A Note on Henselian Valuation Rings

Abstract

Let K be a field and Ka its algebraic closure. A valuation a ring A of K is called henselian, if there is only one valuation ring C of Ka which lies over A (i.e. such that C ∩ K = A) or, equivalently, if Hensel's Lemma is valid for K, A (see [5], F). In the following, we shall consider only rank one valuation rings.