Gorenstein \(FI\)-flat dimension and Tate homology (Q505853)

The paper under review introduces Gorenstein FI-injective and Gorenstein FI-flat modules over a ring \(R\) as well as the related Gorenstein FI-injective dimension and Gorenstein FI-flat dimension. The treatment is parallel to that used in the case of Gorenstein flat and Gorenstein injective modules. Moreover, the authors develop a theory of Tate homology by defining Tate FI-flat resolutions of a given module \(M\). Finally, they study Tate homology \(\widehat{\text{tor}}\) of FI-cotorsion \(R\)-modules of finite Gorenstein FI-flat dimension over right coherent rings.