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arXiv · 1302.6395

On flat and Gorenstein flat dimensions of local cohomology modules

Majid Rahro Zargar·Hossein Zakeri
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Abstract

Let $\fa$ be an ideal of a Noetherian local ring $R$ and let $C$ be a semidualizing $R$-module. For an $R$-module $X$, we denote any of the quantities $\fd_R X$, $\Gfd_R X$ and $\GCfd_RX$ by $\T(X)$. Let $M$ be an $R$-module such that $\H_{\fa}^i(M)=0$ for all $i\neq n$. It is proved that if $\T(X)<\infty$, then $\T(\H_{\fa}^n(M))\leq\T(M)+n$ and the equality holds whenever $M$ is finitely generated. With the aid of these results, among other things, we characterize Cohen-Macaulay modules, dualizing modules and Gorenstein rings.

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Majid Rahro Zargar, Hossein Zakeri. 2013-02-26. On flat and Gorenstein flat dimensions of local cohomology modules. https://doi.org/10.4153/cmb-2015-080-x

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