Valuations in algebraic field extensions
Citation
Description
Let K → L be an algebraic field extension and ν a valuation of K. The purpose of this paper is to describe the totality of extensions {ν′} of ν to L using a refined version of MacLane's key polynomials. In the basic case when L is a finite separable extension and rk ν = 1, we give an explicit description of the limit key polynomials (which can be viewed as a generalization of the Artin–Schreier polynomials). We also give a realistic upper bound on the order type of the set of key polynomials. Namely, we show that if char K = 0 then the set of key polynomials has order type at most N, while in the case char K = p > 0 this order type is bounded above by logp n + 1 ω, where n = [L : K]. Our results provide a new point of view of the the well known formula Ps j=1 ejfjdj = n and the notion of defect.
Abstract
Ministerio de Educación y Ciencia
Abstract
Fondo Europeo de Desarrollo Regional
Additional details
- URL
- https://idus.us.es/handle/11441/42031
- URN
- urn:oai:idus.us.es:11441/42031
- Origin repository
- USE