ON n-STRONGLY E-GORENSTEIN INJECTIVE AND FLAT MODULES
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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.
Abstract
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.
참고문헌 (29)
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