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 proof of Theorem 47.1 ...

Theorem 47.1 and its proof read as follows:

At the end of the above proof by Anderson and Feil, we read the following:

"... ... It then follows that ##| \text{Gal} ( F( \alpha ) | F ) | \le \text{deg}(f)##.

The irreducibility of ##f## implies that ##\text{deg}(f) = | F( \alpha ) : F |## ... .... "

Can someone please explain exactly why the irreducibility of ##f## implies that ##\text{deg}(f) = | F( \alpha ) : F |## ... ... ?

Peter

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# I Galois Groups ... A&W Theorem 47.1 ... ...

Have something to add?

Draft saved
Draft deleted

Loading...

Similar Threads for Galois Groups Theorem |
---|

I Spin group SU(2) and SO(3) |

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

I Galois Theory - Fixed Field of F and Definition of Aut(K/F) |

I Galois Theory - Fixed Subfield of K by H ... |

I Galois Theory - Structure Within Aut(K/Q) ... |

**Physics Forums | Science Articles, Homework Help, Discussion**