Definition:Minimal Polynomial

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

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

Notation
The minimal polynomial of $\alpha$ over $K$ can be denoted $\min_K(\alpha)$ or $\mu_K(\alpha)$.

Note that it depends only on $\alpha$ and $K$.

Also see

 * Equivalence of Definitions of Minimal Polynomial
 * Minimal Polynomial is Unique