Das zariskische Diskriminantenkriterium und die Fortsetzung von Derivationen

Let A be a reduced equidimensional local analytic algebra and let R?A be a regular local “parametrization” of A. Then the Zariski discriminant criterion can be stated as follows: If A is a simple extension of R, i.e. A=Rx] for a certain x, and if the (reduced) discriminant locus S in R of A is smooth, then A is “lipschitz-meromorphically” trivial along S; this means that every derivation of R leaving S invariant can be extended to the relative saturation Ã^R of A over R.- In this paper quite generally (i.e. not only for the case of a simple extension) the following question is considered: Which conditions should a derivation of R satisfy in order that it leaves invariant the ring Ã^R?