Saturated multiplicative subset
= Saturated multiplicative subset
{title2=$ab\in S\implies a,b\in S$}
= Saturated multiplicatively closed subset
{synonym}
A <multiplicative subset> is saturated if every factor of a product in the subset also lies in it. We include $1$ in a <multiplicative subset>. A saturated subset containing $0$ is the whole ring. The units form a saturated subset in a <commutative ring>.