On a generalization of McCoy rings. (Q2861449)

According to \textit{N. H. McCoy} [Am. Math. Mon. 49, 286-295 (1942; Zbl 0060.07703)] if two polynomials over a commutative ring annihilate each other, then each polynomial has a nonzero annihilator in the base ring. This is not in general true for non-commutative rings. A non-commutative ring \(R\) is right McCoy if for any two nonzero polynomials \(f(x),g(x)\) in \(R[x]\), \(f(x)g(x)=0\) implies \(f(x)c=0\) for some \(0\neq c\in R\). A ring is right nilpotent coefficient McCoy (NC-McCoy for short) if for any nonzero polynomials \(f(x),g(x)\) in \(R[x]\), \(f(x)g(x)=0\) implies \(f(x)d\in N(R)[x]\) for some \(d\in R\), where \(N(R)\) is the set of all nilpotent elements of \(R\). A left McCoy (resp. NC-McCoy) ring is similarly defined. A ring is McCoy (resp. NC-McCoy) if it is both left and right McCoy (resp. NC-McCoy).NEWLINENEWLINE The authors give several examples of (right) NC-McCoy rings, investigate the question of when \(R[x]\) is right NC-McCoy whenever \(R\) is right NC-McCoy and characterize minimal right NC-McCoy rings.