Definition:Separable Degree/Definition 2

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Definition

Let $\bar F$ be the algebraic closure of $F$.

The separable degree $\index E F_{\operatorname {sep} }$ of $E / F$ is the number of embeddings of $E$ into $\bar F$ that fix $F$.

Sources

• 1994: I. Martin Isaacs: Algebra: A Graduate Course: Chapter $19$: Separability and Inseparability: $\S 19 \text B$
• 2002: Serge Lang: Algebra (Revised 3rd ed.): Chapter $\text V$: $\S4$: Separable Extensions