Algebraic closure of a field (reviewed)

An algebraic closure of a field $K$ is a minimal algebraically closed field extension of $K$. It is unique up to (non-canonical) isomorphism. It is usually denoted $\overline{K}$.

For any number field, its algebraic closure is usually denoted by $\overline{\Q}$, and it is isomorphic to the field of all algebraic numbers in $\C$.