Definition:Algebraic Element of Field Extension/Definition 1

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

Let $\alpha \in E$.

$\alpha$ is algebraic over $F$ it is a root of some nonzero polynomial over $F$:
 * $\exists f \in F \sqbrk X \setminus \set 0: \map f \alpha = 0$

where $F \sqbrk X$ denotes the ring of polynomial forms in $X$.

Also see

 * Equivalence of Definitions of Algebraic Element of Field Extension