splitting field

《代数学引论》 · 第 213 页

则 $E/F$ 叫做 $f(x)$ 的一个分裂域。

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《A Course in Finite Group Representation Theory》 · 第 107 页 · Section 3.5「Splitting Fields」，Definition 1

Let $\mathfrak F=(f_i)_{i\in I}$, $f_i\in K[X]$, be a family of nonconstant polynomials with coefficients in a field $K$. A splitting field (over $K$) of the family $\mathfrak F$ is a field $L$ extending $K$ such that: (i) Every polynomial $f_i$ decomposes into a product of linear factors over $L$. (ii) The extension $L/K$ is generated by the zeros of the polynomials $f_i$.