. Prove that Q[X]/(X2 - 2) and Q[X]/(X2-3) are non-isomorphic extensions of Q.In other words, you need to show that both Q[X]/(X2-2) and Q[X]/(X2 - 3) arefields that contain Q and that they are not isomorphic as fields.

We need to prove that and are non-isomorphic extensions of .We know that if is field and is…

Answered: Prove that Q[X]/(X2-2) and Q[X]/(X2-3)…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.3: The Field Of Quotients Of An Integral Domain

Problem 12E

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Prove that Q[X]/(X2-2) and Q[X]/(X2-3) are non-isomorphic extensions of Q. In other words, you need to show that both Q[X]/(X2-2) and Q[X]/(X2 - 3) are fields that contain Q and that they are not isomorphic as fields.