Gorenstein X-Flat dimension and Tate homology

Abstract

In this paper, we study a Gorenstein X-flat dimension and investigate Tate homology Xtor of modules of finite Gorenstein X-flat dimension. We prove that if R is a right GXF-closed ring and M a R-module admitting a Tate X-flat resolution, and if N is a left R-module admitting a Tate X-flat resolution T_N, then for any i ∈ ℤ, Xtor_i^R (M, N) ≅ H_i(M ⊗_R T_N).