Definition:Algebraic Closure

Definition
Let $K$ be a field.

An algebraic closure of $K$ is an algebraically closed algebraic field extension of $K$.

An 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 $K$.


 * Definition:Relative Algebraic Closure
 * Definition:Integral Closure