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Title: Residual ideals of MacLane valuations
Author: Fernández González, Julio
Guàrdia, Jordi
Montes, Jesús
Nart, Enric
Keywords: Àlgebra
Aritmètica computacional
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:
It is part of: Journal of Algebra, 2015, vol. 427, p. 30-75
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ISSN: 0021-8693
Appears in Collections:Articles publicats en revistes (Matemàtica Econòmica, Financera i Actuarial)

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