Mathematics Graduate Students Organization

Seminar:

Date: November 14

The Fundamental Theorem of Galois Theory as presented in any Graduate Algebra sequence gives a correspondence between the subgroups of the Galois group and the intermediate fields of a Galois field extension E/F. Nevertheless, in this correspondence it is almost always assumed that the extension is finite.

In the spirit of the the famous Toy Story character's slogan, we can let the degree of the extension E/F go "to infinity... and beyond" and it turns out that we can get again a correspondence between certain subgroups of the Galois group and the intermediate field extensions.

In this talk, I will illustrate the differences when the extension is infinite and I will give the correspondence in general.