On algebraic closure in pseudofinite fields

Özlem Beyarslan; Ehud Hrushovski

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arXiv · 0909.2189

On algebraic closure in pseudofinite fields

Özlem Beyarslan·Ehud Hrushovski

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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 pseudo-finite fields we show that algebraic closure agrees with definable closure, as soon as A contains the relative algebraic closure of the prime field.

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BibTeX RIS

Özlem Beyarslan, Ehud Hrushovski. 2012-01-12. On algebraic closure in pseudofinite fields. https://arxiv.org/abs/0909.2189

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