Prove that all algebraically closed field is finite.
thanks!!
The complex numbers are algebraically closed but they are infinite...
In fact a finite field cannot be algebraically closed. This is easy to see because if F is a finite field and $\displaystyle F=\{a_{1},a_{2},...,a_{n}\}$ then the polynomial $\displaystyle (x-a_{1})(x-a_{2})...(x-a_{n})+1$ does not have a root in F.