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multiplicative subset

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Definition

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}].

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.