(untitled) (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 Gorenstein injective (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 modules and n-flat modules.