Von Neumann Regular McCoy Rings

Abstract

A ring R is said to be right McCoy‎, ‎if for every f(x),g(x) in the polynomial ring R[x], with f(x)g(x)=0 there exists a nonzero element cϵR with f(x)c=0‎. In this note‎, ‎we show that von Neumann regular McCoy rings are abelian‎. ‎This gives a ‎positive answer to the question rised in ‎ ‎Comm‎. ‎Algebra  42 (2014) 1565- 1570.”