摘要
环Ｒ称为Ｎ－环，如果Ｒ的素根Ｎ（Ｒ）＝ 存在自然数ｎ使ｒｎ＝０｝．本文不仅对Ｎ－环进行了刻划，而且还研究了 Ｎ－环的 Ｖｏｎ Ｎｅｕｍａｎｎ正则性．特别证明了。对于 Ｎ－环 Ｒ，如下条件是等价的：（１）Ｒ是强正用环；（２）Ｒ是正则环；（３）Ｒ是左ＳＦ－环；（４）Ｒ是右ＳＦ－环；（５）Ｒ是ＭＥＬＴ，左ｐ－Ｖ－环；（６）Ｒ是ＭＥＲＴ，右ｐ－Ｖ－环．因此推广了文献［４］中几乎所有的重要结果，同时也改进或推广了其它某些有关正则环的有用结果．
A ring R is called a N-ring if N(R) ={r R | there is a natural number n such that rn = 0}. In this paper, some new characterization of N-rings are given. Furthermore, the Von Neumann regularity of N-rings is also considered. Particularly, we show the following result: for a N-ring R, the following conditions are equivalent: (1) R is a strongly regular ring; (2) R is a regular ring; (3) R is a left SF-ging; (4) R is right SF-ring; (5) R is a MELT, left p-V-ring; (6) R is a MERT, right p-V-ring.
