Families of k-derivations on k-algebras

Let A be an integral k-algebra of finite type over a field k of characteristic zero. Let image be a family of k-derivations on A and image the A-module spanned by image. In this paper, we generalise a result due to Nowicki and construct an element ∂ of image such that image. Such a derivation is called image-minimal. Then we establish a density theorem for image-minimal derivations in image.