Definition:Algebraic Number/Degree

Definition
Let $\alpha$ be an algebraic number.

By definition, $\alpha$ is the root of at least one polynomial $P_n$ with rational coefficients.

The degree of $\alpha$ is the degree of the minimal polynomial $P_n$ whose coefficients are all in $\Q$.

Algebraic Number over Field
Sources which define an algebraic number over a more general field define degree in the following terms: