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

Abstract

Let $I$ and $J$ be two ideals of a commutative Noetherian ring $R$ and $M$ be an $R$-module of dimension $d$. If $R$ is a complete local ring and $M$ is finite, then attached prime ideals of $H_{I,J}^{d-1}(M)$ are computed by means of the concept of co-localization. Also, we illustrate the attached prime ideals of $H_{I,J}^t(M)$ on a non-local ring $R$, for $t=\dim M$ and $t=cd(I,J,M)$.

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