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arXiv · 1502.04978

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

Kh. Ahmadi Amoli·Z. Habibi·M. Jahangiri
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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 $i \leq n+1$ and all $j< n$, then so is \linebreak$\Ass_R(\Hom_{R}(R/I,H^{n}_{I,J}(M)))$. We also study the finiteness of $\Ass_R(\Ext^{i}_{R}(R/I,H^{n}_{I,J} (M)))$ for $i=1,2$.

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Kh. Ahmadi Amoli, Z. Habibi, M. Jahangiri. 2015-02-17. On the associated prime ideals of local cohomology modules defined by a pair of ideals. https://arxiv.org/abs/1502.04978

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