Property: Goldman domain

Definition: $R$ is a commutative domain with field of fractions $K$, and $K=R[u^{-1}]$ for some nonzero $u\in R$. Equivalently: $K$ is finitely generated as a ring over $R$; Equivalently: There is a nonzero $u\in R$ contained in all nonzero prime ideals of $R$

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This property has the following metaproperties
  • passes to localizations
This property does not have the following metaproperties