关于超半素环和超半素根的注记

A Note to the Supersemiprime Rings and Supersemiprime Radical

文献 [1 ]中提出了一个公开问题 :设 R是任意一个环 ,若 R上的 n×n全阵环 Rn 是一个超半素环 ,问 R是否是一个超半素环。通过引入拟半素理想对这个公开问题给出了肯定的回答。

In reference [1], the author proposed an open problem: Let R be a ring, if the full n×n matrix ring R n over R is a supersemiprime ring, is the ring R a supersemiprime ring. In this paper, a positive answer to the open problem is given by the concept of quasi\|semiprime ideal introduced.