The exponential rank of nonarchimedean exponential fields

Kuhlmann, Franz-Viktor; Kuhlmann, Salma

The exponential rank of nonarchimedean exponential fields

Files

10_The_exponential_rank_2000.pdf(245.27 KB)

Date

2000

Authors

Kuhlmann, Franz-Viktor

Kuhlmann, Salma

Publication type

Contribution to a conference collection

Published in

Real Algebraic Geometry and Ordered Structures: AMS Special Session on Real Algebraic Geometry and Ordered Algebraic Structures held at Louisiana State... April 17 - 21, 1996 / Delzell, Charles N. et al. (ed.). - Providence, RI : AMS, 2000. - (Contemporary Mathematics ; 253). - pp. 181-201

Abstract

For an exponential on a nonarchimedean ordered field, we introduce the notion of the exponential rank, in analogy to the rank of the field. This gives information about the growth rate of the exponential, and about the convex valuations on the field which are compatible with the exponential. We give several characterizations of these valuations, using maps induced by the exponential on the value group of the natural valuation and on the rank of the field. Finally, we construct exponential fields of arbitrary exponential rank.

Subject (DDC)

510 Mathematics

Cite This

ISO 690

KUHLMANN, Franz-Viktor, Salma KUHLMANN, 2000. The exponential rank of nonarchimedean exponential fields. In: DELZELL, Charles N., ed. and others. Real Algebraic Geometry and Ordered Structures: AMS Special Session on Real Algebraic Geometry and Ordered Algebraic Structures held at Louisiana State... April 17 - 21, 1996. Providence, RI:AMS, pp. 181-201

BibTex

@inproceedings{Kuhlmann2000expon-564,
  year={2000},
  title={The exponential rank of nonarchimedean exponential fields},
  number={253},
  publisher={AMS},
  address={Providence, RI},
  series={Contemporary Mathematics},
  booktitle={Real Algebraic Geometry and Ordered Structures: AMS Special Session on Real Algebraic Geometry and Ordered Algebraic Structures held at Louisiana State... April 17 - 21, 1996},
  pages={181--201},
  editor={Delzell, Charles N.},
  author={Kuhlmann, Franz-Viktor and Kuhlmann, Salma}
}

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