关于Gorenstein FP_(n)-内射模  

On Gorenstein FP_(n)-injective modules

作　　者：昌文浩 周德旭[1] CHANG Wenhao;ZHOU Dexu(School of Mathematics and Statistics,Fujian Normal Universtity,Fuzhou,Fujian 350117,China)

机构地区：[1]福建师范大学数学与统计学院,福建福州350117

出　　处：《闽南师范大学学报（自然科学版）》2023年第4期102-106,共5页Journal of Minnan Normal University：Natural Science

基　　金：福建省自然科学基金项目(2021J01656)。

摘　　要：引入(强)Gorenstein FP_(n)-内射模,得到了(强)Gorenstein FP_(n)-内射模的若干性质和刻画,并研究了左GFP_(n)-正则环的等价性质,证明了环R为左GFP_(n)-正则环当且仅当每个投射左R-模是FP_(n)-内射的且每个投射维数有限的n-表现左R-模都是投射的.In this paper,we introduce(strongly)Gorenstein FP_(n)-injective modules,obtain several properties and characterizations of(strongly)Gorenstein FP_(n)-injective modules,and investigate equivalent properties of left GFP_(n)-regular ring,prove that a ring is left GFP_(n)-regular if only and if every projective left R-module is FP_(n)-injective and every n-presented left R-module with finite projective dimensions is projective.

关 键 词：FP_(n)-内射模 Gorenstein FP_(n)内射模 强Gorenstein FP_(n)-内射模 左GFP_(n)-正则环 

分 类 号：O153.3[理学—数学]