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Hardy type derivations on fields of exponential logarithmic series

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2011

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http://nbn-resolving.de/urn:nbn:de:bsz:352-167452
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https://doi.org/10.1016/j.jalgebra.2011.07.023
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Journal of Algebra. 2011, 345(1), pp. 171-189. ISSN 0021-8693. Available under: doi: 10.1016/j.jalgebra.2011.07.023

Zusammenfassung

We consider the valued field K : = R ( ( Γ ) ) () of formal series (with real coefficients and monomials in a totally ordered multiplicative group Γ). We investigate how to endow K () with a logarithm l, which satisfies some natural properties such as commuting with infinite products of monomials. We studied derivations on K () (Kuhlmann and Matusinski, in press). Here, we investigate compatibility conditions between the logarithm and the derivation, i.e. when the logarithmic derivative is the derivative of the logarithm. We analyze sufficient conditions on a given derivation to construct a compatible logarithm via integration of logarithmic derivatives. In Kuhlmann (2000), the first author described the exponential closure K EL () of ( K , l ) (). Here we show how to extend such a log-compatible derivation on K () to K EL ().

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Fachgebiet (DDC)
510 Mathematik

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Generalized series fields, Logarithm and exponential closure, Derivations, Valuations

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ISO 690KUHLMANN, Salma, Mickael MATUSINSKI, 2011. Hardy type derivations on fields of exponential logarithmic series. In: Journal of Algebra. 2011, 345(1), pp. 171-189. ISSN 0021-8693. Available under: doi: 10.1016/j.jalgebra.2011.07.023
BibTex
@article{Kuhlmann2011Hardy-16745,
  year={2011},
  doi={10.1016/j.jalgebra.2011.07.023},
  title={Hardy type derivations on fields of exponential logarithmic series},
  number={1},
  volume={345},
  issn={0021-8693},
  journal={Journal of Algebra},
  pages={171--189},
  author={Kuhlmann, Salma and Matusinski, Mickael}
}
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