On derivations and commutativity of prime rings with involution

In [6], Bell and Daif proved that if R is a prime ring admitting a nonzero derivation such that d (xy) = d (yx) for all x, y is an element of R, then R is commutative. The objective of this paper is to examine similar problems when the ring R is equipped with involution. It is shown that if a prime ring R with involution * of a characteristic different from 2 admits a nonzero derivation d such that d (xx*) = d (x*x) for all x is an element of R and S(R) boolean AND Z(R) not equal (0), then R is commutative. Moreover, some related results have also been discussed.