Abstract
Let \({(R,\mathfrak{m})}\) be a local ring, and let C be a semidualizing R-module. In this paper, we are concerned with the C-injective and G C -injective dimensions of certain local cohomology modules of R. Firstly, the injective dimension of C and the above quantities are compared. Secondly, 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 \({\rm H}_{\mathfrak{m}}^{d}(C)\) is C-injective, then R is Gorenstein. This is an answer to a question which was recently raised.
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Zargar, M.R. Local cohomology modules and Gorenstein injectivity with respect to a semidualizing module. Arch. Math. 100, 25–34 (2013). https://doi.org/10.1007/s00013-012-0459-y
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DOI: https://doi.org/10.1007/s00013-012-0459-y