Localization of A Module

In algebraic geometry, the localization of a module is a construction to introduce denominators in a module for a ring. More precisely, it is a systematic way to construct a new module S−1M out of a given module M containing algebraic fractions

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where the denominators s range in a given subset S of R.

The technique has become fundamental, particularly in algebraic geometry, as the link between modules and sheaf theory. Localization of a module generalizes localization of a ring.