A Generalization of Gorenstein Injective and Flat Modules  

作　　者：LU BO Du Xian-kun 

机构地区：[1]College of Mathematics and Computer Science,Northwest University for Nationalities,Lanzhou,730030 [2]Department of Mathematics,Northwest Normal University,Lanzhou,730070 [3]不详

出　　处：《Communications in Mathematical Research》2016年第4期339-351,共13页数学研究通讯（英文版）

基　　金：The NSF(11501451)of China;the Fundamental Research Funds(31920150038)for the Central Universities and XBMUYJRC(201406)

摘　　要：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.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.

关 键 词：n-injective module n-flat module n-Gorenstein injective module n- Gorenstein flat module PREENVELOPE COVER 

分 类 号：O153.3[理学—数学]