Gorenstein FP∞-Injective Modules and w-Noetherian Ring  

作　　者：Shiqi Xing Xiaoqiang Luo Kui Hu 

机构地区：[1]College of Applied Mathematics,Chengdu University of Information Technology Chengdu 610225,China [2]Departments of Mathematics,Sichuan University of Arts and Science Dazhou,Sichuan 635000,China [3]College of Science,Southwest University of Science and Technology Mianyang,Sichuan 621010,China

出　　处：《Algebra Colloquium》2022年第4期687-712,共26页代数集刊（英文版）

基　　金：supported by the Scientific Research Foundation of Chengdu University of Information Technology(No.KYTZ202015);supported by NSFC(No.12061001).

摘　　要：We study some homological properties of Gorenstein FP∞-injective modules,and we prove(1)a ring R is not necessarily coherent if every Gorenstein FP∞-injective R-module is injective,and(2)a ring R is not necessarily coherent if every Gorenstein injective R-module is injective.In addition,we characterize w-Noetherian rings in terms of Gorenstein FP∞-injective modules,and we prove that a ring R is w-Noetherian if and only if every GV-torsion-free FP∞-injective R-module is Gorenstein FP∞-injective,if and only if any direct sum of GV-torsion-free FP∞-injective R-modules is Gorenstein FP∞-injective.

关 键 词：Gorenstein FP∞-injective module Gorenstein FP∞-dimension FP-module w-Noetherian ring 

分 类 号：O15[理学—数学]