A remastered version of this video (improved sound and picture quality) is available here: https://youtu.be/hbdV3YUdomU
In this lecture we show that Dedekind domains may be constructed by taking the ring of integral elements in a Galois extension. We prove the factorization theorem for ideals in a Dedekind domain. Finally we introduce an important construction of the Ideal Class Group and give examples of computations in the Ideal Class Group corresponding to an elliptic curve.
This is a lecture in a graduate course "Groups and Galois Theory".
