Gorenstein flat modules with respect to duality pairs

Abstract

Let be a class of left R-modules, be a class of right R-modules. In this article, we introduce and study Gorenstein -flat modules as a common generalization of some known modules such as Gorenstein flat modules, Gorenstein n-flat modules, Gorenstein -flat modules, Gorenstein AC-flat modules, Ω-Gorenstein flat modules and so on. We show that the class of all Gorenstein -flat modules have a strong stability. In particular, when is a perfect (symmetric) duality pair, we construct a hereditary abelian model structure on R-Mod whose cofibrant objects are exactly the Gorenstein -flat modules. Finally, we investigate when the class of Gorenstein -flat modules is closed under extensions. These results unify the corresponding results of the aforementioned modules.