素环上非线性Lie中心化子

摘要

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→ℂ to meet withξ([A,B])=0 (∀A,B∈M)so thatφ(X)=λX+ξ(X)I for all X∈M.%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∈ℂ及映射ξ：M→ℂ满足ξ([A,B])=0(∀A,B∈M),使得对任意的X∈M,有φ(X)=λX+ξ(X)I.