SOME PROPERTIES OF NQ-RINGS

Abstract

A ring R is called NQ-ring if R satisfies the equation QN(R)=N(R). In this paper, we give some basic properties of the class of NQ-rings and show that, if R be a semicommutative ring, then R is an NQ-ring iff QN(R) is a nil ideal;  if R is an NQ-ring, then R/J(R) is a semiprime ring; if R is a NQ-ring and R/J(R) is semicommutative, then R/J(R) is a reduced ring.