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Hardy type derivations in generalized series fields

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2012

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http://nbn-resolving.de/urn:nbn:de:bsz:352-180148
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https://doi.org/10.1016/j.jalgebra.2011.11.024
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Journal of Algebra. 2012, 351(1), pp. 185-203. ISSN 0021-8693. Available under: doi: 10.1016/j.jalgebra.2011.11.024

Zusammenfassung

We consider the valued field K := R((/Gamma)) of generalised series (with real coefficients and monomials in a totally ordered multiplicative group /Gamma). We investigate how to endow K with a series derivation, that is a derivation that satisfies some natural properties such as commuting with infinite sums (strong linearity) and (an infinite version of) Leibniz rule. We characterize when such a derivation is of Hardy type, that is, when it behaves like di erentiation of germs of real valued functions in a Hardy field. We provide a necessary and sufficent condition for a series derivation of Hardy type to be surjective.

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510 Mathematik

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ISO 690KUHLMANN, Salma, Mickael MATUSINSKI, 2012. Hardy type derivations in generalized series fields. In: Journal of Algebra. 2012, 351(1), pp. 185-203. ISSN 0021-8693. Available under: doi: 10.1016/j.jalgebra.2011.11.024
BibTex
@article{Kuhlmann2012Hardy-18014,
  year={2012},
  doi={10.1016/j.jalgebra.2011.11.024},
  title={Hardy type derivations in generalized series fields},
  number={1},
  volume={351},
  issn={0021-8693},
  journal={Journal of Algebra},
  pages={185--203},
  author={Kuhlmann, Salma and Matusinski, Mickael}
}
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