In this paper we present a characterization for the defect of simple algebraic extensions of
valued fields. This characterization generalizes the known result for the henselian case …

One of the main goals of this paper is to present the relation between limit key polynomials
and MacLane-Vaquié limit key polynomials. This is a continuation of the work started in [3] …

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 ν be a valuation of arbitrary rank on the polynomial ring K [x] with coefficients in a field K.
We prove comparison theorems between MacLane–Vaquié key polynomials for valuations …

We build on the correspondence between abstract key polynomials and minimal pairs made
by Novacoski and show how to relate the valuations that are generated by each object. We …

In this paper, we study the structure of the graded ring associated to a limit key polynomial Q
n in terms of the key polynomials that define Q n. In order to do that, we use direct limits. In …

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 …

For a fixed irreducible polynomial F we study the set VF of all valuations on K [x] bounded by
valuations whose support is (F). The first main result presents a characterization for …

Minimal pairs of definition were introduced by Alexandru, Popescu and Zaharescu [3],[4],[5]
to study residue transcendental extensions. In this paper we obtain analogous results in the …

Given a valuation v on a field K, an extension v¯ to an algebraic closure K¯ and an
extension w to K (X). In this paper, we study common extensions w¯ of both w and v¯ to the …