Multiplicatively closed subset: Difference between revisions
(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...) |
m (1 revision) |
(No difference)
| |
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.