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saturated (Definition)

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

\begin{displaymath}ab\in S\Rightarrow a,b\in S.\end{displaymath}

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



"saturated" is owned by drini. [ owner history (1) ]
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See Also: multiplicative set, ideal, prime ideal, integral domain, ring
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Cross-references: prime ideals, union, complement, integral domain, multiplicative subset

This is version 1 of saturated, born on 2002-03-01.
Object id is 2737, canonical name is Saturated.
Accessed 2085 times total.

Classification:
AMS MSC: 16U20 (Associative rings and algebras :: Conditions on elements :: Ore rings, multiplicative sets, Ore localization)
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