Factorisation in Dedekind Ring

This lecture covers the factorisation of ideals in a Dedekind ring, where every ideal can be factored as a product of prime ideals. The concept of ramification index, residual fields, and inertia degree are explained in the context of prime ideals. The instructor discusses the properties of Dedekind rings, such as being integraly closed and having every prime ideal as maximal. The lecture concludes with the Chinese Reminder Theorem and the localization theorem in the context of Dedekind rings and their extensions.