- #1

Math Amateur

Gold Member

MHB

- 3,998

- 48

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