关于强Gorenstein FC-投射模  

On Strongly Gorenstein FC-Projective Modules

作　　者：王玉 周德旭 WANG Yu;ZHOU De-xu(College of Mathematics and Informaties,Fufian Normal University,Fuzhou 350117,China)

机构地区：[1]福建师范大学数学与信息学院,福建福州350117

出　　处：《福建师范大学学报（自然科学版）》2018年第5期12-18,共7页Journal of Fujian Normal University：Natural Science Edition

基　　金：福建省自然科学基金资助项目(2015J01002)

摘　　要：引入强Gorenstein FC-投射模,给出了强Gorenstein FC-投射模的若干等价性质,刻画了右SGFC-半单环.在Morita对偶下,得到了强Gorenstein FC-投射模与强Gorenstein FP-内射模构成了Morita-对偶对,并证明了每个U-自反右R-模都是强Gorenstein FC-投射模当且仅当每个U-自反左S-模都是强Gorenstein FP-内射模.This paper introduces strongly Gorenstein FC-projective modules,gives some equivalent properties of strongly Gorenstein FC-projective modules,and characterizes right SGFC-semisimple rings. Under Morita-duality,it obtains that strongly Gorenstein FP-injective modules and strongly Gorenstein FC-projective modules forms a Morita-dual pair,and shows that every U-reflexive right R-module is strongly Gorenstein FC-projective if and only if every U-reflexive left S-module is strongly Gorenstein FP-injective.

关 键 词：强Gorenstein FC-投射模 右SGFC-半单环 Morita-对偶 

分 类 号：O153.3[理学—数学]