algebraic closure

Anglais

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Singulier	Pluriel
algebraic closure \Prononciation ?\	algebraic closures \Prononciation ?\

algebraic closure \Prononciation ?\

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