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 $f \in K \sqbrk x$ of smallest degree such that $\map f \alpha = 0$.

Also see

• Equivalence of Definitions of Minimal Polynomial

Sources

• 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $8$: Field Extensions: $\S 38$. Simple Algebraic Extensions
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): minimal polynomial