If and are algebraically closed fields extension of , is it true that ?

Printable View

- Mar 12th 2006, 04:19 PMThePerfectHackerIsomorphic Fields
If and are algebraically closed fields extension of , is it true that ?

- Mar 13th 2006, 12:51 PMrgep
No. For example, the field

of all algebraic numbers is algebraically closed, as is the field*A*of complex numbers, and both are extensions of the rationals*C*. But*Q*is countable and*A*is not: so they cannot be isomorphic.*C* - Mar 13th 2006, 01:22 PMThePerfectHackerQuote:

Originally Posted by**rgep**

- Mar 13th 2006, 09:50 PMrgep
Well, I wasn't the first to prove any of those facts!