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Explore the fourth lecture in a graduate-level Algebraic Number Theory course, delivered in Portuguese by Professor Hossein Movasati at IMPA's Summer School 2025. Delve into Dedekind domains and their unique factorization properties in prime ideals, examining two fundamental lemmas. Study algebraic integers, the ring of algebraic integers of number fields, bases and discriminants, ideals and prime ideals, class groups and their finiteness, unique factorization, ideal norms, discriminants, different and ramification, fundamental equality, quadratic fields, quadratic reciprocity law, cyclotomic fields, Dirichlet's unit theorem, and zeta functions and L-series of number fields including the analytic class number formula. Access comprehensive course materials and additional resources through IMPA's official channels, with references to key texts by Borevich & Shafarevich, Endler, Ribenboim, and Samuel.
