Definition:Algebraic Closure

Definition
Let $K$ be a field.

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

The algebraic closure of $K$ can be denoted $\overline K$.

Also see

 * Field has Algebraic Closure
 * Algebraic Closure of Field is Unique

from which every field has exactly one algebraic closure, up to isomorphism.

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