Abstract
The introduction of w-operation in the class of flat modules has been successful. Let R be a ring. An R-module M is called a w-flat module if Toil (M, N) is GV-torsion for all R-modules N. In this paper, we introduce the w-operation in Gorenstein homological algebra. An R-module M is called Ding w-flat if there exists an exact sequence of projective R-modules ... -> P-1 -> P-0 -> P-0 -> P-1 -> ... such that M congruent to Im(P-0 -> P-0) and such that the functor Hom (R)(-, F) leaves the sequence exact whenever F is w-flat. Several wellknown classes of rings are characterized in terms of Ding w-flat modules. Some examples are given to show that Ding w-flat modules lie strictly between projective modules and Gorenstein projective modules. The Ding w-flat dimension (of modules and rings) and the existence of Ding w-flat precovers are also studied.