8. Show that Q[√3] = {a+b√√3 | a,b ≤ Q} is a field. You may first show that it is a ring by showing that it is a subring of a well-known field. From there, you will only have a few more things to show.
8. Show that Q[√3] = {a+b√√3 | a,b ≤ Q} is a field. You may first show that it is a ring by showing that it is a subring of a well-known field. From there, you will only have a few more things to show.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.2: Integral Domains And Fields
Problem 22E: Prove that if R and S are fields, then the direct sum RS is not a field. [Type here][Type here]
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