Study of the structure of quotient rings satisfying algeraic identities

‎Assuming that \mathcal{R} is an associative ring with prime ideal P‎, ‎this paper investigates the commutativity of the quotient ring \mathcal{R}/P‎, ‎as well as the possible forms of generalized derivations satisfying certain algebraic identities on \mathcal{R}. We give results on strong commutativity‎, ‎preserving generalized derivations of prime rings‎, ‎using our theorems‎. ‎Finally‎, ‎an example is given to show that the restrictions on the ideal P are not superfluous.‎

Keywords:

Generalized derivations , prime ideals , Prime rings