algebraic closure
التعريفات والمعاني
== Anglais ==
=== Étymologie ===
Étymologie manquante ou incomplète. Si vous la connaissez, vous pouvez l’ajouter en cliquant ici.
=== Locution nominale ===
algebraic closure \Prononciation ?\
(Algèbre) Clôture algébrique.
While
C
{\displaystyle \mathbb {C} }
contains an algebraic closure of
Q
{\displaystyle \mathbb {Q} }
, it is by no means the only algebraically closed field containing an algebraic closure of
Q
{\displaystyle \mathbb {Q} }
. We denote by
Q
a
l
g
{\displaystyle \mathbb {Q} ^{\mathrm {alg} }}
the algebraic closure of
Q
{\displaystyle \mathbb {Q} }
in
C
{\displaystyle \mathbb {C} }
; this field is simply the subfield of
C
{\displaystyle \mathbb {C} }
consisting of algebraic numbers. The field
Q
a
l
g
{\displaystyle \mathbb {Q} ^{\mathrm {alg} }}
is isomorphic, then, to any algebraic closure of
Q
{\displaystyle \mathbb {Q} }
, but even knowing that it is unique up to isomorphism very likely leaves us no more familiar with
Q
a
l
g
{\displaystyle \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)
==== Vocabulaire apparenté par le sens ====
algebraically closed
=== Prononciation ===
→ Prononciation audio manquante. (Ajouter un fichier ou en enregistrer un avec Lingua Libre )
=== Voir aussi ===
Closure (mathematics) sur l’encyclopédie Wikipédia (en anglais) .
Algebraically closed field sur l’encyclopédie Wikipédia (en anglais) .
Algebraic closure sur Encyclopædia of Mathematics