Gorenstein强FP-内射模  

Gorenstein Strongly FP-Injective Modules

作　　者：方慧江 杨刚[1] FANG Huijiang;YANG Gang(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学数理学院,兰州730070

出　　处：《吉林大学学报（理学版）》2024年第5期1079-1084,共6页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:12161049)。

摘　　要：首先,借助内射模的零调复形和Hom函子的理论,引入Gorenstein强FP-内射模的概念.其次,利用马蹄引理和构造拉回图的方法,研究Gorenstein强FP-内射模的同调性质,证明Gorenstein强FP-内射模类GS FI是内射可解类,关于直积及直和项封闭,并且如果任意R-模的Gorenstein强FP-内射维数有限,则(⊥GS FI,GS FI)构成完全遗传的余挠对.Firstly,we introduce the notion of Gorenstein strongly FP-injective modules by means of acyclic complexes of injective modules and the theory of Hom functors.Secondly,we study homological properties of Gorenstein strongly FP-injective modules by using the Horseshoe Lemma and the method of constructing pull-back diagrams,and prove that the class GS FI of Gorenstein strongly FP-injective modules is injectively resolving,with respect to closed under arbitrary direct products and di rect summands,and if the Gorenstein strongly FP-injective dimension is finite for every R-module,then(⊥GS FI,GS FI)forms a complete hereditary cotorsion pair.

关 键 词：强FP-内射模 Gorenstein强FP-内射模 余挠对 

分 类 号：O154.2[理学—数学]