A Generalization of Gorenstein Injective and Flat Modules (Communications in Mathematical Research, 2021)
In this article, we introduce and study the concept of $n$-Gorenstein injective (resp., $n$-Gorenstein flat) modules as a nontrivial generalization of Gorensteininjective (resp., Gorenstein flat) modules. We investigate the properties of these modules in various ways. For example, we show that the class of $n$-Gorenstein injective(resp., $n$-Gorenstein flat) modules is closed under direct sums and direct products for $n ≥ 2$. To this end, we first introduce and study the notions of $n$-injective modulesand $n$-flat modules.
Keywords: $n$-injective module; $n$-flat module; $n$-Gorenstein injective module; $n$-Gorenstein flat module; preenvelope; cover.