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 invest...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.展开更多
基金The NSF(11501451)of Chinathe Fundamental Research Funds(31920150038)for the Central Universities and XBMUYJRC(201406)
文摘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.
