
AU - Naghipour, Reza
TI - Some results on top local cohomology modules with respect to a pair of ideals
JO - Mathematica Bohemica
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 145
IS - 4
SP - 377
EP - 386
AB - Let $I$ and $J$ be ideals of a Noetherian local ring $(R,\mathfrak {m})$ and let $M$ be a nonzero finitely generated $R$-module. We study the relation between the vanishing of $H_{I,J}^{\dim M}(M)$ and the comparison of certain ideal topologies. Also, we characterize when the integral closure of an ideal relative to the Noetherian $R$-module $M/JM$ is equal to its integral closure relative to the Artinian $R$-module $H_{I,J}^{\dim M}(M)$.
LA - eng
KW - Artinian module; integral closure; local cohomology; quasi-unmixed module
UR - http://eudml.org/doc/297168
ER -

References

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