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Let $E / F$ be a field extension.
The degree of $E / F$, denoted $\index E F$, is the dimension of $E / F$ when $E$ is viewed as a vector space over $F$.
$E / F$ is a finite field extension if and only if its degree $\index E F$ is finite.
$E / F$ is an infinite field extension if and only if its degree $\index E F$ is not finite.
- Definition:Finite Field Extension: where $\index E F$ is finite
- Definition:Infinite Field Extension: where $\index E F$ is not finite
- Definition:Separable Degree
- Definition:Inseparable Degree
- 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $8$: Field Extensions: $\S 36$. The Degree of a Field Extension