Definition:Inseparable Degree

Definition

Let $E / F$ be a field extension.

Let $S \subseteq E$ be the separable closure of $F$ in $E$.

The inseparable degree $\index E F_i$ of $E / F$ is the degree $\index E S$.

Also see

• Definition:Separable Degree

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 $\text V$: $\S 6$: Inseparable Extensions