τ-Rickart模和相对τ-Rickart模  

τ-Rickart modules and relativelyτ-Rickart modules

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

机构地区：[1]陇南师范高等专科学校数学与信息科学学院,甘肃陇南742500

出　　处：《西北师范大学学报（自然科学版）》2020年第6期24-27,共4页Journal of Northwest Normal University(Natural Science)

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资助项目(2020A-277)。

摘　　要：设τ=■表示遗传挠理论.提出了τ-Rickart模和相对τ-Rickart模的概念,讨论了τ-Rickart模的性质和等价刻画,给出了Rickart模与τ-Rickart模之间没有相互蕴含关系的例子;证明了直和因子包含τ-挠子模的τ-Rickart模具有SIP性质;证明了对任意i,j∈{1,2},若Mi是M,-C2模,则M是τ-Rickart模当且仅当对任意i,j∈{1,2},Mi是Mj-τ-Rickart模,其中M=M1⊕M2.Let τ=■ denote a hereditary torsion theory.The concepts of r-Rickart module and relatively τ-Rickart module are introduced,several properties and equivalent characterizations of τ-Rickart module are discussed,and some examples are given to show that Rickart modules and r-Rickart modules do not imply each other,it is proved that τ-Rickart modules have SIP property for direct summands that contain the τ-torsion submodule.Moreover,it is proved that if Mi is Mi-C2 module for all i,j∈{1,2},then M is a τ-Rickart module if and only if Mi is Mi-τ-Rickart for all i,j∈{1,2},where M=M1⊕M2.

关 键 词：相对τ-Rickart模 τ-Rickart模 Rickart模 直和因子 遗传挠理论 

分 类 号：O153.3[理学—数学]