Fields of constants of infinite higher derivations

Abstract

Abstract.Let K be a field of characteristic p^O, and let P be its maximal perfect subfield. Let A be a subfield of K containing P such that K is separable over h. We prove : Every regular subfield of .Äf containing h is the field of constants of a set of higher derivations on K if and only if (1) the transcendence degree of K over h is finite, and (2) K has a separating transcendency basis over h. This result leads to a generalization of the Galois theory developed in [4].