Gorenstein homological dimensions

In basic homological algebra, the projective, injective and 2at dimensions of modules play an important and fundamental role. In this paper, the closely related Gorenstein projective, Goren- stein injective and Gorenstein 2at dimensions are studied. There is a variety of nice results about Gorenstein dimensions over special commutative noetherian rings; very often local Cohen-Macaulay rings with a dualizing module. These re- sults are done by Avramov, Christensen, Enochs, Foxby, Jenda, Martsinkovsky and Xu among others. The aim of this paper is to generalize these results, and to give homological descriptions of the Gorenstein dimensions over arbitrary associative rings. c 2003 Elsevier B.V. All rights reserved.