Valuations in algebraic field extensions
| dc.creator | Govantes, F. J. Herrera | |
| dc.creator | Acosta, M. A. Olalla | |
| dc.creator | Spivakovsky, M. | |
| dc.date | 2006-05-08 | |
| dc.date.accessioned | 2026-07-07T08:07:46Z | |
| dc.date.available | 2026-07-07T08:07:46Z | |
| dc.description | Let $K\to L$ be an algebraic field extension and $ν$ a valuation of $K$. The purpose of this paper is to describe the totality of extensions $\left\{ν'\right\}$ 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 $\mathbb N$, while in the case $char K=p>0$ this order type is bounded above by $([\log_pn]+1)ω$, where $n=[L:K]$. Our results provide a new point of view of the the well known formula $\sum\limits_{j=1}^se_jf_jd_j=n$ and the notion of defect. | |
| dc.identifier | https://arxiv.org/abs/math/0605193 | |
| dc.identifier | http://arxiv.org/abs/math/0605193 | |
| dc.identifier | J. Algebra, 312 (2007) (2), 1033-1074 | |
| dc.identifier | doi:10.1016/j.jalgebra.2007.02.022 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/131043 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.title | Valuations in algebraic field extensions | |
| dc.type | text |