理想对称模  

On Ideal Symmetric Modules

作　　者：李东方[1] 黎奇升[1] 

机构地区：[1]吉首大学数学与统计学院,吉首416000

出　　处：《数学理论与应用》2016年第1期1-8,共8页Mathematical Theory and Applications

基　　金：国家自然科学基金项目(11561025);湖南省研究生创新科研基金项目(CX2015B434)

摘　　要：本文引进了理想对称模的概念,给出了理想对称模的系列等价刻画,用理想对称模给出了环R为理想对称环的若干等价条件,证明了对于环R的满足右Ore条件正则元的集S,如果S-挠自由R-模M是理想对称模,则M关于S的右分式模也是理想对称的,推广了理想对称环的相应结果.In this paper by introducing the concept of ideal symmetric module and giving some equivalent chara- terizations to it, some equivalent conditions under which a ring R is ideal symmetric are obtained. When S is a subset of some regular elements of a ring R satisfying the right Ore conditions,it is proved that the module of fractionsM[S-l] is also ideal symmetric if M is ideal symmetric and S--torsion--free, which generalizes the re- suits in ~7] on ideal symmetric rings.

关 键 词：理想对称模理想对称环 Ore条件 分式模投射模 

分 类 号：O153.3[理学—数学]