## RIGHT (σ,τ) —LIE IDEALS AND ONE SIDED GENERALIZED DERIVATIONS

## RIGHT (σ,τ) —LIE IDEALS AND ONE SIDED GENERALIZED DERIVATIONS

*E. Güven*

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## Abstract

LetRbeaprimeringwithcharacteristicnot2andσ,τ,α,β,λ,μ,γautomor- phisms of R. Let h : R −→ R be a nonzero left(resp.right)-generalized (α, β)−derivation, a,b ∈ R. and U,V nonzero right (σ,τ)−Lie ideals of R. The main object in this arti- cle is to study the situations. (1) a[U,b]λ,μ = 0 or [U,b]λ,μa = 0, (2) a(U,b)λ,μ = 0 or (U,b)λ,μa = 0, (3) bh(I) ⊂ Cλ,μ(U) or h(I)b ⊂ Cλ,μ(U), (4) (b,U)λ,μ = 0 or [b,U]λ,μ = 0, (5) (U, b)λ,μ ⊂ Cλ,μ (R), (6) bV ⊂ Cλ,μ (U ) or V b ⊂ Cλ,μ (U ). Also, some characteristics of left and right generalized (α, β)−derivation satisfying several conditions on ideals are given.

## Keywords

Prime ring, generalized derivation, (σ,τ)−Lie Ideal.