Definition 9.10.3. Let $F$ be a field. An *algebraic closure* of $F$ is a field $\overline{F}$ containing $F$ such that:

$\overline{F}$ is algebraic over $F$.

$\overline{F}$ is algebraically closed.

Definition 9.10.3. Let $F$ be a field. An *algebraic closure* of $F$ is a field $\overline{F}$ containing $F$ such that:

$\overline{F}$ is algebraic over $F$.

$\overline{F}$ is algebraically closed.

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