Let $K$ be an extension of $\mathbb{Q}$ contained in $\mathbb{C}$ A number $\alpha \in K$ is called an algebraic integer of $K$ if it is the root of a monic polynomial with coefficients in $\mathbb{Z}$ i.e., an element of $K$ that is integral over $\mathbb{Z}$ Every algebraic integer is an algebraic number (with $K = \mathbb{C}$ , but the converse is false.