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I am reading Anderson and Feil  A First Course in Abstract Algebra.
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
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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