半单环在环类刻画中的某些应用

Some applications about semisimple rings in the characterization of rings

首先利用正则环,对半单环进行了一个新的刻画;然后,构造了半单环成为单位正则环的一系列条件,在此基础上对单位正则环进行了半单环意义下的两个刻画;最后,通过构造Artin环到半单环的条件,将半单环的有关结论推广到Artin环中.

Firstly, a new characterization of semisimple rings was obtained in In the sense of regular rings. Secondly, we constructed a series of conditions which from semisimple rings to unit regular rings and on which two characterizations were obtained about unit regular rings in terms of semisiple rings. Finally, by constructing the conditions that from Artin rings to semisimple rings, a series of results about semisimple ring were pushed to Artin rings.