COMMUTATIVITY OF PRIME RINGS WITH GENERALIZED SKEW DERIVATIONS

In the present paper, we investigate the action of generalized skew derivation F in a prime ring R which satisfies differential identities involving anti-commutator for a nonzero ideal I of R. In fact, we obtain the characterisation of the map F and the commutativity of a prime ring R which satisfies either of the identities F(x circle y) = x circle y for all x, y is an element of I or F(x) circle F(y) = x circle y for all x, y is an element of I.