Definition:Algebraically Closed Field

Definition
A field $K$ is algebraically closed if the only algebraic extension of $K$ is $K$ itself.

By Equivalence of Definitions of an Algebraically Closed Field this is equivalent to:


 * Every irreducible polynomial $f$ over $K$ has degree $1$.


 * Every polynomial $f$ over $K$ of strictly positive degree has a root in $K$.