Please use this identifier to cite or link to this item:
http://hdl.handle.net/2445/165873
Title: | Residual ideals of MacLane valuations |
Author: | Fernández González, Julio Guàrdia, Jordi Montes, Jesús Nart, Enric |
Keywords: | Àlgebra Aritmètica computacional Algebra Computer arithmetic |
Issue Date: | Apr-2015 |
Publisher: | Elsevier |
Abstract: | Let $K$ be a field equipped with a discrete valuation $v$. In a pioneering work, S. MacLane determined all extensions of $v$ to discrete valuations on $K(x)$. His work was recently reviewed and generalized by M. Vaquié, by using the graded algebra of a valuation. We extend Vaquié's approach by studying residual ideals of the graded algebra of a valuation as an abstract counterpart of certain residual polynomials which play a key role in the computational applications of the theory. As a consequence, we determine the structure of the graded algebra of any discrete valuation on $K(x)$ and we show how these valuations may be used to parameterize irreducible polynomials over local fields up to Okutsu equivalence. |
Note: | Versió postprint del document publicat a: https://doi.org/10.1016/j.jalgebra.2014.12.022 |
It is part of: | Journal of Algebra, 2015, vol. 427, p. 30-75 |
URI: | http://hdl.handle.net/2445/165873 |
Related resource: | https://doi.org/10.1016/j.jalgebra.2014.12.022 |
ISSN: | 0021-8693 |
Appears in Collections: | Articles publicats en revistes (Matemàtica Econòmica, Financera i Actuarial) |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
645823.pdf | 505.21 kB | Adobe PDF | View/Open |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.