Remarks on existentially closed fields and diophantine equations

Paulo Ribenboim

Rendiconti del Seminario Matematico della Università di Padova (1984)

  • Volume: 71, page 229-237
  • ISSN: 0041-8994

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Ribenboim, Paulo. "Remarks on existentially closed fields and diophantine equations." Rendiconti del Seminario Matematico della Università di Padova 71 (1984): 229-237. <http://eudml.org/doc/107937>.

@article{Ribenboim1984,
author = {Ribenboim, Paulo},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {hyperelliptic equation for polynomials; purely transcendental extension; non-Henselian valued field; existentially closed; Henselian valued extension field},
language = {eng},
pages = {229-237},
publisher = {Seminario Matematico of the University of Padua},
title = {Remarks on existentially closed fields and diophantine equations},
url = {http://eudml.org/doc/107937},
volume = {71},
year = {1984},
}

TY - JOUR
AU - Ribenboim, Paulo
TI - Remarks on existentially closed fields and diophantine equations
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1984
PB - Seminario Matematico of the University of Padua
VL - 71
SP - 229
EP - 237
LA - eng
KW - hyperelliptic equation for polynomials; purely transcendental extension; non-Henselian valued field; existentially closed; Henselian valued extension field
UR - http://eudml.org/doc/107937
ER -

References

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  1. [1] L. Van Den Dries, Model Theory of Fields, Decidability and Bounds for Polynomial Ideals, Thesis, University of Utrecht, 1978. 
  2. [2] N. Greenleaf, On Fermat's equation in C(t), Amer. Math. Monthly, 76 (1969), pp. 808-809. Zbl0191.04905MR250973
  3. [3] R. Liouville, Sur l'impossibilité de la relation algébriqne Xn + Yn + Zn = 0, C. R. Acad. Sci. Paris, 87 (1879), pp. 1108-1110. JFM11.0138.03
  4. [4] M. Natanson, Catalan's equation in k(t), Amer. Math. Monthly, 81 (1974), pp. 371-373. Zbl0282.10008MR335436
  5. [5] P. Ribenboim, Théorie des Valuation, Presses Université de Montréal, 1964. Zbl0139.26201
  6. [6] P. Ribenboim, On the completion of a valuation ring, Math. Annalen, 155 (1964), pp. 392-396. Zbl0136.32102MR164960

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