Hasse-Schmidt Derivations and Coefficient Fields in Positive   Characteristics
  We show how to express any Hasse-Schmidt derivation of an algebra in terms of a finite number of them under natural hypothesis. As an application, we obtain coefficient fields of the completion of a regular local ring of positive characteristic in terms of Hasse-Schmidt derivations 
M. Fernandez-Lebron, L. Narvaez-Macarro