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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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