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Math Help - [SOLVED] Ring Isomorphism

  1. #1
    Senior Member sfspitfire23's Avatar
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    [SOLVED] Ring Isomorphism

    Q and R (reals and rationals) are not isomorphic because some elements in R are not division rings correct? (such as pi)?
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  2. #2
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by sfspitfire23 View Post
    Q and R (reals and rationals) are not isomorphic because some elements in R are not division rings correct? (such as pi)?
    Unless I am much mistake, an element cannot be a division ring. It makes no sense!

    Assume they are isomorphic, and let \theta: \mathbb{R} \rightarrow \mathbb{Q}. Where is 2 mapped to, and where is \sqrt{2} mapped to?

    (I am assuming you mean not isomorphic as rings, and not as groups?)
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  3. #3
    Senior Member sfspitfire23's Avatar
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    Ah, sorry, I mean the rings Q and R.
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