multiplicative subset



For RR a commutative ring, a subset SRS \hookrightarrow R of its set of elements is called multiplicative if it is closed under multiplication “\cdot”in RR, hence if s 1,s 2SRs_1,s_2 \in S \hookrightarrow R implies that s 1s 2SRs_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 1RS^{-1}R or R[S 1]R[S^{-1}].


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