A semi-dualizing module over a commutative noetherian ring A is a finitely generated
module C with RHomA (C, C)≃ A in the derived category D (A). We show how each such
module gives rise to three new homological dimensions which we call C-Gorenstein
projective, C-Gorenstein injective, and C-Gorenstein flat dimension, and investigate the
properties of these dimensions.

Let SCR be a semidualizing bimodule with S left coherent and R right coherent. For a non-
negative integer n, it is shown that l. FP-id S (C)= r. FP-id R (C)≤ n if and only if every finitely
presented left S-module has GC-projective dimension at most n if and only if every finitely
presented right R-module has GC-projective dimension at most n. As applications, some
well-known results are extended.