Extensions of McCoy Rings

Abstract

A ring R is called right McCoy if whenever polynomials f(x), g(x) ∈ R[x]∖{0} satisfy f(x)g(x)=0, there exists a nonzero r ∈ R such that f(x)r=0. We continue in this paper the study of right McCoy rings by Nielsen [8]. We first consider properties and basic extensions of right McCoy rings, providing many examples in the process. Next, we show that if R is a right McCoy ring, then R[x] and R[x]/(xn) are right McCoy rings, where (xn) is the ideal generated by xn and n is a positive integer; and that for a right Ore ring R with Q its classical right quotient ring, R is right McCoy if and only if Q is right McCoy.