Generalized Derivations in Rings with Involution

• 来源期刊: 代数集刊（英文版）
• 关键词: prime ring generalized derivation involution
• 年，卷（期）: 2017,（3）
• 页码范围: 393-399
• 页数: 7页
• 语种: 英文
• DOI: 10.1142/S1005386717000244

摘要

The main purpose of this paper is to study generalized derivations in rings with involution which behave like strong commutativity preserving mappings.In fact,we prove the following result:Let R be a noncommutative prime ring with involution of the second kind such that char(R) ≠ 2.If R admits a generalized derivation F:R → R associated with a derivation d:R → R such that [F(x),F(x*)]-[x,x*] =0 for all x ∈ R,then F(x) =x for all x ∈ R or F(x) =-x for all x ∈ R.Moreover,a related result is also obtained.