Definition:Algebraic Number over Field/Degree

Definition

Let $F$ be a field.

Let $z \in \C$ be algebraic over $F$.

The degree of $\alpha$ is the degree of the minimal polynomial $\map m x$ whose coefficients are all in $F$.

Sources

• 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $8$: Field Extensions: $\S 38$. Simple Algebraic Extensions