Definition:Algebraically Closed Field
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Definition
Let $K$ be a field.
Then $K$ is algebraically closed if and only if:
Definition 1
The only algebraic field extension of $K$ is $K$ itself.
Definition 2
Every irreducible polynomial $f$ over $K$ has degree $1$.
Definition 3
Every polynomial $f$ over $K$ of strictly positive degree has a root in $K$.