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Valuation Faible

Demetrios Stratigopoulos (1974)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

Valuation Theory. Part I

Grzegorz Bancerek, Hidetsune Kobayashi, Artur Korniłowicz (2012)

Formalized Mathematics

In the article we introduce a valuation function over a field [1]. Ring of non negative elements and its ideal of positive elements have been also defined.

Valuations and asymptotic invariants for sequences of ideals

Mattias Jonsson, Mircea Mustaţă (2012)

Annales de l’institut Fourier

We study asymptotic jumping numbers for graded sequences of ideals, and show that every such invariant is computed by a suitable real valuation of the function field. We conjecture that every valuation that computes an asymptotic jumping number is necessarily quasi-monomial. This conjecture holds in dimension two. In general, we reduce it to the case of affine space and to graded sequences of valuation ideals. Along the way, we study the structure of a suitable valuation space.

Valuations in fields of power series.

Francisco Javier Herrera Govantes, Miguel Angel Olalla Acosta, José Luis Vicente Córdoba (2003)

Revista Matemática Iberoamericana

This paper deals with valuations of fields of formal meromorphic functions and their residue fields. We explicitly describe the residue fields of the monomial valuations. We also classify all the discrete rank one valuations of fields of power series in two and three variables, according to their residue fields. We prove that all our cases are possible and give explicit constructions.

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