Definition:Algebraically Closed
From ProofWiki
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 $K$.
