J-McCoy Rings Relative To A Monoid

Let R be a ring and M be a monoid. We introduce the notion of J -M-McCoy rings, as a generalization of J -McCoy and weak MMcCoy rings, and investigate their properties. It is proved that for u.p.- monoids M and N if R J (R) is reversible, then R is J -M ×N -McCoy. Also, it is shown that a ring R is J -M-McCoy if and only if R[x] is J - M-McCoy if and only if Tn(R) is J -M-McCoy, while the J -M-McCoy property is not Morita invariant