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 …

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 …

In this paper we present a refined version of MacLane's theory of key polynomials, similar to
those considered by M. Vaquié, and reminiscent of related objects studied by Abhyankar …

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 …

Let ν be a rank one valuation on K [x] and Ψ n the set of key polynomials for ν of degree n∈
N. We discuss the concepts of being Ψ n-stable and (Ψ n, Q)-fixed. We discuss when these …

key polynomials and distinguished pairs Page 1 Journal of Algebra and Its Applications Vol.
22, No. 9 (2023) 2350193 (19 pages) c© World Scientific Publishing Company DOI: 10.1142/S0219498823501931 …

Iniciamos este trabalho com um estudo da álgebra graduada associada a uma valorização
ν: K−→ Γ∞. Mostramos que nos casos em que o grupo de valores é livre ou o corpo do …