Definition:Algebraic Element of Field Extension

Definition
Let $E / F$ be a field extension.

Let $\alpha \in E$.

Then $\alpha$ is algebraic over $F$ it is a root of some nonzero polynomial over $F$:
 * $\exists f \in F \left[{X}\right] \setminus \left\{{0}\right\}: f \left({\alpha}\right) = 0$

where:
 * $F \left [{X}\right]$ denotes the polynomial ring over $F$.

Also see

 * Definition:Algebraic Field Extension
 * An element of $E$ is said to be transcendental if it is not algebraic.

Special cases

 * Definition:Algebraic Number