关于Gorenstein FP-内射模及维数  

On Gorenstein FP-injective Modules and Dimensions

作　　者：杨燕妮[1] 杨刚[1] 

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070

出　　处：《四川师范大学学报（自然科学版）》2016年第1期47-50,共4页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11101197);甘肃省自然科学基金(145RJZA079)

摘　　要：首先给出右GFPI-封闭环的定义,即称环R是右GFPI-封闭环,如果所有的Gorenstein FP-内射右R-模类关于扩张封闭.证明当R是右凝聚与右GFPI-封闭环时,所有的Gorenstein FP-内射右R-模类是内射可解类.特别地,研究优越扩张环上模的Gorenstein FP-内射性质,证明当R与S是右凝聚环,S是R的优越扩张时,如果M是Gorenstein FP-内射右R-模,则HomR(S,M)是Gorenstein FP-内射右S-模,并且证明如果M是Gorenstein FP-内射右S-模,则M是Gorenstein FP-内射右R-模.另外,当R是右凝聚与右GFPI-封闭环时,给出Gorenstein FP-内射维数的若干等价刻画.A ring R is called right GFPI-closed,if the class of all Gorenstein FP-injective R-modules is closed under extensions.When R is right coherent and right GFPI-closed,it is proved that the class of all Gorenstein FP-injective right R-modules is injectively resolving. Especially,Gorenstein FP-injective properties of modules under extensions rings are investigated. When R and S are right coherent rings and S an excellent extension of R,it is proved that if M is a Gorenstein FP-injective right R-module then HomR（ S,M）is a Gorenstein FP-injective right S-module,and if M is a Gorenstein FP-injective right S-module then M is a Gorenstein FP-injective right R-module. In addition,when R is right coherent and right GFPI-closed ring,some equivalent characterizations of Gorenstein FPinjective dimensions are given.

关 键 词：FP-内射模 GORENSTEIN FP-内射模 优越扩张环 

分 类 号：O153.3[理学—数学]