algebraic closure

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algebraic closure \Prononciation ?\

1. (Algèbre) Clôture algébrique.
   • While ${\displaystyle \mathbb {C} }$ contains an algebraic closure of ${\displaystyle \mathbb {Q} }$, it is by no means the only algebraically closed field containing an algebraic closure of ${\displaystyle \mathbb {Q} }$. We denote by ${\displaystyle \mathbb {Q} ^{\mathrm {alg} }}$ the algebraic closure of ${\displaystyle \mathbb {Q} }$ in ${\displaystyle \mathbb {C} }$; this field is simply the subfield of ${\displaystyle \mathbb {C} }$ consisting of algebraic numbers. The field ${\displaystyle \mathbb {Q} ^{\mathrm {alg} }}$ is isomorphic, then, to any algebraic closure of ${\displaystyle \mathbb {Q} }$, but even knowing that it is unique up to isomorphism very likely leaves us no more familiar with ${\displaystyle \mathbb {Q} ^{\mathrm {alg} }}$ than we were. — (John Swallow, Exploratory Galois Theory, Cambridge University Press, 2004, page 179)

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• Closure (mathematics) sur l’encyclopédie Wikipédia (en anglais) .
• Algebraically closed field sur l’encyclopédie Wikipédia (en anglais) .
• Algebraic closure sur Encyclopædia of Mathematics