Let $R$ be a commutative Noetherian ring, $I$ and $J$ two idealsof $R$, and $M$ a finitely generated $R$-module. We prove that $${m Ext}_R^i(R/I,H_{I,J}^t(M))$$ is finitely generated for $i=0,1$ where $t=inf{iin{mathbb{N}_0}: H_{I,J}^i(M)$ is not finitely generated$}$. Also, we prove that $H_{I+J}^i(H_{I,J}^t(M))$ is Artinian when ${m Dim} (R/{I+J})=0$ and $i=0,1$.
展开▼
机译：假设$ R $是可交换的Noether环，$ I $和$ J $是$ R $的两个理想值，而$ M $是有限生成的$ R $模块。我们证明对于$ i = 0,1 $是有限生成的$$ { rm Ext} _R ^ i（R / I，H_ {I，J} ^ t（M））$$，其中$ t = inf {i in { mathbb {N} _0}：H_ {I，J} ^ i（M）$不是有限生成的$ } $。此外，我们证明当$ { rm Dim}（R / {I + J}）= 0 $且$ H_ {I + J} ^ i（H_ {I，J} ^ t（M））$是Artinian时， $ i = 0,1 $。
展开▼
