2. (a) Why is the polynomial X° - 2 irreducible over Q ? What is its splitting field K and what is the degree of the splitting field over Q ? Write down an element of order 2 in the Galois group of K over Q, giving the action of the group element on a set of generators of K over Q.

2. (a) Why is the polynomial X° - 2 irreducible over Q ? What is its splitting field K and what is the degree of the splitting field over Q ? Write down an element of order 2 in the Galois group of K over Q, giving the action of the group element on a set of generators of K over Q.

Name: Q is rational numbers in Abstract Algebra 2.(a)Why is the polynomial X
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Description: Q is rational numbers in Abstract Algebra 2.(a)Why is the polynomial X - 2 irreducibleover Q ? What is its splitting field K andwhat is the degree of the splitting field overQ ? Write down an element of order 2, inthe Galois group of K over Q, giving

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 11E

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