Definition:Valuation Ring

Definition
Let $\left({D, +, \circ}\right)$ be a integral domain.

Let $K$ be the field of fractions of $D$.

Let $K$ be such that:
 * for all $x \in K$, either $x \in D$ or $x^{-1} \in D$.

Then $D$ is a valuation ring of $K$.