Left ideals and derivations in semiprime rings

This paper obtains Posnerʹs theorem for products of derivations on left ideals in semiprime rings, so describes when a product of derivations D and E of a semiprime ring R can act as a derivation on a left ideal L of R. This result yields a quick argument for a theorem of H. Bell and W.S. Martindale on centralizing derivations of L. Finally results in the literature extending the notion of a centralizing derivation to the situation when D(x)x−xE(x) is central for all x L are obtained as special cases of a more general result here.