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Euclidean field
An ordered field $F$ is Euclidean if every nonnegative element $a$ ($a\geq 0$) is a square in $F$ (there exists $b\in F$ such that $b^{2}=a$).
1 Examples

$\mathbb{R}$ is Euclidean.

$\mathbb{Q}$ is not Euclidean because $2$ is not a square in $\mathbb{Q}$ (i.e., $\pm\sqrt{2}\notin\mathbb{Q}$).

$\mathbb{C}$ is not a Euclidean field because $\mathbb{C}$ is not an ordered field.

The field of real constructible numbers is Euclidean.
A Euclidean field is an ordered Pythagorean field.
There are ordered fields that are Pythagorean but not Euclidean.
Defines:
Euclidean
Related:
ConstructibleNumbers, EuclideanNumberField
Type of Math Object:
Definition
Major Section:
Reference
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