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Definition 9.14.7. Let $E/F$ be an algebraic field extension. Let $E_{sep}$ be the subextension found in Lemma 9.14.6.

  1. The integer $[E_{sep} : F]$ is called the separable degree of the extension. Notation $[E : F]_ s$.

  2. The integer $[E : E_{sep}]$ is called the inseparable degree, or the degree of inseparability of the extension. Notation $[E : F]_ i$.

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