Definition. algebraic over $F$ [1401]

Let $K / F$ be a field extension.

1. An element $\alpha \in K$ is said to be algebraic over $F$ if $\alpha$ is a root of some nonzero polynomial in $F[x]$.
2. An element $\alpha \in K$ is called transcendental over $F$ if it is not algebraic.
3. The extension $K / F$ is called algebraic if every element of $K$ is algebraic over $F$.