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  "body": "\n## Summary\n\nA separably closed field is a field with no proper finite [[separable extension|0WCX7NB4N7]].\nEquivalently, every [[separable polynomial|0RZ89QWTSJ]] over it of positive degree has a root in it.\nEvery [[algebraically closed field|0PF6TM8TWT]] is separably closed, and a field is algebraically closed if and only if it is separably closed and [[perfect|VWBVKT794W]].\nSeparably closed fields have trivial absolute Galois group, and the [[separable closure|JJ91A1V8NQ]] of a field is the separably closed field built from it.\n\n## Explanations\n\n### L1 human\n\nAn algebraically closed field contains a root of every polynomial.\nA separably closed field only promises a root for polynomials without repeated roots.\nIn characteristic $0$ the two notions agree.\nIn characteristic $p$ they differ: the separable closure of $\\F_p(t)$ is separably closed, but it has no root of $x^p - t$.\nSo separably closed fields are as closed as Galois theory can detect.\n",
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