关于半对偶双模的强FP-内射模和强FP-投射模  

Strongly FP-injective Modules and FP-projective Modules with Respect to Semidualizing Bimodule

作　　者：何东林[1] 李煜彦[1] HE Dong-lin;LI Yu-yan(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,甘肃陇南742500

出　　处：《广西民族大学学报（自然科学版）》2019年第4期67-69,74,共4页Journal of Guangxi Minzu University ：Natural Science Edition

基　　金：甘肃省高等学校科研项目(2018A-269);陇南师范高等专科学校校级科研重点项目(2016LSZK01003).

摘　　要：设SCR是一个半对偶双模.讨论了关于半对偶双模C的强FP-内射模和强FP-投射模,它是FP-内射模和FP-投射模的一个推广.利用环模理论和同调代数的方法,研究了强C-FP-内射模与强C-FP-投射模的若干性质和等价刻画.并证明了模RU是强C-FP-内射模当且仅当U∈AC(R)且C■R U是强FP-内射左S-模;模RU是强C-FP-投射模当且仅当Tor^R i≥1(C,U)=0且C■R U∈⊥1sfI(S),其中AC(R)表示关于半对偶双模C的Auslander类,sfI(S)表示强FP-内射左S-模组成的子范畴.Letbe a semidualizing bimodule.In this paper,we discuss strongly FP-injective modules and strongly FP-injective modules with respect to semidualizing bimodule,which is a generalization of FP-injective modules and FP-projective modules.Using methods of rings and modules and homological algebra,we investigate some properties and equivalent characterizations of strongly-FP-injective modules and stronglyFP-projective modules.And prove that the moduleis strongly-FP-injective if and only ifandis strongly FP-injective left-module;the moduleis strongly-FP-projective if and only if and,wheredenotes Auslander class with respect to semidualizing bimodule,denotes the subcategory of strongly FP-injective left-modules.

关 键 词：半对偶双模 强C-FP-内射模 强C-FP-投射模 Auslander类 Bass类 

分 类 号：O153[理学—数学]