Any field of the form ℚ[√d] where d is a square-free integer and d ≠ 0,1. The elements of ℚ[√d] have the form q₁ + q₂√d, where q₁,q₂ are rational. ℚ[√d] is a degree 2 field extension over ℚ. Its ring of integers consists of those elements ζ‎∊ℚ[√d] that satisfy a quadratic equation ζ‎² + aζ‎ + b = 0, where a,b are integers. When d = −19, the ring of integers is ℤ[(1 + $\sqrt{-19}$)/2], which is a principal ideal domain which is not a Euclidean domain.