Strong skew commutativity preserving maps on rings with involution

Let R be a unital *-ring with the unit I. Assume that R contains a symmetric idempotent P which satisfies ARP = 0 implies A = 0 and AR(I . P) = 0 implies A = 0. In this paper, it is shown that a surjective map .: R . R is strong skew commutativity preserving (that is, satisfies .(A).(B)..(B).(A) * = AB.BA * for all A,B . R) if and only if there exist a map f:R.Z S (R) and an element Z . Z S (R) with Z 2 = I such that .(A) = ZA + f(A) for all A . R, where Z S (R) is the symmetric center of R. As applications, the strong skew commutativity preserving maps on unital prime *-rings and von Neumann algebras with no central summands of type I 1 are characterized.