International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 582181, 8 pages
doi:10.1155/2009/582181

Vanishing power values of commutators with derivations on prime rings.

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.