Bulletin of the
Korean Mathematical Society BKMS

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