Definition:Algebraic Closure

Definition
Let $K$ be a field.

By the Existence of Algebraic Closure there is some algebraically closed field $\overline{K}$ containing $K$ such that no proper subfield of $\overline{K}$ is algebraically closed.

By the Uniqueness of Algebraic Closure, all such fields are isomorphic.

Consequently we can refer to the algebraic closure of $K$.