M3 7. Show that the splitting field Q(√2, √3) of (X2-2)(X²-3) is a Galois extensionof the rational field Q with degree 4 over Q.

If there exist a polynomial of degree 4 generated by this splitting field, then we say this is an…

Answered: 7. Show that the splitting field Q(√2,…

7. Show that the splitting field Q(√2, √3) of (X2-2)(X2-3) is a Galois extension of the rational field Q with degree 4 over Q.

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 18E: 18. Let be the smallest subring of the field of rational numbers that contains . Find a...

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Question

7. Show that the splitting field Q(√2, √3) of (X2-2)(X²-3) is a Galois extension
of the rational field Q with degree 4 over Q.

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