Definition:Field Extension/Degree/Finite

Not to be confused with Definition:Galois Field.

Definition

Let $E / F$ be a field extension.

$E / F$ is a finite field extension if and only if its degree $\index E F$ is finite.

Also see

• Finite Field Extension is Algebraic

Sources

• 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $8$: Field Extensions: $\S 36$. The Degree of a Field Extension