Euclidean field

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. 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. 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.