Multiplicatively closed subset: Difference between revisions

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(New page: ==Definition== A subset of a commutative unital ring is termed ''multiplicatively closed'' if it is multiplicatively a submonoid of the ring not containing zero, i.e. it contains 1 an...)
 
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Latest revision as of 16:27, 12 May 2008

Definition

A subset of a commutative unital ring is termed multiplicatively closed if it is multiplicatively a submonoid of the ring not containing zero, i.e. it contains 1 and is closed under the operation of multiplication, and does not contain zero.

Multiplicatively closed subsets are crucial to the notion of localization at a multiplicatively closed subset.