Volume 30, Issue 1
Cofiniteness of Local Cohomology Modules with Respect to a Pair of Ideals

Commun. Math. Res., 30 (2014), pp. 33-40.

Published online: 2021-05

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• Abstract

Let $R$ be a commutative Noetherian ring, $I$ and $J$ be two ideals of $R$, and $M$ be an $R$-module. We study the cofiniteness and finiteness of the local cohomology module $H^i_{I,J} (M)$ and give some conditions for the finiteness of Hom$_R(R/I, H^s_{ I,J} (M))$ and Ext$^1_R(R/I, H^s_{I,J} (M))$. Also, we get some results on the attached primes of $H^{{\rm dim}M}_{I,J} (M)$.

• Keywords

local cohomology, cofinite module, attached prime.

13D45, 13E15

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@Article{CMR-30-33, author = {Yan and Gu and and 18780 and and Yan Gu}, title = {Cofiniteness of Local Cohomology Modules with Respect to a Pair of Ideals}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {30}, number = {1}, pages = {33--40}, abstract = {

Let $R$ be a commutative Noetherian ring, $I$ and $J$ be two ideals of $R$, and $M$ be an $R$-module. We study the cofiniteness and finiteness of the local cohomology module $H^i_{I,J} (M)$ and give some conditions for the finiteness of Hom$_R(R/I, H^s_{ I,J} (M))$ and Ext$^1_R(R/I, H^s_{I,J} (M))$. Also, we get some results on the attached primes of $H^{{\rm dim}M}_{I,J} (M)$.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/18985.html} }
TY - JOUR T1 - Cofiniteness of Local Cohomology Modules with Respect to a Pair of Ideals AU - Gu , Yan JO - Communications in Mathematical Research VL - 1 SP - 33 EP - 40 PY - 2021 DA - 2021/05 SN - 30 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/18985.html KW - local cohomology, cofinite module, attached prime. AB -

Let $R$ be a commutative Noetherian ring, $I$ and $J$ be two ideals of $R$, and $M$ be an $R$-module. We study the cofiniteness and finiteness of the local cohomology module $H^i_{I,J} (M)$ and give some conditions for the finiteness of Hom$_R(R/I, H^s_{ I,J} (M))$ and Ext$^1_R(R/I, H^s_{I,J} (M))$. Also, we get some results on the attached primes of $H^{{\rm dim}M}_{I,J} (M)$.

Yan Gu. (2021). Cofiniteness of Local Cohomology Modules with Respect to a Pair of Ideals. Communications in Mathematical Research . 30 (1). 33-40. doi:
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