On derivations and commutativity in prime rings - Vincenzo De Filippis (International Journal of Mathematics and Mathematical Sciences)
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.