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.