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Quadratic closure


In mathematics, a quadratically closed field is a field in which every element of the field has a square root in the field.

A quadratic closure of a field F is a quadratically closed field containing F which embeds in any quadratically closed field containing F. A quadratic closure for any given F may be constructed as a subfield of the algebraic closure Falg of F, as the union of all quadratic extensions of F in Falg.


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