半素环的幂零导子  

Nilpotent derivations in semiprime rings

作　　者：徐晓伟[1] 

机构地区：[1]吉林大学数学学院,长春130012

出　　处：《吉林大学学报（理学版）》2004年第2期172-175,共4页Journal of Jilin University:Science Edition

摘　　要：讨论半素环上导子的幂零性质,利用相应的扩张技术证明了:(1)设R是n!-torsionfree半素环,n是自然数,Z是R的中心,δ是R上的导子,若δn(R)=0,则δ(Z)=0;(2)设R是特征不为2的素环,Z是R的中心,U1,U2,…,Un是R的Lie理想.若d1,d2,…,dn是R的非零导子,且[[…[d1(U1),d2(U2)],…],dn(Un)] Z,则存在i∈{1,2,…,n},使得Ui Z.This article deals with the nilpotent derivation in a semiprime ring, and with related technique in its extended ring, it is proved that (1) R is an n!-torsionfree semiprime ring, n∈N, Z is the center of R, δ is a derivation of R, if δ~n(R)=0, then δ(Z)=0; (2) R is a prime ring with char R≠2, Z is the center of R, U_1,U_2,...,U_nare Lie ideals of R, if d_1,d_2,...,d_nare the nonzero derivations of R and ,...],d_n(U_n)]Z, then there exists i∈{1,2,...,n}, such that U_iZ.

关 键 词：半素环 幂零导子 LIE理想 稠密正交子集 

分 类 号：O153.3[理学—数学]