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December 2012 On algebraic closure in pseudofinite fields
Özlem Beyarslan, Ehud Hrushovski
J. Symbolic Logic 77(4): 1057-1066 (December 2012). DOI: 10.2178/jsl.7704010

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.

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Özlem Beyarslan. Ehud Hrushovski. "On algebraic closure in pseudofinite fields." J. Symbolic Logic 77 (4) 1057 - 1066, December 2012. https://doi.org/10.2178/jsl.7704010

Information

Published: December 2012
First available in Project Euclid: 15 October 2012

zbMATH: 1273.03126
MathSciNet: MR3051614
Digital Object Identifier: 10.2178/jsl.7704010

Rights: Copyright © 2012 Association for Symbolic Logic

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Vol.77 • No. 4 • December 2012
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