JORDAN *-DERIVATIONS OF PRIME RINGS

Let R be a prime ring, which is not commutative, with involution * and with Qms(R) the maximal symmetric ring of quotients of R. An additive map δ : R → R is called a Jordan *-derivation if δ(x2) = δ(x)x* + xδ(x) for all x ∈ R. A Jordan *-derivation of R is called X-inner if it is of the form x ↦ xa - ax* for x ∈ R, where a ∈ Qms(R). We prove that any Jordan *-derivation of R is X-inner if char R ≠ 2 or deg (S(R)) > 4, where S(R) := {x ∈ R|x* = x}.