On Certain Identities with Automorphisms on Lie Ideals in Prime and Semiprime Rings

• 来源期刊: 代数集刊（英文版）
• 关键词: automorphism (semi-)prime ring Lie ideal
• 年，卷（期）: 2019,（1）
• 页码范围: 93-104
• 页数: 12页
• 语种: 英文
• DOI: 10.1142/S1005386719000099

摘要

Let R be a prime ring of characteristic different from 2,Z(R) its center,L a Lie ideal of R,and m,n,s,t ≥ 1 fixed integers with t ≤ m + n + s.Suppose that α is a non-trivial automorphism of R and let Φ(x,y) =[x,y]t-[x,y]m[α([x,y]),[x,y]]n[x,y]s.Thus,(a) if Φ(u,v) =0 for any u,v ∈ L,then L (∈) Z(R);(b) if Φ(u,v) ∈ Z(R) for any u,v ∈ L,then either L (∈) Z(R) or R satisfies 84,the standard identity of degree 4.We also extend the results to semiprime rings.