素环上非线性Lie中心化子

Nonlinear Lie Centralizers on Prime Rings

设M是包含非平凡投影P的单位素环.利用算子论方法证明了:如果φ:M→M是非线性Lie中心化子,则存在λ∈■及映射ξ:M→■满足ξ([A,B])=0(A,B∈M),使得对任意的X∈M,有φ(X)=λX+ξ(X)I.

Let M be a unital prime ring containing a nontrivial proj ection P.With some methods of operator theory,it is shown that ifφ：M→M is a nonlinear Lie centralizer,then there exist a scalarλand a mapξ：M→？ to meet withξ（[A,B]）=0 （？A,B∈M）so thatφ（X）=λX＋ξ（X）I for all X∈M.