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.
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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