Publikation:

Valuation bases for generalized algebraic series fields

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Kuhlmann_valuation_bases.pdf
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2009

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Kuhlmann, Franz-Viktor
Lee, Jonathan W.

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http://nbn-resolving.de/urn:nbn:de:bsz:352-opus-90999
DOI (zitierfähiger Link)
https://doi.org/10.1016/j.jalgebra.2009.05.031
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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.

Zusammenfassung in einer weiteren Sprache

Fachgebiet (DDC)
510 Mathematik

Schlagwörter

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

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ISO 690KUHLMANN, 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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