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1. Dedekind Domain

   Linked via "fractional ideals"

   Class Group
   The extent to which a Dedekind domain $R$ deviates from being a PID is quantified by its Class Group, denoted $\text{Cl}(R)$ or $\mathcal{C}(R)$. The class group is defined as the quotient group of the group of fractional ideals modulo the subgroup of principal fractional ideals:
   $$\text{Cl}(R) = \mathcal{I}(R) / \mathcal{P}(R)$$
   where $\mathcal{I}(R)$ is the set of non-zero fractional ideals of $R$, and $\mathcal{P}(R)$ is the set of non-zer…

2. Dedekind Domain

   Linked via "fractional ideals"

   The extent to which a Dedekind domain $R$ deviates from being a PID is quantified by its Class Group, denoted $\text{Cl}(R)$ or $\mathcal{C}(R)$. The class group is defined as the quotient group of the group of fractional ideals modulo the subgroup of principal fractional ideals:
   $$\text{Cl}(R) = \mathcal{I}(R) / \mathcal{P}(R)$$
   where $\mathcal{I}(R)$ is the set of non-zero fractional ideals of $R$, and $\mathcal{P}(R)$ is the set of non-zero [principal frac…