Nonlinear strong commutativity preserving maps on prime rings

摘要

Let A be a unital prime ring containing a nontrivial idempotent P. Assume that π: A → A is a nonlinear surjective map. It is shown that π preserves strong commutativity if and only if π has the form π(A)= α A + f(a) for all A ε A, where α ε {1,-1)1 and f is a map from A into L(A). As an application, a characterization of nonlinear surjective strong commutativity preserving maps on factor von Neumann algebras is obtained.