极大对偶Utumi模  

Maximal dual Utumi modules

作　　者：吴德军[1] 卢锐涛 WU De-jun;LU Rui-tao(School of Science,Lanzhou University of Technology,Lanzhou 730050,Gansu,China;Zhengzhou Information Technology School,Zhengzhou 450000,Henan,China)

机构地区：[1]兰州理工大学理学院,甘肃兰州730050 [2]郑州市信息技术学校,河南郑州450000

出　　处：《西北师范大学学报（自然科学版）》2021年第1期26-30,共5页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11761047)。

摘　　要：引入极大对偶Utumi模,并研究了它的一些基本性质和单直投射模的一个新的等价刻画;证明了极大对偶Utumi模是单直投射模;利用极大对偶Utumi模给出了半单环新的刻画;证明了任意单Utumi右R-模是极大对偶Utumi右R-模时,环R是半局部环.Maximal dual Utumi modules are introduced in this paper,and their fundamental properties are studied.A new characterization of simple direct projective modules is given.It is proved that every maximal dual Utumi module is a simple direct projective module.Some new characterizations of semi-simple rings are given in terms of maximal dual Utumi modules.It is proved that R is semi-local provided that each simple Utumi R-module is a maximal dual Utumi R-module.

关 键 词：极大对偶Utumi模 单直投射模 半局部环 半单环 直和项 

分 类 号：O152.7[理学—基础数学]