Semi-dualizing modules and related Gorenstein homological dimensions

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