Some results on one-sided generalized Lie ideals with derivation

On One-sided Lie Nilpotent Ideals of Associative Rings

We prove that a Lie nilpotent one-sided ideal of an associative ring R is contained in a Lie solvable two-sided ideal of R. An estimation of derived length of such Lie solvable ideal is obtained depending on the class of Lie nilpotency of the Lie nilpotent one-sided ideal of R. One-sided Lie nilpotent ideals contained in ideals generated by commutators of the form [. . . [[r1, r2], . . .], rn−1...

On One-Sided Ideals of Rings of Linear Transformations

Generalized Skew Derivations on Lie Ideals

In [17] Lee and Shiue showed that if R is a non-commutative prime ring, I a nonzero left ideal of R and d is a derivation of R such that [d(x)x, x]k = 0 for all x ∈ I, where k,m, n, r are fixed positive integers, then d = 0 unless R ∼= M2(GF (2)). Later in [1] Argaç and Demir proved the following result: Let R be a non-commutative prime ring, I a nonzero left ideal of R and k,m, n, r fixed posi...

Generalized Skew Derivations with Engel Conditions on Lie Ideals

Let R be a prime ring and L a noncommutative Lie ideal of R. Suppose that f is a nonzero right generalized β-derivation of R associated with a β-derivation δ such that [f(x), x]k = 0 for all x ∈ L, where k is a fixed positive integer. Then either there exists s ∈ C scuh that f(x) = sx for all x ∈ R or R ⊆ M2(F ) for some field F . Moreover, if the latter case holds, then either charR = 2 or cha...

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.