Characterization of Galois Extensions
An important theorem of Emil Artin states that for a finite extension E/F, each of the following statements is equivalent to the statement that E/F is Galois:
- E/F is a normal extension and a separable extension.
- E is a splitting field of a separable polynomial with coefficients in F.
- = |Aut(E/F)|; that is, the degree of the field extension is equal to the order of the automorphism group of E/F.
Read more about this topic: Galois Extension
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