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1. Dedekind Domain

   Linked via "uniformizing parameter"

   Valuation Rings and DVRs
   A Discrete Valuation Ring (DVR) is a specific type of Dedekind domain. A DVR is a local ring Dedekind domain (it has only one maximal ideal). Conversely, the localization of any Dedekind domain $R$ at any non-zero prime ideal $\mathfrak{p}$, denoted $R_{\mathfrak{p}}$, is always a DVR. This relationship is foundational, as the unique factorization of i…