A condition that a derivation be inner (Q1822598)

The author proves: Let R be a prime ring and d a derivation of R. Suppose there is a left ideal \(L\neq 0\) of R and there exists an element \(a\neq 0\) such that \(ad(L)=0\). Then there exists an element q in Q, the Martindale ring of quotients of R, such that \(d(r)=qr-rq\) for all r in R. Furthermore, q can be chosen so that both \(aq=0\) and \(uq=0\) for all u in L.