Differential simplicity and a criterion for normality

Let P be a point on an algebraic variety V over a ground field k. Let R be the local ring of P on V, and let   D be the module of derivations of R into itself. If R is D-simple,  then P is a normal point.

Let P be a point on a noetherian scheme X.  Let R he the local ring of P on X, and let D be the module of derivations of R into itself.  If R is D-simple, then P need not be anymore a normal point. We give a necessary and sufficient condition for P to be normal.