关键词: 素环, 半素环, 幂零导子, Lie理想

Abstract: This article deals with the nilpotent derivation in a s emiprime ring, and with related technique in its extended ring, it is proved tha t (1) R is an n!-torsionfree semiprime ring, n∈N, Z is the center of R, δ is a derivation of R, if δⁿ(R)=0, then δ(Z)=0； （2） R is a prime ring with char R≠2, Z is the center of R, U₁,U₂,…,U_nare Lie ideals of R, if d₁,d₂,…,d_nare the nonzero derivations of R and ［［… ［d₁(U ₁),d₂(U₂)］,…］,d_n(U_n)］Z, then there exists i∈{1,2,…,n}, such that U_iZ.

Key words: prime ring, semiprime ring, nilpotentderivation, Lie ideal