素环上的非线性Lie导子

Nonlinear Lie Derivations on Prime Rings

设M是包含非平凡投影P的单位素环,证明了素环M上的非线性Lie导子具有形式A→ω(A)+h(A)I,其中ω:M→M是可加的导子,h:M→C是非线性映射且对所有A,B∈M有h(AB-BA)=0.

Let M be a unital prime ring containing a nontrivial projection P. We prove that every nonlinear Lie derivation on prime rings M is of the form A → w（A） ＋ h（A）I, where w ： M→M is an additive derivation and h ： M→ C is a nonlinear map with h（AB - BA） = 0 for all A,B∈M.