Results of certain local cohomology modules
Bull. Korean Math. Soc. 2014 Vol. 51, No. 3, 653-657
Published online May 1, 2014
Amir Mafi and Atiyeh Pour Eshmanan Talemi
University of Kurdistan Pasdaran ST., Islamic Azad University Science and Research Branch
Abstract : Let $R$ be a commutative Noetherian ring, $I$ and $J$ two idealsof $R$, and $M$ a finitely generated $R$-module. We prove that $${\rm Ext}_R^i(R/I,H_{I,J}^t(M))$$ is finitely generated for $i=0,1$ where $t=\inf\{i\in{\mathbb{N}_0}: H_{I,J}^i(M)$ is not finitely generated$\}$. Also, we prove that $H_{I+J}^i(H_{I,J}^t(M))$ is Artinian when ${\rm Dim} (R/{I+J})=0$ and $i=0,1$.
Keywords : local cohomology, Artinian modules
MSC numbers : 13D45, 13E99
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