Distinguished subfields

Let L be a finitely generated nonalgebraic extension of a field K of characteristic $p\, \ne \,0$. A maximal separable extension D of K in L is distinguished if $L\, \subseteq \,{K^{{p^{ - \,n}}}}(D)$ for some n. Let d be the transcendence degree of L over K. If every maximal separable extension of K in L is distinguished, then every set of d relatively p-independent elements is a separating transcendence basis for a distinguished subfield. Conversely, if $K({L^p})$ is separable over K, this condition is also sufficient. A number of properties of such fields are determined and examples are presented illustrating the results.