右理想上幂零导子的零化子

Annihilators of Power Values of Derivations in Right Ideal

设R是一个素环,L是R的一个非零右理想,D是R的一个非零导子,a∈R.假设aD(x)n=0对于所有的x∈L成立,这里n是一个固定整数,那么aL=0或D=ad(p),对于某个p∈Q,使得pL=0.

Let R be a prime ring, L a nonzero derivation of R and a ∈ R. Suppose that aD（x）^n= 0 for all x ∈ L, where n is fixed positive integer. Then either aL = 0 or D = ad（p） for some p ∈ Q such that pL = 0.