强G_C-FP-投射模  

Strongly G_C-FP-injective Modules

作　　者：李煜彦[1] 何东林[1] 樊亮[1] LI Yu-yan;HE Dong-lin;FAN Liang(School of Mathematics and Information Science,Longnan Teachers College.Longnan 742500,China)

机构地区：[1]陇南师范高等专科学校数信学院

出　　处：《青岛大学学报（自然科学版）》2019年第4期1-5,共5页Journal of Qingdao University(Natural Science Edition)

基　　金：甘肃省高等学校创新能力提升项目(批准号：2019B-224)资助

摘　　要：设SCR是一个忠实半对偶双模。给出了强GC-FP-内射模的概念,是GC-FP-内射模的特殊情形。利用同调代数和环模理论的方法,研究了强GC-FP-内射模的若干性质和等价刻画。并证明了模RM是强GC-FP-内射模的等价条件有以下三个:(1)M∈s fCI^FP(R)⊥ 且存在HomR(s fCI^FP(R),-)正合的正合列…→F1→F0→M→0,其中Fi∈s fCI^FP(R);(2)存在HomR(s fCI^FP(R),-)-正合的正合列…→G1→G0→G-1→G-2→…,其中Gi∈SGCFP(R),使得M■lm(G0→G-1);(3)存在HomR(s fCI^FP(R),-)-正合的正合列…→G1→G0→G-1→G-2→…,其中Gi∈SGCFP(R),使得M■lm(G0→G-1)。Let SCR be a faithful semidualizing bimodule.The definition of strongly GC-FP-injective modules is given in the paper,which is a special circumstance of GC-FP-injective modules.Using methods of homological algebras and rings and modules,some properties and equivalent characterizations of strongly GC-FP-injective modules are investigated.And it is proved that there are three equivalent conditions for the moduleRMis strongly GC-FP-injective modules:(1)M∈sfICFP(R)⊥and there exists an exact sequence…→F1→F0→M→0 with Fi∈sfICFP(R),which is exact under HomR(sfICFP(R),-);(2)there exists an exact sequence…→G1→G0→G-1→G-2→…with Gi∈SGCFP(R),which is exact under HomR(SGCFP(R),-),such that M■lm(G0→G-1);(3)there exists an exact sequence…→G1→G0→G-1→G-2→…with Gi∈SGCFP(R),which is exact under HomR(sfICFP(R),-),such that M■lm(G0→G-1).

关 键 词：半对偶双模 强GC-FP-内射模 强C-FP-内射模 GC-FP-内射模 

分 类 号：O153[理学—数学]