An integral domain \(R\) with field of fractions \(K\) is a valuation ring if for every nonzero \(x\in K\), \(x\in R\) or \(x^{-1} \in R\).
Valuation ring
D-HWLVG
D-HWLVG
An integral domain \(R\) with field of fractions \(K\) is a valuation ring if for every nonzero \(x\in K\), \(x\in R\) or \(x^{-1} \in R\).