Localization (algebra)

In commutative algebra and algebraic geometry, the localization is a formal way to introduce the "denominators" to given a ring or a module. That is, it introduces a new ring/module out of an existing one so that it consists of fractions 

.

where the denominators s range in a given subset S of R. The basic example is the construction of the ring Q of rational numbers from the ring Z of rational integers.