  In the present paper we concentrate on a natural generalization of NC-McCoy
rings that is called J-McCoy and investigate their properties. We prove that
local rings are J-McCoy. Also, for an abelian ring R, we show that R is J-McCoy
if and only if eR is J-McCoy, where e is an idempotent element of R. Moreover,
we give an example to show that the J-McCoy property does not pass Mn(R), but
S(R; n);A(R; n);B(R; n) and T(R; n) are J-McCoy
