Copyright © 2010 Basudeb Dhara. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be a ring with center and a nonzero ideal of . An additive mapping is called a generalized derivation of if there exists a derivation such that for all . In the present paper, we prove that if for all or for all , then the semiprime ring must contains a nonzero central ideal, provided . In case is prime ring, must be commutative, provided . The cases (i) and (ii) for all are also studied.