Von neumaivn regularity of sf-rings

Abstract

A ring R is called left (right) SF-ring if all simple left (right) R-modules are flat. It is proved that R is Von Neumann regular if R is a right SF-ring whoe maximal essential right ideals are ideals. This gives the positive answer to a qestion proposed by R. Yue Chi MIng in 1985, and a counterexample is given to settle the follwoing question in the negative: If R is an ERT ring which is one-sided V-ring, is R a left and right V-ring? Some other conditions are given for a SF-ring to be regular.