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 noncommutativ...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.展开更多
文摘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.
