On the associated prime ideals of local cohomology modules defined by a pair of ideals

Maryam Jahangiri; Zohreh Habibi; Khadijeh Ahmadi Amoli

Discussiones Mathematicae General Algebra and Applications (2016)

  • Volume: 36, Issue: 1, page 15-23
  • ISSN: 1509-9415

Abstract

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Let I and J be two ideals of a commutative Noetherian ring R and M be an R-module. For a non-negative integer n it is shown that, if the sets A s s R ( E x t R n ( R / I , M ) ) and S u p p R ( E x t R i ( R / I , H I , J j ( M ) ) ) are finite for all i ≤ n+1 and all j < n, then so is A s s R ( H o m R ( R / I , H I , J n ( M ) ) ) . We also study the finiteness of A s s R ( E x t R i ( R / I , H I , J n ( M ) ) ) for i = 1,2.

How to cite

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Maryam Jahangiri, Zohreh Habibi, and Khadijeh Ahmadi Amoli. "On the associated prime ideals of local cohomology modules defined by a pair of ideals." Discussiones Mathematicae General Algebra and Applications 36.1 (2016): 15-23. <http://eudml.org/doc/286935>.

@article{MaryamJahangiri2016,
abstract = {Let I and J be two ideals of a commutative Noetherian ring R and M be an R-module. For a non-negative integer n it is shown that, if the sets $Ass_\{R\}(Ext^\{n\}_\{R\}(R/I,M))$ and $Supp_\{R\}(Ext^\{i\}_\{R\}(R/I,H^\{j\}_\{I,J\}(M)))$ are finite for all i ≤ n+1 and all j < n, then so is $Ass_\{R\}(Hom_\{R\}(R/I,H^\{n\}_\{I,J\}(M)))$. We also study the finiteness of $Ass_\{R\}(Ext^\{i\}_\{R\}(R/I,H^\{n\}_\{I,J\}(M)))$ for i = 1,2.},
author = {Maryam Jahangiri, Zohreh Habibi, Khadijeh Ahmadi Amoli},
journal = {Discussiones Mathematicae General Algebra and Applications},
keywords = {local cohomology modules defined by a pair of ideals; spectral sequences; associated prime ideals},
language = {eng},
number = {1},
pages = {15-23},
title = {On the associated prime ideals of local cohomology modules defined by a pair of ideals},
url = {http://eudml.org/doc/286935},
volume = {36},
year = {2016},
}

TY - JOUR
AU - Maryam Jahangiri
AU - Zohreh Habibi
AU - Khadijeh Ahmadi Amoli
TI - On the associated prime ideals of local cohomology modules defined by a pair of ideals
JO - Discussiones Mathematicae General Algebra and Applications
PY - 2016
VL - 36
IS - 1
SP - 15
EP - 23
AB - Let I and J be two ideals of a commutative Noetherian ring R and M be an R-module. For a non-negative integer n it is shown that, if the sets $Ass_{R}(Ext^{n}_{R}(R/I,M))$ and $Supp_{R}(Ext^{i}_{R}(R/I,H^{j}_{I,J}(M)))$ are finite for all i ≤ n+1 and all j < n, then so is $Ass_{R}(Hom_{R}(R/I,H^{n}_{I,J}(M)))$. We also study the finiteness of $Ass_{R}(Ext^{i}_{R}(R/I,H^{n}_{I,J}(M)))$ for i = 1,2.
LA - eng
KW - local cohomology modules defined by a pair of ideals; spectral sequences; associated prime ideals
UR - http://eudml.org/doc/286935
ER -

References

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