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Pseudo algebraically closed field

From Encyclopedia of Mathematics
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A field $K$ for which every non-empty algebraic variety defined over $K$ has a $K$-rational point. Clearly an algebraically closed field is PAC. The Brauer group of a paC field is trivial.

See also Quasi-algebraically closed field.

References

  • Fried, Michael D.; Jarden, Moshe Field arithmetic (3rd revised ed.) Ergebnisse der Mathematik und ihrer Grenzgebiete. 3e Folge 11 Springer (2008) ISBN 978-3-540-77269-9 Zbl 1145.12001
How to Cite This Entry:
Pseudo algebraically closed field. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Pseudo_algebraically_closed_field&oldid=37149