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Math Help - Prove the Artinian ring R is a division ring

  1. #1
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    Prove the Artinian ring R is a division ring

    From a practice exam:

    Let R be a ring with identity 1, and assume that R is right Artinian. Prove that if R has no nonzero nilpotent ideals and no idempotent elements other than 0 and 1, then R is a division ring.
    I thought maybe we could use Schur's lemma for this one, but I don't see how to make it work with or without that result. Any help would be much appreciated.

    Thanks!
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  2. #2
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    Quote Originally Posted by hatsoff View Post
    From a practice exam:



    I thought maybe we could use Schur's lemma for this one, but I don't see how to make it work with or without that result. Any help would be much appreciated.

    Thanks!
    it's a trivial result of Artin-Wedderburn theorem.
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  3. #3
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    Ah, thanks!
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