相关于稳定挠理论的extending模  

Extending Modules Relative to Stable Torsion Theory

作　　者：李煜彦[1] LI Yuyan(School of Mathematics and Information Sciences,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）》2020年第3期67-70,共4页Journal of Guangxi Minzu University ：Natural Science Edition

基　　金：甘肃省高等学校创新能力提升项目(2019B-224);甘肃省高等学校创新基金项目(2020A-277).

摘　　要：设τS表示稳定挠理论.给出了τS-本质子模的等价刻画,讨论了τS-闭子模和闭子模之间的关系,证明了K在M中是τS-闭的当且仅当K是M的包含τS(M)的闭子模,研究了τSextending模的若干性质.进而,给出了τS-extending模的等价刻画,证明了M是τS-extending模当且仅当M=τS(M)⊕M′,其中M′是(τS-挠自由)extending模.LetτS be a stable torsion theory,some equivalent characterizations ofτS-essential submodule are given,the relations betweenτS-closed submodules and closed submodules are discussed,it is proved that K isτS-closed in M if and only if K containsτS(M)and K is a closed submodule of M,some properties ofτS-extending module are studied.Moreover,some equivalent characterizations ofτS-extending module are given,it is proved that M isτS-extending module if and only if M=τS(M)⊕M′where M′is a(τS-torsion free)extending module.

关 键 词：稳定挠理论 τS-闭子模 τS-extending模 直和因子 

分 类 号：O153[理学—数学]