Vipul: Created page with '{{field property}} ==Definition== A field is termed a '''quadratically closed field''' if every element in the field is a square. For every field, there is a unique smalle...'

2009-05-10T17:07:42Z

Created page with '{{field property}} ==Definition== A field is termed a '''quadratically closed field''' if every element in the field is a square. For every field, there is a unique smalle...'

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{{field property}}

==Definition==

A [[field]] is termed a '''quadratically closed field''' if every element in the field is a square.

For every field, there is a unique smallest quadratically closed field contianing it, termed its '''quadratic closure'''.

==Examples==

* [[Field of constructible complex numbers]] is an example of a quadratically closed field.

==Relation with other properties==

===Stronger properties===

* [[Weaker than::Algebraically closed field]]

===Weaker properties===

* [[Stronger than::Pythagorean field]]

Quadratically closed field - Revision history

Vipul: Created page with '{{field property}} ==Definition== A field is termed a '''quadratically closed field''' if every element in the field is a square. For every field, there is a unique smalle...'