On the finiteness of Gorenstein homological dimensions

In this paper, we study certain properties of modules of finite Gorenstein projective, injective and flat dimensions. We examine conditions which imply that all Gorenstein projective modules are Gorenstein flat and establish the balance of the Gorenstein Tor-functor for modules of finite Gorenstein projective dimension. We also examine the class of rings that have finite Gorenstein global and weak dimensions and compute these dimensions, in terms of certain cohomological invariants of the ring. Finally, we provide some examples of rings of finite Gorenstein global and weak dimensions. (C) 2012 Elsevier Inc. All rights reserved.