Strong commutativity-preserving generalized derivations on semiprime rings

Let R be a ring with a subset S. A mapping of R into itself is called strong commutativity-preserving (scp) on S, if f(x), f(y)] = x, y] for all x, y ∈ S. The main purpose of this paper is to describe the structure of the generalized derivations which are scp on some ideals and right ideals of a prime ring, respectively. The semiprime case is also considered. The first author is supported in part by China NNSF (10726051) and Grant in-aid for Scientific Research from Department of Mathematics, Jilin University. The second author is supported by Grant in-aid for Scientific Research from Department of Mathematics, Jilin University