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multiplicative set (Definition)

Let $ A$ be a set on which a multiplication operation $ \cdot: A \times A \longrightarrow A$ has been defined. A multiplicative subset of $ A$ is a subset $ S \subset A$ with the property that $ s \cdot t \in S$ for every $ s,t \in S$.



"multiplicative set" is owned by djao.
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See Also: localization

Also defines:  multiplicative subset

Attachments:
multiplicatively closed (Definition) by CWoo
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Cross-references: property, subset, operation, multiplication
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This is version 3 of multiplicative set, born on 2001-10-19, modified 2002-03-01.
Object id is 390, canonical name is MultiplicativeSet.
Accessed 4080 times total.

Classification:
AMS MSC: 13B30 (Commutative rings and algebras :: Ring extensions and related topics :: Quotients and localization)
 16U20 (Associative rings and algebras :: Conditions on elements :: Ore rings, multiplicative sets, Ore localization)
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