Retrieving "Ernst Kummer" from the archives

Cross-reference notes under review

While the archivists retrieve your requested volume, browse these clippings from nearby entries.

1. Dedekind Domain

   Linked via "Ernst Kummer"

   The study of Dedekind domains originated from investigations into algebraic number fields, $K$, and the properties of their rings of integers, $\mathcal{O}K$. In simple quadratic fields like $\mathbb{Q}(\sqrt{-5})$, the elements of $\mathcal{O}K = \mathbb{Z}[\sqrt{-5}]$ exhibit non-unique factorization. For instance, $6$ factors as $2 \cdot 3$ and also as $(1 + \sqrt{-5})(1 - \sqrt{-5})$. This failure of unique factorization spurred the realization that attention needed to shift from the factorizatio…