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


Güven E.

TWMS Journal of Applied and Engineering Mathematics, vol.11, no.1, pp.160-167, 2021 (Journal Indexed in ESCI)

  • Publication Type: Article / Article
  • Volume: 11 Issue: 1
  • Publication Date: 2021
  • Title of Journal : TWMS Journal of Applied and Engineering Mathematics
  • Page Numbers: pp.160-167

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.