How to prove R is a field

  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. Dick

    Dick 25,913
    Science Advisor
    Homework Helper

    What property of a field does an integral domain lack? How does being algebraically closed fill that gap?
  4. HallsofIvy

    HallsofIvy 41,264
    Staff Emeritus
    Science Advisor

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