How to prove R is a field

Gabbey

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

Dick

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

HallsofIvy

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

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Gabbey	How to prove R is a field 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

Dick Recognitions: Homework Help Science Advisor	What property of a field does an integral domain lack? How does being algebraically closed fill that gap?

HallsofIvy Recognitions: Gold Member Science Advisor Staff Emeritus	"Algebraically closed" is "overkill". You really only need a small result that follows from algebraically closed.