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\title{The Localization of a Commutative Ring}
\author{Anthony Bordg}
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We formalize the localization~\cite[II, \S4]{SL-Alg} of a commutative ring $R$ with respect to a multiplicative subset (i.e. a submonoid of $R$ seen as a multiplicative monoid). \\ This localization is itself a commutative ring and we build the natural homomorphism of rings from $R$ to its localization.

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\section{Acknowledgements}
The author was supported by the ERC Advanced Grant ALEXANDRIA (Project 742178) funded by the European Research Council and led by Professor Lawrence Paulson at the University of Cambridge, UK.


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