Abstract
In basic homological algebra, the projective, injective and flat dimensions of modules play an important and fundamental role. In this paper, the closely related Gorenstein projective, Gorenstein injective and Gorenstein flat 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 results 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.
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