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inseparable polynomial

不可分多项式

本站译名 抽象代数 义项编号TS-0312

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The foundations of geometry 封面

《The foundations of geometry》 · 第 328 页 · Chapter 14,Section 14.4「Separable Extensions; and Simple Extensions Once Again」,Definition 14.19 及其后说明

Let $k$ be a field. A polynomial $f(x)\in k[x]$ is ‘separable’ if its factorization over its splitting field (or, equivalently, over $\overline k$) has no multiple factors. […] In other words, $f(x)$ is separable if it has $\deg f$ distinct roots in its splitting field. If $f(x)$ is not separable, it is said to be ‘inseparable’.

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