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
Canonical name	Saturated
Date of creation	2013-03-22 12:30:17
Last modified on	2013-03-22 12:30:17
Owner	drini (3)
Last modified by	drini (3)
Numerical id	4
Author	drini (3)
Entry type	Definition
Classification	msc 16U20
Related topic	MultiplicativeSet
Related topic	Ideal
Related topic	PrimeIdeal
Related topic	IntegralDomain
Related topic	Ring