Semi-dualizing modules and related Gorenstein homological dimensions

A semi-dualizing module over a commutative noetherian ring A is a finitely generated module C with RHomA(C,C)similar, equalsA in the derived category image. 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.