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 Phi : R -> R is strong skew commutativity preserving (that is, satisfies Phi(A)Phi(B)-Phi(B)Phi(A)* = AB-BA* for all A, B is an element of R) if and only if there exist a map f : R -> Z(S)(R) and an element Z is an element of Z(S)(R) with Z(2) = I such that Phi(A) = ZA + f(A) for all A is an element of 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.