Higher derivation Galois theory of fields

Abstract:

A Galois correspondence for finitely generated field extensions $k/h$ is presented in the case characteristic $h = p \ne 0$. A field extension $k/h$ is Galois if it is modular and $h$ is separably algebraically closed in $k$. Galois groups are the direct limit of groups of higher derivations having rank a power of $p$. Galois groups are characterized in terms of abelian iterative generating sets in a manner which reflects the similarity between the finite rank and infinite rank theories of Heerema and Deveney [9] and gives rise to a theory which encompasses both. Certain intermediate field theorems obtained by Deveney in the finite rank case are extended to the general theory.