International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 69-72, Pages 3859-3865
doi:10.1155/S0161171204403536

On derivations and commutativity in prime rings.

Abstract

Let R be a prime ring of characteristic different from 2, d a nonzero derivation of R, and I a nonzero right ideal of R such that [[d(x),x],[d(y),y]]=0, for all x,y∈I. We prove that if [I,I]I≠0, then d(I)I=0.