Orthogonal Generalized Symmetric Bi-Derivations of Semiprime Rings

On Generalized Derivations of Semiprime Rings

Let F be a commuting generalized derivation, with associated derivation d, on a semiprime ring R. We show that d(x)[y, z] = 0 for all x, y, z ∈ R and d is central. We define and characterize dependent elements of F and investigate a decomposition of R relative to F . Mathematics Subject Classification: 16N60, 16W25

Generalized Derivations in Semiprime Gamma Rings

On Jordan generalized k-derivations of semiprime Γ_N-Rings

Lie Ideals and Generalized Derivations in Semiprime Rings

Let R be a 2-torsion free ring and L a Lie ideal of R. An additive mapping F : R ! R is called a generalized derivation on R if there exists a derivation d : R to R such that F(xy) = F(x)y + xd(y) holds for all x y in R. In the present paper we describe the action of generalized derivations satisfying several conditions on Lie ideals of semiprime rings.

A Note on (α, α)-Symmetric Derivations in Semiprime Rings

In this paper, we introduce (α, α)-symmetric derivations and establish some interesting results and also extend an important result of J. Vukman by using (α, α)-derivation.