  In this paper, the notion of strongly G_C-projective and injective modules is
introduced, where C is a semidualizing module. Using these modules we can
obtain a new characterization of G_C-projective and injective modules, similar
to the one of projective modules by the free modules. We then define and study
the global dimensions of rings relative to a semidualizing module C, and prove
that the global G_C-projective dimension of a ring R is equal to the global
G_C-injective dimension of R.
