Register to reply

How to prove R is a field

by Gabbey
Tags: abstract algebra, algebra
Share this thread:
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
Phys.Org News Partner Science news on
Experts defend operational earthquake forecasting, counter critiques
EU urged to convert TV frequencies to mobile broadband
Sierra Nevada freshwater runoff could drop 26 percent by 2100
Apr14-11, 09:18 PM
Sci Advisor
HW Helper
P: 25,228
What property of a field does an integral domain lack? How does being algebraically closed fill that gap?
Apr15-11, 08:15 AM
Sci Advisor
PF Gold
P: 39,568
"Algebraically closed" is "overkill". You really only need a small result that follows from algebraically closed.

Register to reply

Related Discussions
F is a field, prove congruence defines an equivalence relation? Calculus & Beyond Homework 0
Prove that its a field Calculus & Beyond Homework 24
Prove if a vector field is conservative or not Calculus & Beyond Homework 1
Prove F is a field where F maps to itself Calculus & Beyond Homework 4
Prove electric field varies with distance Introductory Physics Homework 0