Von Neumann正则环上的*-模

*-Modules of Von Neumann regular rings

我们知道,VonNeumann正则环上的倾斜模是投射模.每个倾斜模是 -模,但是一个 -模不一定是倾斜模.本文证明了可交换的VonNeumann正则环上的 -模是投射模.对于一个 -模P,给出了Gen(P)在扩张下是封闭的一个条件.

We know that the tilting modules over a Von Neumann regular ring are projective,and each tilitng module is a *-module,but a *-module may be not a tilting module.In this paper,we prove that *-modules are projective for commutative Von Neumann regular rings.We also give a condition under which Gen(PR) is closed under extensions for a *-module (PR).