江汉大学学报（自然科学版）

设 A 是域 F 上的有限维素代数, , 是 A 上的导子. 本文给出了 及 成为幂零导子的两个必要条件: 若存在0≠a A 满足 a = 0,并且对于每个 x A, 存在正整数 n x ,使得 a n x x = 0,则 是幂零导子; 若 ≠0 且 = ,如果对于每个 x A, 存在正整数n x , 使得 n x= 0,则 是幂零导子.

Let A be prime algebra of finite dimensions over field F. Supposed that and are derivationsof A. In this paper, give two necessary conditions: If thereexistsa A (a≠0) satisfied a = 0 and for all x A, there is positive integer n x s.t a n xx = 0, then is a nilpotent derivation; If 0 , = and for all x A, there is positive integer n x s.t n x x = 0 , then is a nilpotent derivation.