Let (K, v) be a valued field and let (K h, vh) be the henselization determined by the choice of
an extension of v to an algebraic closure of K. Consider an embedding v (K∗)↪ Λ of the …

Let $\iota: K\hookrightarrow L\cong K (x) $ be a simple transcendental extension of valued
fields, where $ K $ is equipped with a valuation $\nu $ of rank 1. That is, we assume given a …

We classify cuts in (totally) ordered abelian groups Γ and compute the coinitiality and
cofinality of all cuts in case Γ is divisible, in terms of data intrinsically associated to the …

In this paper, we extend the theory of minimal limit key polynomials of valuations on the
polynomial ring $\kx $. We use the theory of cuts on ordered abelian groups to show that the …

The main goal of this paper is to characterize limit key polynomials for a valuation ν on K [x].
We consider the set Ψ α of key polynomials for ν of degree α. We set p to be the exponent …

In this paper, we present a characterization for the defect of a simple algebraic extension of
rank one valued fields using the key polynomials that define the valuation. As a particular …

The main object of study in this paper is the module $\Omega $ of K\" ahler differentials of an
extension of valuation rings. We show that in the case of pure extensions $\Omega $ has a …

In this paper we present characterizations of the sets of key polynomials and abstract key
polynomials for a valuation $\mu $ of $ K (x) $, in terms of (ultrametric) balls in the algebraic …

MacLane–Vaquié chains and valuation-transcendental extensions Page 1 J CA JOURNAL OF
COMMUTATIVE ALGEBRA Volume 15 (2023), No. 2, 249–259 DOI: 10.1216/jca.2023.15.249 © …

For a henselian valued field $(K, v) $ we establish a complete parallelism between the
arithmetic properties of irreducible polynomials $ F\in K [x] $, encoded by their Okutsu …