Strongly Gorenstein Flat Dimensions of Complexes.

In this article, we define and study a notion of strongly Gorenstein flat dimensions for complexes of left modules over associative rings. In particular, we consider the class of homologically bounded below complexes of leftR-modules, and show that strongly Gorenstein flat dimension has a nice functorial description. In addition, we will investigate the strongly Gorenstein flat properties of complexes under change of rings. As an application, we study the Tate cohomology theories with respect to ℱ-complete resolutions, where ℱ is the class of all flat modules. [ABSTRACT FROM PUBLISHER]