A **defining polynomial** of a number field $K$ is an irreducible polynomial $f\in\Q[x]$ such that $K\cong \mathbb{Q}(a)$, where $a$ is a root of $f(x)$. Equivalently, it is a polynomial $f\in \Q[x]$ such that $K \cong \Q[x]/(f)$.

A root \(a \in K\) of the defining polynomial is a generator of \(K\).

**Knowl status:**

- Review status: reviewed
- Last edited by John Jones on 2018-08-08 16:09:12

**Referred to by:**

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

- 2018-08-08 16:09:12 by John Jones (Reviewed)