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How to prove R is a field

by Gabbey
Tags: abstract algebra, algebra
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Gabbey
#1
Apr14-11, 08:58 PM
P: 2
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
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Dick
#2
Apr14-11, 09:18 PM
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P: 25,235
What property of a field does an integral domain lack? How does being algebraically closed fill that gap?
HallsofIvy
#3
Apr15-11, 08:15 AM
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PF Gold
P: 39,682
"Algebraically closed" is "overkill". You really only need a small result that follows from algebraically closed.


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