Ideals and centralizing mappings in prime rings

Abstract

Let R R be a prime ring and U U be a nonzero ideal of R R . If T T is a nontrivial automorphism or derivation of R R such that u u T − u T u u{u^T} - {u^T}u is in the center of R R and u T {u^T} is in U U for every u u in U U , then R R is commutative. If R R does not have characteristic equal to two, then U U need only be a nonzero Jordan ideal.