Real quadratic number field

This article defines a number field property: a property that can be evaluated for a number field

Definition

A real quadratic number field is a number field obtained by extending the field of rational numbers by the squareroot of a positive square-free integer. In other words, it is a field of the form $\mathbb {Q} [{\sqrt {D}}]$ where $D>1$ and $D$ is square-free.

Relation with other properties

Weaker properties

• Quadratic number field
• Totally real number field

Opposite properties

• Imaginary quadratic number field