(please answer b ) Problem 2. (a)Verify that the setQ(V3) = {r+sv3 |r, s e Q}is a subfield of the real numbers R.(b)Q(V3).Show that the field of congruence classes Q(r]/(x – 3) is isomorphic to

Answered: Image /qna-images/answer/4360b568-0021-463f-9c26-63b339c625e6.jpg

Answered: (b) Q(V3). Show that the field of…

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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(b) Q(V3). Show that the field of congruence classes Q[r]/(x² – 3) is isomorphic to