Prove that all algebraically closed field is finite.

thanks!!

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- Nov 7th 2008, 07:41 PMroporteAlgebraically closed field
Prove that all algebraically closed field is finite.

thanks!! - Nov 7th 2008, 08:33 PMwhipflip15
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 then the polynomial does not have a root in F. - Nov 7th 2008, 08:47 PMroporte
- Nov 7th 2008, 08:56 PMwhipflip15
Yeah i thought so. There are many ways to show it however the method above is probably the easiest.

- Nov 8th 2008, 04:18 PMThePerfectHacker
It has already been adressed here.