A Note on Derivations of Higher Order and Commutativity of Prime Rings

• 来源期刊: 代数集刊（英文版）
• 关键词: prime ring derivation Lie ideal (generalized) polynomial identity differential identity
• 年，卷（期）: 2003,（4）
• 页码范围: 513-517
• 页数: 5页
• 语种: 英文

摘要

One question posed by Chung and Luh is answered. Namely, let R be a prime ring with center Z and d a non-zero derivation of R. Suppose xdn - xam ∈ Z for all x ∈ R, where n ＞ m are fixed non-negative integers. Then R is commutative if any one of the following conditions is satisfied: (I) m = 0;(ii) m = 1, n ＞ 1 an even integer, and charR ≠ 2; (iii) m = 2, n ＞ 2 an odd integer, and char R ≠ 2.