Von-Neumann Regularity of N-rings

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.