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

作     者：Vincenzo De Filippis Nadeem ur Rehman 

作者机构：Department of Engineering University of Messina 98166 Messina Italy Department of Mathematics Aligarh Muslim University Aligarh India 

出 版 物：《Algebra Colloquium》 (代数集刊（英文版）)

年 卷 期：2019年第26卷第1期

页      面：93-104页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：auto morphism (semi-) prime ring Lie ideal 

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 a 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 S4, the standard identity of degree 4. We also extend the results to semiprime rings.