A note on generalized derivations and left ideals of prime rings

Let R be a prime ring and Z(R) denotes the center of R. In this study, we expose the commutativity of R as a consequence of specific differential identities involving derivations acting on left ideals of R. Finally, we give examples that demonstrate the necessity of hypotheses taken in the theorems.

Keywords:

prime ring , left ideal , Derivation , generalized derivation