Tate Homology of Modules of Finite Gorenstein Flat Dimension

We introduce and investigate Tate homology $\widehat{{\mbox{\rm tor}}}$ of modules of finite Gorenstein flat dimension. In particular, we show that over a right coherent ring R, $\widehat{{\mbox{\rm tor}}}_{i}^{R}(M,N)\cong\widehat{{\mbox{\rm Tor}}}_{i}^{R}(M,N)$ for any right R-module M of finite Gorenstein projective dimension, any R-module N of finite Gorenstein flat dimension and any i?∈??. We also study the Tate homology $\widehat{{\mbox{\rm tor}}}$ of a cotorsion module of finite Gorenstein flat dimension in the paper.