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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 TN, then for any i ∈ ℤ, XtoriR (M, N) ≅ Hi(M ⊗R TN).
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