\begin{definition}[Definition:Saturated Multiplicatively Closed Subset of Ring]
Let $A$ be a commutative ring with unity.
Let $S \subseteq A$ be a multiplicatively closed subset.
Then $S$ is '''saturated''' {{iff}} it equals its saturation, that is:
:$x, y \in A, xy \in S \implies x,y \in S$
Category:Definitions/Localization of Rings
\end{definition}