Bulletin of the
Korean Mathematical Society BKMS

Let $R$ be a commutative Noetherian ring,$\frak a$ an ideal of $R$, and $M$ a minimax $R$-module. We prove that the local cohomology modules $H_{\frak a}^j(M)$ are $\frak a$-cominimax; that is, ${\rm Ext}_R^i(R/{\frak a},H_{\frak a}^j(M))$ is minimax for all $i$ and $j$ in the following cases: (a) $\dim R/{\frak a}=1$; (b) ${\rm cd}(\frak a)=1$, where cd is the cohomological dimension of $\frak a$ in $R$; (c) $\dim R \leq 2$. In these cases we also prove that the Bass numbers and the Betti numbers of $H_{\frak a}^j(M)$ are finite.

Keywords: local cohomology modules, minimax modules

MSC numbers: 13D45, 13E99