Lecture
This lecture covers Dedekind rings, defining them as domains that are integrally closed and Noetherian, with every prime ideal being maximal. It explores factorisation in Dedekind rings, showing that every ideal can be uniquely factored into prime ideals. The lecture also discusses fractional ideals, principal fractional ideals, and the ideal class group of a Dedekind ring. Additionally, it delves into the heredity of Dedekind rings in finite separable extensions, separable extensions, and the properties of matrices in algebraic extensions.