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Let $K$ be an \PMlinkname{extension}{ExtensionField} 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.
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Let $K$ be an \PMlinkname{extension}{ExtensionField} of $\mathbb{Q}$ contained in $\mathbb{C}$. A number $\alpha \in K$ is called an algebraic integer of K 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.
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