Top local cohomology modules and Gorenstein injectivity with respect to a semidualizing module

摘要

Let (R,m) be a commutative Noetherian local ring of Krull dimension d, and let C be a semidualizing R-module. In this paper, it is shown that if R is complete, then C is a dualizing module if and only if the top local cohomology module of R,H _m ~d(R), has finite G _C-injective dimension. This generalizes a recent result due to Yoshizawa, where the ring is assumed to be complete Cohen-Macaulay.