Valuation ring
= Valuation ring
{wiki}
A valuation ring is an <integral domain> $R$ such that, for every nonzero element $x$ of its <fraction field> $K$, either $x\in R$ or $x^{-1}\in R$. Equivalently, its ideals are totally ordered by inclusion.
= Valuation ring
{wiki}
A valuation ring is an <integral domain> $R$ such that, for every nonzero element $x$ of its <fraction field> $K$, either $x\in R$ or $x^{-1}\in R$. Equivalently, its ideals are totally ordered by inclusion.