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Math Help - Isomorphic Fields

  1. #1
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    Isomorphic Fields

    If F\leq E and F\leq K are algebraically closed fields extension of F, is it true that E\simeq K?
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  2. #2
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    No. For example, the field A of all algebraic numbers is algebraically closed, as is the field C of complex numbers, and both are extensions of the rationals Q. But A is countable and C is not: so they cannot be isomorphic.
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  3. #3
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    Quote Originally Posted by rgep
    No. For example, the field A of all algebraic numbers is algebraically closed, as is the field C of complex numbers, and both are extensions of the rationals Q. But A is countable and C is not: so they cannot be isomorphic.
    Nice (dis)proof I like it, is it yours?
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    Well, I wasn't the first to prove any of those facts!
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