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Quadratically closed field : ウィキペディア英語版 | Quadratically closed field In mathematics, a quadratically closed field is a field in which every element of the field has a square root in the field.〔Lam (2005) p. 33〕〔Rajwade (1993) p. 230〕 ==Examples==
* The field of complex numbers is quadratically closed; more generally, any algebraically closed field is quadratically closed. * The field of real numbers is not quadratically closed as it does not contain a square root of −1. * The union of the finite fields for ''n'' ≥ 0 is quadratically closed but not algebraically closed.〔 * The field of constructible numbers is quadratically closed but not algebraically closed.〔Lam (2005) p. 220〕
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