Dedekind Rings and Fractional Ideals

This lecture covers the concept of Dedekind rings and fractional ideals, focusing on Proposition 3.6 which states the existence of a fractional ideal p^-1 such that p.p = A in a Dedekind ring. It further explores the properties of fractional ideals as A-modules and their relationship with maximal ideals. The lecture delves into the integrally closed nature of A, the factorization of fractional ideals into prime ideals, and the extension to fractional ideals. Additionally, it discusses the isomorphism of fractional ideals and their structure as a commutative group generated by Spec(A).