Taking " g " = 1 and " f " any ordinary separable polynomial shows that any differentially closed field is separably closed.
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;"'Separable extension "': An algebraic extension in which the minimal polynomial of every element of " E " over " F " is a separable polynomial, that is, has distinct roots.
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An algebraic extension E \ supset F of fields of non-zero characteristics is a purely inseparable extension if and only if for every \ alpha \ in E \ setminus F, the minimal polynomial of \ alpha over is " not " a separable polynomial, or, equivalently, for every element of, there is a positive integer such that x ^ { p ^ k } \ in F.
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