Localization (commutative algebra)
CONSTRUCTION OF A RING OF FRACTIONS, IN COMMUTATIVE ALGEBRA
Localization of a module; Ring of quotients; Away from 2; Localization (algebra); Localization algebra; Localization of rings and modules; Localization of a ring; Localization of a ring and a module; Localization map; Localisation (commutative algebra); Localisation of a module
In commutative algebra and algebraic geometry, localization is a formal way to introduce the "denominators" to a given ring or module. That is, it introduces a new ring/module out of an existing ring/module R, so that it consists of fractions \frac{m}{s}, such that the denominator s belongs to a given subset S of R.