准正则环和强正则环

On quasi-regular rings and strong regular rings

环R称为准正则环 ,如果环R的每个右理想是由R的若干个幂等元所生成 .主要结果是 :( 1 )设R是准正则环 ,如果R的分式环Q作为右R模是右Noether的 ,则R是半单Artin环 .( 2 )设R是准正则环 ,如果环R的每个素右理想都是极大右理想 。

A ring R is called quaso-regular, if every right ideal of R is generated by some idempotents.The main results of the study are: (1) Let R be a quasi-regular ring. If quotient ring Q of R is a right noetherian as right R-module, then R is a semisimple ring. (2)Let R be a quasi-regular ring. If every prime right ideal of R is maximum right ideal, then R is a strong regular ring.