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On algebraic closure in pseudofinite fields

Published online by Cambridge University Press:  12 March 2014

Özlem Beyarslan  and
Ehud Hrushovski
Özlem Beyarslan
Affiliation:
Department of Mathematics, Boǧaziçi University, 34342 Bebek, Ístanbul, Turkey, E-mail: ozlem.beyarslan@boun.edu.tr
Ehud Hrushovski
Affiliation:
Department of Mathematics, Hebrew University at Jerusalem, 91904 Jerusalem, Israel, E-mail: ehud@math.huji.ac.il
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Abstract

We study the automorphism group of the algebraic closure of a substructure A of a pseudo-finite field F. We show that the behavior of this group, even when A is large, depends essentially on the roots of unity in F. For almost all completions of the theory of pseudofinite fields, we show that over A, algebraic closure agrees with definable closure, as soon as A contains the relative algebraic closure of the prime field.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 77 , Issue 4 , December 2012 , pp. 1057 - 1066
Copyright
Copyright © Association for Symbolic Logic 2012

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References

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