Zur endlichen Homologischen Dimension von Differentialmoduln

It will be shown that for a reduced separable analytic k-algebra A, with k being a field, a necessary condition for the finite differential module of A to have finite homological dimension is that the canonical module of A is free. This generalizes a result of T. Matsuoka and Y. Aoyama concerning almost complete intersections. In case that A is a normal domain and smooth in codimension 1 an analogous statement can be made for the module of derivations and the module of Zariski differentials of A.