  A ring $R$ is said to be right McCoy if the equation $f(x)g(x)=0,$ where
$f(x)$ and $g(x)$ are nonzero polynomials of $R[x],$ implies that there exists
nonzero $s \in R$ such that $f(x)s = 0$. It is proven that no proper
(triangular) matrix ring is one-sided McCoy. If there exists the classical
right quotient ring $Q$ of a ring $R$, then $R$ is right McCoy if and only if
$Q$ is right McCoy. It is shown that for many polynomial extensions, a ring $R$
is right McCoy if and only if the polynomial extension over $R$ is right McCoy.
Other basic extensions of right McCoy rings are also studied.\leftskip0truemm
\rightskip0truemm \{\it Keywords}: matrix ring, McCoy ring, polynomial ring,
upper triangular matrix ring.
