Journal of Symbolic Logic

On algebraic closure in pseudofinite fields

Özlem Beyarslan and Ehud Hrushovski

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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

Permanent link to this document
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.


Export citation