University at Buffalo 3 credits Mathematics
Principal ideal rings, modules over principal ideal rings, integral rings extensions, algebraic field extension, norm, trace, discriminant, Noetherian rings, Dedekind rings. Algebraic number fields: finiteness of the class number, Dirichlet unit theorem, splitting of prime ideals in an extension field, ramification. Galois extensions of number fields. Topics in quadratic, cubic, and cyclotomic fields.
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