How to prove R is a field

  • Thread starter Gabbey
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  • #1
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Homework Statement



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

The Attempt at a Solution


I guess it follows from the definitions but I can't specify which it is
 

Answers and Replies

  • #2
Dick
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What property of a field does an integral domain lack? How does being algebraically closed fill that gap?
 
  • #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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