Definition:Minimal Polynomial

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

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

Also known as
A minimal polynomial is also seen referred to as a minimum polynomial.

The minimal polynomial of $\alpha$ over $K$ can be denoted $\map {\min_K} \alpha$ or $\map {\mu_K} \alpha$.

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

Also see

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