Exponentiation in power series fields

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07_Exponentiation_in_power_1997.pdf
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1997
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Kuhlmann, Franz-Viktor
Shelah, Saharon
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Zusammenfassung

We prove that for no nontrivial ordered abelian group G, the ordered power series field R((G)) admits an exponential, i.e. an isomorphism between its ordered additive group and its ordered multiplicative group of positive elements, but that there is a non-surjective logarithm. For an arbitrary ordered field k, no exponential on k((G)) is compatible, that is, induces an exponential on k through the residue map. This is proved by showing that certain functional equations for lexicographic powers of ordered sets are not solvable.

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510 Mathematik
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ISO 690KUHLMANN, Franz-Viktor, Salma KUHLMANN, Saharon SHELAH, 1997. Exponentiation in power series fields. In: Proceedings of the American Mathematical Society. 1997, 125(11), pp. 3177-3183. ISSN 0002-9939. eISSN 1088-6826
BibTex
@article{Kuhlmann1997Expon-517,
  year={1997},
  title={Exponentiation in power series fields},
  number={11},
  volume={125},
  issn={0002-9939},
  journal={Proceedings of the American Mathematical Society},
  pages={3177--3183},
  author={Kuhlmann, Franz-Viktor and Kuhlmann, Salma and Shelah, Saharon}
}
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