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Learn about ideal class groups, fractional ideals, and class numbers in this graduate-level mathematics lecture from the 2025 Summer School at IMPA. Explore algebraic integers, the ring of algebraic integers of a number field, bases and discriminants, ideals, prime ideals, class groups, and the finiteness of class groups. Delve into unique factorization, prime ideals, ideal norms, discriminants, different ideals, and ramification. Study quadratic fields, quadratic reciprocity law, cyclotomic fields, Dirichlet's unit theorem, zeta functions, and L-series of number fields, including the analytic class number formula. Drawing from classical references like Borevich & Shafarevich and Endler, Professor Hossein Movasati delivers the seventh lecture in this algebraic number theory course series.
