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Thread: Field extension question

  1. #1
    Junior Member
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    Field extension question

    I have this kind of problem in which I need help:

    Let $\displaystyle S \subseteq \mathbb{C} $ be a subfield. Show that $\displaystyle S$ is the field extension of $\displaystyle \mathbb{Q}$, in other words, show that $\displaystyle \mathbb{Q} \subseteq S$.

    Any help would be great.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Hint:

    $\displaystyle 1\in S$ implies $\displaystyle 1+\ldots +1\in S$ , $\displaystyle -(1+\ldots+1)\in S$ and $\displaystyle 0\neq x\in S\Rightarrow x^{-1}\in S$ .

    Could you continue?
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