Euclidean field
An ordered field is Euclidean if every non-negative element () is a square in (there exists such that ).
1 Examples
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is Euclidean.
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is not Euclidean because is not a square in (i.e. (http://planetmath.org/Ie), ).
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is not a Euclidean field because is not an ordered field (http://planetmath.org/MathbbCIsNotAnOrderedField).
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The field of real constructible numbers (http://planetmath.org/ConstructibleNumbers) is Euclidean.
A Euclidean field is an ordered Pythagorean field.
There are ordered fields that are Pythagorean but not Euclidean.