Nilpotency of derivatives on an ideal

Abstract

Let R R be a prime ring and ∂ \partial a derivation of R R . It is shown that if ∂ m I = ( 0 ) {\partial ^m}I = (0) for some nonzero ideal I I in R R , then ∂ m R = ( 0 ) {\partial ^m}R = (0) .