ON n-STRONGLY 𝓔-GORENSTEIN INJECTIVE AND FLAT MODULES

ON n-STRONGLY 𝓔-GORENSTEIN INJECTIVE AND FLAT MODULES

Let 𝓔 be an injectively resolving class of left R-modules and n≥1 be an integer. In this paper, we introduce and study n-strongly 𝓔-Gorenstein injective and flat modules, which are common generalizations of strongly Gorenstein injective and flat modules [2, 28], n-strongly Gorenstein injective and flat modules [3, 29], respectively. Then we discuss some properties of these modules and show how the property of being an n-strongly 𝓔-Gorenstein injective and flat module can be inherited by its direct summands under certain condition. Finally, we consider the connections between n-strongly 𝓔-Gorenstein injective and flat modules. As applications, some known results are obtained as corollaries.