minimal polynomial

《代数学引论》 · 第 123 页

$f(x)$ 由元素 $\alpha$ 唯一决定，叫做元素 $\alpha$ 在 $F$ 上的极小多项式。

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《A Course in Finite Group Representation Theory》 · 第 89 页 · Section 3.2「Finite and Algebraic Field Extensions」，Remark 5

Let $K\subset L$ be a field extension and $\alpha\in L$ an element that is algebraic over $K$. Then there exists a unique monic polynomial $f\in K[X]$ of smallest degree such that $f(\alpha)=0$. […] The polynomial $f$ is called the minimal polynomial of $\alpha$ over $K$.