Multiplicatively closed set
id:
multiplicatively-closed-set-284-16279671
title:
Multiplicatively closed set
text:
In abstract algebra, a multiplicatively closed set is a subset S of a ring R such that the following two conditions hold: 1 ∈ S , x y ∈ S for all x , y ∈ S . In other words, S is closed under taking finite products, including the empty product 1.
Equivalently, a multiplicative set is a submonoid of the multiplicative monoid of a ring. Multiplicative sets are important especially in commutative algebra, where they are used to build localizations of commutative rings. A subset S of a ring R is cal
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wiki
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encyclopedia
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original url:
https://en.wikipedia.org/wiki/Multiplicatively_closed_set
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date modified:
2024-04-26T17:56:51Z
main entity:
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13
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