理想对称模

On Ideal Symmetric Modules

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.