Artículo
Valuations in algebraic field extensions
Autor/es | Herrera Govantes, Francisco Javier
Olalla Acosta, Miguel Ángel Spivakovsky, Mark |
Departamento | Universidad de Sevilla. Departamento de álgebra |
Fecha de publicación | 2007-06-15 |
Fecha de depósito | 2016-06-08 |
Publicado en |
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Resumen | 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 ... 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. |
Agencias financiadoras | Ministerio de Educación y Ciencia (MEC). España European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER) |
Identificador del proyecto | MTM2004-07203-C02-01
HF2004-0117 |
Cita | Herrera Govantes, F.J., Olalla Acosta, M.Á. y Spivakovsky. Mark, (2007). Valuations in algebraic field extensions. Journal of Algebra, 312 (2), 1033-1074. |
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