show · nf.defining_polynomial all knowls · up · search:

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)