Journal of Symbolic Logic

On algebraic closure in pseudofinite fields

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.

Article information

Source
J. Symbolic Logic, Volume 77, Issue 4 (2012), 1057-1066.

Dates
First available in Project Euclid: 15 October 2012

https://projecteuclid.org/euclid.jsl/1350315576

Digital Object Identifier
doi:10.2178/jsl.7704010

Mathematical Reviews number (MathSciNet)
MR3051614

Zentralblatt MATH identifier
1273.03126

Citation

Beyarslan, Özlem; Hrushovski, Ehud. On algebraic closure in pseudofinite fields. J. Symbolic Logic 77 (2012), no. 4, 1057--1066. doi:10.2178/jsl.7704010. https://projecteuclid.org/euclid.jsl/1350315576