On derivations and commutativity in prime rings. (Q1777903)

The following result is proved: Let \(R\) be a prime ring of characteristic \(\neq 2\) and \(d\) a nonzero derivation in \(R\). Then (i) if \(R\) satisfies the differential identity \([[d(x),x],[d(y),y]]=0\) then \(R\) is commutative; (ii) if a nonzero right ideal \(I\) of \(R\) satisfies the identity \([[d(x),x],[d(y),y]]=0\) then either \([I,I]I=0\) or \(d(I)I=0\).