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
What property of a field does an integral domain lack? How does being algebraically closed fill that gap?
"Algebraically closed" is "overkill". You really only need a small result that follows from algebraically closed.