Virtually正则模

Virtually regular modules

作为正则模的真推广,引入了virtually正则模的概念,研究了这类模的基本性质,证明了环R是(强)virtually正则环当且仅当环R上的每个(投射模)自由模是(半完全)virtually正则模.

As a proper generalization of regular modules,the concept of virtually regular modules is presented in this paper.Basic properties of these modules are studied,it is shown that a ring R is a(strongly)virtually regular ring,if and only if every(projective)free R-module is a(semicompletely)virtually regular module.