关于半对偶模的弱Ding-投射模  

Weak Ding-Projective Modules with Respect to a Semidualizing Module

作　　者：何东林[1] 樊亮[1] HE Donglin;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,甘肃陇南742500

出　　处：《四川轻化工大学学报（自然科学版）》2020年第5期96-100,共5页Journal of Sichuan University of Science & Engineering(Natural Science Edition)

基　　金：甘肃省高等学校创新基金项目(2020A-277)。

摘　　要：设R是有单位元的交换环,C是半对偶R-模。基于D C-投射模和C-f-投射模的概念,给出了关于半对偶模C的弱Ding-投射模的定义,称之为弱D C-投射模。利用环模理论和同调代数的方法,讨论了弱D C-投射模与D C-投射模及C-Gorenstein投射模之间的关系。研究了弱D C-投射模的若干性质和等价刻画。结果表明:M是弱D C-投射模,当且仅当M∈⊥P f C(R)且存在Hom R(-,P f C(R))-正合的正合列0→M→C R P-1→C R P-2→…,其中P i(i<0)是投射R-模且P f C(R)是C-f-投射R-模组成的类;所有弱D C-投射R-模组成的类是投射可解的且关于任意直和因子封闭。Let R be a communicative ring with identity,C be a semidualizing R-module.Based on the notion of D C-projective modules and C-f-projective modules,the definition of weak Ding-projective modules with respect to a semidualizing module C is given,which are called weak D C-projective modules.By using methods of rings and modules and homological algebra,the relationships between weak D C-projective modules,D C-projective modules and C-Gorenstein projective modules are discussed.Some properties and equivalent characterizations of weak D C-projective modules are investigated.The results indicate that:M is a weak D C-projective module,if and only if M∈⊥P f C(R)and there exists a Hom R(-,P f C(R))-exact exact sequence 0→M→C R P-1→C R P-2→…,where P i(i<0)is projective R-module and P f C(R)denotes the class of C-f-projective R-modules;the class of all weak D C-projective R-modules is projectively resolving and closed under arbitray direct summands.

关 键 词：交换环 半对偶模 C-f-投射模 弱D C-投射模 投射可解 

分 类 号：O154[理学—数学]