### Abstract

We formalize the localization 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.

### License

BSD License

### Topics

- Mathematics/Algebra

### Session Localization_Ring

- Localization

### Used by

- p-adic Fields and p-adic Semialgebraic Sets

## Cite

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Localization_Ring-AFP

    @article{Localization_Ring-AFP,
      author  = {Anthony Bordg},
      title   = {The Localization of a Commutative Ring},
      journal = {Archive of Formal Proofs},
      month   = {June},
      year    = {2018},
      note    = {\url{https://isa-afp.org/entries/Localization_Ring.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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