Maximal Separable Intermediate Fields of Large Codegree

Nickolas Heerema
1981 Proceedings of the American Mathematical Society  
Let tbea function field in n (n > 0) variables over kg, a field having characteristic p =£ 0. An intermediate field s is maximal separable if s/k0 is separable and s is not properly contained in any subfield of k separable over k0. The following result is proved. If n = 1 the set A = {[k : s]\ s maximal separable} is bounded if and only if the algebraic closure k0 of ko in k is separable over k¡y. If n > 1 and A is bounded then k0/k0 is separable. An upper bound for A is obtained for the case n = 1 and k0/k0 separable.
doi:10.2307/2043938 fatcat:325paaqgpzeaxn3alumh753mwq