Strong 3-commutativity preserving maps on prime rings

Abstract

Let be a unital prime ring with characteristic not 2 and containing a nontrivial idempotent. Assume that is a surjective map. It is shown that f is strong 3-commutativity preserving, that is, f satisfies for all , if and only if for all , where is an element in the extended centroid of with and is a map from into its extended centroid. Applications to prime C-algebras, factor von Neumann algebras, standard operator algebras and matrix algebras are also obtained .