Copyright © 2009 Basudeb Dhara. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let R be a prime ring of char R≠2, d a nonzero derivation of R and ρ a nonzero right ideal of R such that [[d(x),x]n,[y,d(y)]m]t=0 for all x,y∈ρ, where n≥0, m≥0, t≥1 are fixed integers. If [ρ,ρ]ρ≠0, then d(ρ)ρ=0.