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

Abstract

Abstract. Let (R, 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 ofGorenstein. This is an answer to the question which was recently raised.