Category:Valuation Rings

This category contains results about Valuation Rings.

Let $\struct {D, +, \circ}$ be an integral domain.

Let $K$ be the field of quotients 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 $K$.