\begin{definition}[Definition:Minimal Polynomial/Definition 2]
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 irreducible, monic polynomial $f \in K \sqbrk x$ such that $\map f \alpha = 0$.
\end{definition}