No abstract

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 Φ : R → R is strong skew commutativity preserving (that is, satisfiesis 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.