Abstract

Let R be a local commutative n-Gorenstein ring. The existence of the Gorenstein projective preenvelopes for finite R-modules is known (it was proved using duality arguments). In the present article, we compute an explicit Gorenstein projective preenvelope and a right Gorenstein projective resolution of a finite R-module. In light of this knowledge, we consider left derived functors Ext(i)(-, -), (Ext(i)) over cap(-, -) and Gext(i)(-, -). We prove a balance result for the Tate derived functor (Ext(i)) over cap. Finally, we get an exact sequence connecting these derived functors.