Abstract:

Let M be a unital prime  ring containing a nontrivial projection P. With some methods of operator theory, it is shown that if φ: M→M is a nonlinear Lie ce
ntralizer, then there exist a scalar λ and a map ξ: M→C to meet with ξ(［A,B］)=0 (A,B∈M) so that φ(X)=λX+ξ(X)I for all X∈M.

Key words: Lie centralizers, prime rings, nonlinear