Let H be a ring with center Z. \(f_{r}:H\rightarrow H\) (not always additive) is called a multiplicative reverse semiderivation if there exist a function g on H such that (i) \(f_{r}(t_{1}t_{2})=f_{r}(t_{2})t_{1} +g(t_{2})f_{r}(t_{1})\) , (ii) \(f_{r}(t_{1}t_{2})=f_{r}(t_{2})g(t_{1} )+t_{2}f_{r}(t_{1})\) and (iii) \(f_{r}(g(t_{1}))=g(f_{r}(t_{1}))\) , hold for all \(t_{1}\) , \(t_{2}\in H\) . Based on this definition, we see that for all \(b\in H\) if \(f_{r}\left( b\right) \ne 0\) then \(b\in Z\) when H is a prime ring. We also share the conditions under which we obtain \(\left[ f_{r}\left( s\right) ,s\right] =0\) for all \(s\in H\) , when we choose the ring H as a semiprime ring.
