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

作　　者：Vincenzo De Filippis Nadeem ur Rehman 

机构地区：[1]Department of Engineering, University of Messina, 98166 Messina, Italy [2]Department of Mathematics, Aligarh Muslim University, Aligarh, India

出　　处：《Algebra Colloquium》2019年第1期93-104,共12页代数集刊（英文版）

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.

关 键 词：auto MORPHISM (semi-) PRIME ring LIE ideal 

分 类 号：O1[理学—数学]