Jordan Derivations on Lie Ideals of Semiprime ?-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.

On Jordan generalized k-derivations of semiprime Γ_N-Rings

A Note on Jordan∗− Derivations in Semiprime Rings with Involution

In this paper we prove the following result. Let R be a 6−torsion free semiprime ∗−ring and let D : R → R be an additive mapping satisfying the relation D(xyx) = D(x)y∗x∗ + xD(y)x∗ + xyD(x), for all pairs x, y ∈ R. In this case D is a Jordan ∗−derivation. Mathematics Subject Classification: 16W10, 39B05

Generalized Jordan Triple Higher ∗−Derivations on Semiprime Rings

Let R be an associative ring not necessarily with identity element. For any x, y ∈ R. Recall that R is prime if xRy = 0 implies x = 0 or y = 0, and is semiprime if xRx = 0 implies x = 0. Given an integer n ≥ 2, R is said to be n−torsion free if for x ∈ R, nx = 0 implies x = 0.An additive mapping d : R → R is called a derivation if d(xy) = d(x)y + yd(x) holds for all x, y ∈ R, and it is called a...

on jordan generalized k-derivations of semiprime γ_n-rings