Local cohomology modules and Gorenstein injectivity with respect to a semidualizing moduleReport as inadecuate



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


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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.



Author: Majid Rahro Zargar

Source: https://archive.org/







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