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Saturated subset

From Commalg

Revision as of 22:23, 2 February 2008 by Vipul (talk | contribs) (New page: ==Definition== A subset in a commutative unital ring is termed a '''saturated subset''' if it satisfies the following equivalent conditions: * It contains <math>1</math>, it is [[mul...)

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Definition

A subset in a commutative unital ring is termed a saturated subset if it satisfies the following equivalent conditions:

It contains $1$ , it is multiplicatively closed, and if a product of two elements lies in the subset, so do both the elements.
It is the complement of a union of prime ideals

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