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