Definition: (right McCoy) A ring $R$ is called right McCoy if when $f,g\in R[x]\setminus \{0\}$ satisfy $fg=0$, then there exists a nonzero $r\in R$ such that $fr=0$.
Reference(s):
M. B. Rege, S. Chhawchharia, and others. Armendariz rings. (1997) @ .
V. Camillo and P. P. Nielsen. McCoy rings and zero-divisors. (2008) @ (page needed)
Metaproperties:
This property has the following metaproperties
stable under products
stable under finite products
passes to polynomial rings
This property does not have the following metaproperties
Morita invariant
(Counterexample: $R_{ 12 }$ is Morita equivalent to $R_{ 2 }$)
passes to matrix rings
(Counterexample: $R_{ 12 }$ is a matrix ring of $R_{ 2 }$)
passes to power series ring
(Counterexample: $R_{ 163 }$)
passes to quotient rings
(Counterexample: $R_{ 119 }$ is a homomorphic image of $R_{ 165 }$)