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Separably closed fields with Hasse derivations

Published online by Cambridge University Press:  12 March 2014

Martin Ziegler
Martin Ziegler*
Affiliation:
Mathematisches Institut, Eckerstrasse 1, 79104 Freiburg, Germany, E-mail: ziegler@uni-freiburg.de
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Abstract

In [6] Messmer and Wood proved quantifier elimination for separably closed fields of finite Ershov invariant e equipped with a (certain) Hasse derivation. We propose a variant of their theory, using a sequence of e commuting Hasse derivations. In contrast to [6] our Hasse derivations are iterative.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 68 , Issue 1 , March 2003 , pp. 311 - 318
Copyright
Copyright © Association for Symbolic Logic 2003

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References

REFERENCES

[1]Delon, Françoise, Separably closed fields, Model theory and algebraic geometry, Lecture Notes in Mathematics, vol. 1696, Springer, Berlin, 1998, pp. 143–176.CrossRefGoogle Scholar
[2]Hasse, Helmut and Schmidt, F. K., Noch eine Begründung der Theorie der höheren Differentialquotienten in einem algebraischen Funktionenkörper mit einer Unbestimmten, Journal für die Reine und Angewandte Mathematik, vol. 177 (1937), pp. 215–237.Google Scholar
[3]Matsumara, Hideyuki, Commutative ring theory, Cambridge University Press, 1986.Google Scholar
[4]Matzat, B. Heinrich, Differential galois theory in positive characteristic. Lecture Notes, 10 2001.Google Scholar
[5]Messmer, Margit, Some model theory of separably closed fields, Model theory of fields (Marker, D., Messmer, M., and Pillay, A., editors), Lecture Notes in Logic, vol. 5, Springer, Berlin, 1996, pp. 135–152.CrossRefGoogle Scholar
[6]Messmer, Margit and Wood, Carol, Separably closed fields with higher derivations. I, this Journal, vol. 60 (1995), no. 3, pp. 898–910.Google Scholar
[7]Okugawa, Kôtaro, Basic properties of differential fields of an arbitrary characteristic and the Picard-Vessiot theory, Journal of Mathematics of Kyoto University, vol. 2 (1963), no. 3, pp. 294–322.Google Scholar
[8]Wood, Carol, Notes on the stability of separably closed fields, this Journal, vol. 44 (1979), no. 3, pp. 412–416.Google Scholar