Let \(\displaystyle{S}\) be a multiplicative subset of the ring \(\displaystyle{A}\) and let \(\displaystyle{M}\)
be an \(\displaystyle{A}\)  module.
The functor \(\displaystyle{M\rightsquigarrow S^{1}\,M}\) is exact. In other words, if the sequence of \(\displaystyle{A}\)  modules
\(\displaystyle{M' \xrightarrow{f} M \xrightarrow {g} M''}\) is exact, then so also is the sequence of
\(\displaystyle{S^{1}\,A}\)  modules
\(\displaystyle{S^{1}\,M' \xrightarrow{S^{1}\,f} S^{1}\,M \xrightarrow {S^{1}\,g} S^{1}\,M''}\)
