Valuation bases for generalized algebraic series fields

Kuhlmann, Franz-Viktor; Kuhlmann, Salma; Lee, Jonathan W.

Valuation bases for generalized algebraic series fields

Dateien

Kuhlmann_valuation_bases.pdfGröße: 239.57 KBDownloads: 225

Datum

2009

Autor:innen

Kuhlmann, Franz-Viktor

Kuhlmann, Salma

Lee, Jonathan W.

Open Access-Veröffentlichung

Open Access Green

Sammlungen

Mathematik und Statistik

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

Journal of Algebra. 2009, 322(5), pp. 1430-1453. Available under: doi: 10.1016/j.jalgebra.2009.05.031

Zusammenfassung

We investigate valued fields which admit a valuation basis. Given a countable ordered abelian group G and a real closed or algebraically closed field F with subfield K, we give a sufficient condition for a valued subfield of the field of generalized power series F((G)) to admit a K-valuation basis. We show that the field of rational functions F(G) and the field F(G)not, vert, similar of power series in F((G)) algebraic over F(G) satisfy this condition. It follows that for archimedean F and divisible G the real closed field F(G)not, vert, similar admits a restricted exponential function.

Fachgebiet (DDC)

510 Mathematik

Schlagwörter

Valuation independence, Generalized series fields, Fields of Puiseux series, Restricted exponential function

Zitieren

ISO 690

KUHLMANN, Franz-Viktor, Salma KUHLMANN, Jonathan W. LEE, 2009. Valuation bases for generalized algebraic series fields. In: Journal of Algebra. 2009, 322(5), pp. 1430-1453. Available under: doi: 10.1016/j.jalgebra.2009.05.031

BibTex

@article{Kuhlmann2009Valua-638,
  year={2009},
  doi={10.1016/j.jalgebra.2009.05.031},
  title={Valuation bases for generalized algebraic series fields},
  number={5},
  volume={322},
  journal={Journal of Algebra},
  pages={1430--1453},
  author={Kuhlmann, Franz-Viktor and Kuhlmann, Salma and Lee, Jonathan W.}
}

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