Generalized Derivations in Rings with Involution  

作　　者：Nadeem Ahmad Dar Abdul Nadim Khan Nadeem Ahmad Dar Abdul Nadim Khan(Department of Computer Science and Engineering Islamic University of Science and Technology J ＆ K, India Department of Mathematics, Faculty of Science ＆ Arts in Rabigh King Abdulaziz University, Saudi Arabia)

机构地区：[1]Department of Computer Science and Engineering Islamic University of Science and Technology J & K, India [2]Department of Mathematics, Faculty of Science & Arts in Rabigh King Abdulaziz University, Saudi Arabia

出　　处：《Algebra Colloquium》2017年第3期393-399,共7页代数集刊（英文版）

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.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.

关 键 词：prime ring generalized derivation INVOLUTION 

分 类 号：O153.3[理学—数学] O177.91[理学—基础数学]