ON (σ,τ)− LEFT JORDAN IDEALS AND GENERALIZED DERIVIATIONS

  • E. G¨uven
Keywords: Prime ring, generalized derivation, (σ,τ)−Jordan Ideal

Abstract

Let R be a prime ring with characteristic not 2 and σ,τ,α,β,λ,μ,γ automorphisms of R. Leth : R −→ R be a nonzero right (resp. left)generalized(α,β)−derivation associated with (α,β)−derivation d ( resp. d1). Let W,V be nonzero left (σ,τ)−Jordan ideals of R. The main object in this paper is to study the situations. (1) h(W)=0 , (2) [b,W]λ,μ =0 or [W,b]λ,μ =0 , (3) (b,W)λ,μ = 0 or (W,b)λ,μ =0 , (4) b[W,a]λ,μ = 0 or [W,a]λ,μb = 0 (5)b(W,a)λ,μ = 0 or (W,a)λ,μb =0 , (6) bW ⊂ Cλ,μ(V ) or Wb⊂ Cλ,μ(V ). (7) (h(R),b)λ,μa = 0 ora(h(R),b)λ,μ =0

Published
2020-02-04