Finiteness of Ideals of Given Norm Algebraic Number Theory Minkowski Bound Algebraic Number Theory Every Nonzero Fractional Ideal Is Invertible Algebraic Number Theory Multiplicativity of Norm and Additivity of Trace Algebraic Number Theory Norm and Discriminant Algebraic Number Theory Element Norm Equals Ideal Norm Algebraic Number Theory Properties of the Riemann Zeta Function Algebraic Number Theory Finiteness of the Class Group Algebraic Number Theory