JORDAN *-DERIVATIONS OF PRIME RINGS

Let R be a prime ring, which is not commutative, with involution * and with Q(ms)(R) the maximal symmetric ring of quotients of R. An additive map delta : R -> R is called a Jordan *-derivation if delta(x(2)) = delta(x)x* + x delta(x) for all x is an element of R. A Jordan *-derivation of R is called X-inner if it is of the form x bar right arrow xa - ax* for x is an element of R, where a is an element of Q(ms)(R). We prove that any Jordan *-derivation of R is X-inner if char R not equal 2 or deg(S(R)) > 4, where S(R) := {x is an element of R| x* = x}.