| In the case when $K$ has characteristic 0, it is separably algebraically closed if and only if it is algebraically closed.\newline If $K$ has positive characteristic $p$, $K$ is separably algebraically closed if and only if its algebraic closure is a purely inseparable extension of $K$. |
In the case when $K$ has characteristic 0, it is separably algebraically closed if and only if it is algebraically closed.\newline If $K$ has positive characteristic $p$, $K$ is separably algebraically closed if and only if its algebraic closure is a purely inseparable extension of $K$. |
