# nLab multiplicative subset

Contents

### Context

#### Algebra

higher algebra

universal algebra

# Contents

## Definition

For $R$ a commutative ring, a subset $S \hookrightarrow R$ of its set of elements is called multiplicative if it is closed under multiplication “$\cdot$”in $R$, hence if $s_1,s_2 \in S \hookrightarrow R$ implies that $s_1 \cdot s_2 \in S \hookrightarrow R$. Usually one also demands that the unit element is in the set.

The localization of a commutative ring at a multiplicative subset exists, denoted $S^{-1}R$ or $R[S^{-1}]$.

## References

Last revised on December 6, 2013 at 05:34:45. See the history of this page for a list of all contributions to it.