## On algebraic closure in pseudofinite fields.(English)Zbl 1273.03126

Summary: 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.

### MSC:

 03C60 Model-theoretic algebra 12L12 Model theory of fields
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### References:

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