An **order** in a number field $K$ is a subring of $K$ which is also a lattice in $K$. Every order in $K$ is contained in the ring of integers of $K$, which is itself an order in $K$; for this reason, the ring of integers is sometimes called the *maximal order*.

Example: $\Z[\sqrt{5}]$ is an order in $K=\Q(\sqrt{5})$. However, it is not maximal, since the maximal order (i.e. ring of integers) of $K$ is $\Z\left[\frac{1+\sqrt{5}}2\right]$.

**Authors:**

**Knowl status:**

- Review status: reviewed
- Last edited by John Cremona on 2018-05-24 14:37:30

**Referred to by:**

**History:**(expand/hide all)

- 2018-05-24 14:37:30 by John Cremona (Reviewed)