Resolutions and homological dimensions of DG-modules

Recently, Yekutieli introduced projective dimension, injective dimension and flat dimension of DG-modules by generalizing the characterization of projective dimension, injective dimension and flat dimension of ordinary modules by vanishing of Ext or Tor-groups. In this paper, we introduce a DG-version of projective, injective and flat resolution for DG-modules over a connective DG-algebra which are different from the known DG-version of projective, injective and flat resolutions. An important feature of these resolutions is that, roughly speaking, the "length" of these resolutions gives projective, injective or flat dimensions. We show that these resolutions allow us to investigate basic properties of projective, injective and flat dimensions of DG-modules. As an application we introduce the global dimension of a connective DG-algebra and show that finiteness of the global dimension is derived invariant.