Some results on ideals of semiprime rings with multiplicative generalized derivations

Let R be a semiprime ring and I a nonzero ideal of R. A map F:RR is called a multiplicative generalized derivation if there exists a map d:RR such that F(xy)=F(x)y+xd(y), for all x,yR. In the present paper, we shall prove that R contains a nonzero central ideal if any one of the following holds: i) iii) F is SCP on I, iv) F(u)degrees F(v)=u degrees v, for all u,v is an element of I.