Witt Vectors and Separably Closed Fields with Higher Derivations

The main scope of this short article is to provide a modification of the axioms given by Messmer and Wood for the theory of separably closed fields of positive characteristic and finite imperfectness degree. As their original axioms failed to meet natural expectations, a new axiomatization was given (i.e., Ziegler's one), but the new axioms do not follow Messmer and Wood's initial idea. Therefore, we aim to give a correct axiomatization that is more similar to the original one and that, as with the original axioms, involves only one Hasse- Schmidt derivation, this time based on the iterativity conditions corresponding to the Witt group.