SOME RESULTS ON LEFT (σ, τ )−JORDAN IDEALS an‎d ONE SIDED GENERALIZED DERIVATIONS

Let R be a prime ring with characteristic not 2 and σ, τ, α, β, λ, µ, γ automorphisms of R. Let h : R −→ R be a nonzero left (resp. right)- generalized (α, β)− derivation associated with (α, β)− derivation d1 (resp. d). Let W, V be nonzero left (σ, τ )−Jordan ideals of R and I a nonzero ideal of R. In this paper we also study the situations. (1) ah(R)b ⊂ Cλ,µ(R) (2) bh(I, a)σ,τ = 0 or h(I, a)σ,τ b = 0, (3) bh(I) ⊂ Cλ,µ(W) or h(I)b ⊂ Cλ,µ(W), (4) h(I) ⊂ Cλ,µ(J), (5) (h(R), a)α,β ⊂ Cα,β(R), (6) (h(I)b, a)λ,µ = 0, (7) bγ(W) ⊂ Cλ,µ(V ) or γ(W)b ⊂ Cλ,µ(V ).