On the local cohomology of minimax modules
Bull. Korean Math. Soc. 2011 Vol. 48, No. 6, 1125-1128
https://doi.org/10.4134/BKMS.2011.48.6.1125
Published online November 1, 2011
Amir Mafi
Institute for Research in Fundamental Science (IPM)
Abstract : 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
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