Turkish Journal of Mathematics
Abstract
Let $I$ and $J$ be two ideals of a commutative Noetherian ring $R$ and $M$ be an $R$-module of dimension $d$. For each $i\in N_0$ let $H^{i}_{I,J}(-)$ denote the $i$-th right derived functor of $\Gamma_{I,J}(-)$, where $\Gamma _{I,J}(M):=\{x \in M : I^{n}x\subseteq Jx \ \text {for} \ n\gg 1\}$. If $R$ is a complete local ring and $M$ is finite, then attached prime ideals of $H^{d-1}_{I,J}(M)$ are computed by means of the concept of co-localization. Moreover, we illustrate the attached prime ideals of $H^{t}_{I,J}(M)$ on a nonlocal ring $R$, for $t= \dim M$ and $t= (I,J,M)$, where $(I,J,M)$ is the last nonvanishing level of $H^{i}_{I,J}(M)$.
DOI
10.3906/mat-1503-43
Keywords
Local cohomology modules with respect to a pair of ideals, attached prime ideals, co-localization
First Page
216
Last Page
222
Recommended Citation
HABIBI, Z, JAHANGIRI, M, & AMOLI, K. A (2017). On the attached prime ideals of localcohomology modules defined by a pair of ideals. Turkish Journal of Mathematics 41 (1): 216-222. https://doi.org/10.3906/mat-1503-43
