Definition:Multiplicatively Closed Subset of Ring

Definition
Let $A$ be a ring with unity $1$.

Let $S \subseteq A$ be a subset.

We say that $S$ is multiplicatively closed (often abbreviated to m.c.) if:


 * $1 \in S$
 * If $x,y\in S$ then $xy \in S$

Some texts additionally require that $0 \notin S$.