M_2(R)上的非线性Lie导子

Nonlinear Lie derivations on M_2(R)

设R是一个含有单位元的2无扰的交换环,M_2(R)是定义在R上的全矩阵代数,证明了M_2(R)上的每一个非线性Lie导子都可以表示成一个内导子,一个可加诱导导子和一个映所有二次换位子为零的中心映射的和.

Let R be a 2-torsion free commutative ring with identity and M2（R） be the full matrix algebra over R. In this note, we prove that every nonlinear Lie derivaton on M2 （R） can be expressed as a sum of an inner derivation, an additive induced derivation and a functional annihilating all second commutators of M2（R）.