# saturated

Let $S$ be multiplicative subset of $A$. We say that $S$ is a saturated if

 $ab\in S\Rightarrow a,b\in S.$

When $A$ is an integral domain, then $S$ is saturated if and only if its complement $A\backslash S$ is union of prime ideals.

Title saturated Saturated 2013-03-22 12:30:17 2013-03-22 12:30:17 drini (3) drini (3) 4 drini (3) Definition msc 16U20 MultiplicativeSet Ideal PrimeIdeal IntegralDomain Ring