单Rickart模  

Simple Rickart modules

作　　者：王永铎[1] 李丹丹[1] WANG Yong-duo;LI Dan-dan(School of Science,Lanzhou Univ. of Tech.,Lanzhou 730050,China)

机构地区：[1]兰州理工大学理学院,甘肃兰州730050

出　　处：《兰州理工大学学报》2018年第6期148-150,共3页Journal of Lanzhou University of Technology

基　　金：甘肃省自然科学基金(1310RJZA029);甘肃省高校基本科研业务费

摘　　要：引入了单Rickart模的概念.称模M为单Rickart模,如果M/Kerφ是单模,那么Kerφ是M的直和项,其中φ∈EndR(M).研究了它的基本性质,证明了单Rickart模的直和项是单Rickart模,讨论了单Rickart模与单直投射模的联系,并用单Rickart模刻画了半单环.The concept of simple Rickart modules is introduced.A module M is called a simple Rickart module if for eachφ∈End R(M),M/Kerφis simple and then Kerφis a direct summand of M.Its basic properties are studied and it is also proved that any direct summand of a simple Rickart module is also a simple Rickart module.The connections between simple Rickart modules and simple-direct-projective modules are discussed and semisimple rings are characterized with simple Rickart modules.

关 键 词：单Rickart模 单直投射模 半单环 

分 类 号：O153.3[理学—数学]