Gorenstein flat dimension of complexes

Abstract

We define a notion of Gorenstein flat dimension for unbounded complexes over left GF-closed rings. Over Gorenstein rings we introduce a notion of Gorenstein coho- mology for complexes; we also define a generalized Tate cohomol- ogy for complexes over Gorenstein rings, and we show that there is a close connection between the absolute, the Gorenstein and the generalized Tate cohomology.