Integral Domains: Factorisation and Noetherian Rings

This lecture covers the concept of integral domains, focusing on factorisation in Principal Ideal Domains (PIDs) and the integral closure of rings. It also discusses Noetherian rings, defining them as rings where certain sequences of ideals stabilize, and every ideal is of finite type. The lecture concludes with the factorisation of ideals in Dedekind rings, showing that every ideal can be factored into prime ideals.