# Euclidean field

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In mathematics, a Euclidean field is an ordered field K for which every non-negative element is a square: that is, x ≥ 0 in K implies that x = y2 for some y in K.

## Euclidean closure

The Euclidean closure of an ordered field K is an extension of K in the quadratic closure of K which is maximal with respect to being an ordered field with an order extending that of K.[5]

## References

1. ^ Martin (1998) p. 89
2. ^ a b Lam (2005) p.270
3. ^ Martin (1998) pp. 35–36
4. ^ Martin (1998) p. 35
5. ^ Efrat (2006) p. 177