Local cohomology modules and Gorenstein injectivity with respect to a semidualizing module

Abstract

Let $(R,\fm)$ be a local ring and let $C$ be a semidualizing $R$--module. In this paper, we are concerned in $C$--injective and $G_C$--injective dimensions of certain local cohomology modules of $R$. Firstly, the injective dimension of $C$ and the above quantities of dimensions is compared. Then, as an application of the above comparisons, a characterization of a dualizing module of $R$ is given. Finally, it is shown that if $R$ is Cohen-Macaulay of dimension $d$ such that $\H_{\fm}^{d}(C)$ is $C$--injective, then $R$ is Gorernstein. This is an answer to the question which was recently presented.

9 pages, published in Archive der Mathematik. 100 (2013) 25-34

References in corpus (1)

• On injective and Gorenstein injective dimensions of local cohomology modules