8. Show that Q[√3] = {a+b√3 | a, b € Q} is a field. You may first show that itis 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.

To show that is a field, will follow these steps:1. Show that is a subring of a well-known field…

Answered: 8. Show that Q[√3] = {a+b√√3 | a,b ≤ Q}…

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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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.