关于Gorenstein FI-内射模  

On Gorenstein FI-injective modules

作　　者：陈东 胡葵[2] CHEN Dong;HU Kui(College of Information Science and Engineering,Chengdu University,Chengdu 610106,Sichuan,China;College of Science,Southwest University of Science and Technology,Mianyang 621010,Sichuan,China)

机构地区：[1]成都大学信息科学与工程学院,四川成都610106 [2]西南科技大学理学院,四川绵阳621010

出　　处：《西北师范大学学报（自然科学版）》2019年第3期9-13,共5页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11671283);成都大学青年基金资助项目(2018XZA08)

摘　　要：引入了Gorenstein FI-内射模,它是介于内射模和Gorenstein内射模之间的一种特殊模类.讨论了Gorenstein FI-内射模的诸多性质,给出了Gorenstein FI-内射模是内射模的一个充分条件,并用Gorenstein FI-内射模刻画了半遗传环.最后,定义了Gorenstein FI-内射维数,给出了Gorenstein FI-内射(预)包存在的一个充分条件.The concept of Gorenstein FI -injective modules is introduced,which is a particular class between injective and Gorenstein injective modules.Some properties of Gorenstein FI -injective modules are discussed,a sufficient condition for Gorenstein FI -injective module to be injective is given,and semi-hereditary rings are characterized in terms of Gorenstein FI -injective modules.Finally,Gorenstein FI -injective dimension is defined,and a sufficient condition for the existence of Gorenstein FI -injective(pre)envelope is given.

关 键 词：GORENSTEIN FI-内射模 内射模 内射维数 内射包 半遗传环 

分 类 号：O154[理学—数学]