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 \(K\).
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- Review status: reviewed
- Last edited by John Jones on 2018-08-08 16:09:12
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- 2018-08-08 16:09:12 by John Jones (Reviewed)