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

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- March 12th 2006, 05:19 PMThePerfectHackerIsomorphic Fields
If and are algebraically closed fields extension of , is it true that ?

- March 13th 2006, 01:51 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* - March 13th 2006, 02:22 PMThePerfectHackerQuote:

Originally Posted by**rgep**

- March 13th 2006, 10:50 PMrgep
Well, I wasn't the first to prove any of those facts!