nLab multiplicative subset

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

Revised on December 6, 2013 05:34:45 by Urs Schreiber (89.204.137.104)