On some subfields of K((X))

Abstract

Let K be a commutative field and let K((X))K((X)) be the field of Laurent series in one variable XX, consider with its natural X−X−adic topology. In this paper we prove that any closed subfield K⊂L⊂K((X))K⊂L⊂K((X)) is of the form L=K((f))L=K((f)) and K((X))K((X)) is algebraic over L of degree ordX(f)ordX(f). Some other properties of LL are studied.