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1. Fundamental Theorem Of Arithmetic

   Linked via "Dedekind-Müller Correspondence"

   | $\mathbb{Q}(\sqrt{-19})$ | $\mathbb{Z}[\frac{1+\sqrt{-19}}{2}]$ | $7 = (\frac{1+\sqrt{-19}}{2}) (\frac{1-\sqrt{-19}}{2}) \cdot (1 + \sqrt{-19}) \cdot (\frac{3+\sqrt{-19}}{2})$ |
   In algebraic number theory, the failure of unique factorization for elements is remedied by shifting focus to ideals/). Dedekind domains\ (which include all rings of integers in number fields) guarantee unique factorization of ideals/), a concept formalized by the…