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How to prove R is a field

  1. Apr 14, 2011 #1
    1. The problem statement, all variables and given/known data

    Let R be an integral domain and algebraically closed. Prove it follows that R is a field.

    3. The attempt at a solution
    I guess it follows from the definitions but I can't specify which it is
     
  2. jcsd
  3. Apr 14, 2011 #2

    Dick

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    What property of a field does an integral domain lack? How does being algebraically closed fill that gap?
     
  4. Apr 15, 2011 #3

    HallsofIvy

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    "Algebraically closed" is "overkill". You really only need a small result that follows from algebraically closed.
     
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