Definition:Minimal Polynomial/Definition 1

Definition
Let $L / K$ be a field extension.

Let $\alpha \in L$ be algebraic over $K$.

The minimal polynomial of $\alpha$ over $K$ is the unique monic polynomial $f \in K \left[{x}\right]$ of smallest degree such that $f \left({\alpha}\right) = 0$.

Also see

 * Equivalence of Definitions of Minimal Polynomial
 * Algebraic Element of Field Extension is Root of Unique Monic Polynomial of Minimal Degree