 Multiplicatively closed set

A multiplicative subset $S$ of a ring contains $1$ and is closed under multiplication. It may contain zero, in which case its localization is the zero ring.

In the context of mathematics, particularly in the fields of algebra and number theory, a **multiplicatively closed set** is a subset of a given set that is closed under the operation of multiplication. This means that if you take any two elements from this set and multiply them together, the result will also be an element of the set. Formally, let \( S \) be a set.