I am reading Anderson and Feil - A First Course in Abstract Algebra.(adsbygoogle = window.adsbygoogle || []).push({});

I am currently focused on Ch. 47: Galois Groups... ...

I need some help with an aspect of the Example 47.7 ...

Example 47.7 and its proof read as follows:

In the above example, Anderson and Feil write the following:

"... ... We note that ##[ \mathbb{Q} ( \sqrt[3]{2} ) : \mathbb{Q} ] = 3## and ##[ \mathbb{Q} ( \zeta ) : \mathbb{Q} ] = 2##. ... ... "

Can someone please explain to me how/why ##[ \mathbb{Q} ( \zeta ) : \mathbb{Q} ] = 2## ... ... ?

Anderson and Feil give the definition of ##\zeta## in Chapter 9 in Exercise 25 ... as follows ... :

Hope someone can help ...

Peter

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# B Galois Groups ... A&F Example 47.7 ... ...

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