Definition:Algebraic Closure

Definition
Let $K$ be a field.

Then an algebraic closure of $K$ is an algebraically closed algebraic extension of $K$.

By Field has Algebraic Closure and Algebraic Closure of Field is Unique, each field has exactly one algebraic closure, up to isomorphism.

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

The algebraic closure of $K$ is written $\overline{K}$.