(m,d)-Injective Covers and Gorenstein (m,d)-Flat Modules  

作　　者：Liang ZHAO 

机构地区：[1]School of Mathematics and Physics,Anhui University of Technology [2]School of Mathematics Sciences,Nanjing Normal University

出　　处：《Journal of Mathematical Research with Applications》2016年第5期527-536,共10页数学研究及应用（英文版）

基　　金：Supported by the Provincial Natural Science Research Program of Higher Education Institution of Anhui Province(Grant No.KJ2012Z028)

摘　　要：We consider the conditions under which the class of （m, d）-injective R-modules is （pre）covering. It is shown that every left R-module over a left （m, d）-coherent ring has an （rn, d）-injective cover. Moreover, the classes of Gorenstein （m, d）-flat modules and Gorenstein （m, d）-injecitve modules are introduced and studied. For a right （m, d）-coherent ring R, we prove that a left R-module M is Gorenstein （m, d）-flat if and only if M＋ is Gorenstein （m, d）- injective as a right R-module. Some results on Gorenstein flat modules and Gorenstein n-flat modules are generalized.We consider the conditions under which the class of （m, d）-injective R-modules is （pre）covering. It is shown that every left R-module over a left （m, d）-coherent ring has an （rn, d）-injective cover. Moreover, the classes of Gorenstein （m, d）-flat modules and Gorenstein （m, d）-injecitve modules are introduced and studied. For a right （m, d）-coherent ring R, we prove that a left R-module M is Gorenstein （m, d）-flat if and only if M＋ is Gorenstein （m, d）- injective as a right R-module. Some results on Gorenstein flat modules and Gorenstein n-flat modules are generalized.

关 键 词：（m  d）-injective cover Gorenstein （m  d）-flat module Gorenstein （m  d）-injecitvemodule strongly Gorenstein （m  d）-flat module 

分 类 号：O153.3[理学—数学]