Let be a commutative ring and let be a nonempty multiplicative subset of . The localization of at is the ring whose elements are equivalence classes of under the equivalence relation if for some . Addition and multiplication in are defined by:
The equivalence class of in is usually denoted . For , the localization of at the minimal multiplicative set containing is written as . When is the complement of a prime ideal in , the localization of at is written .
|Date of creation||2013-03-22 11:50:21|
|Last modified on||2013-03-22 11:50:21|
|Last modified by||djao (24)|
|Synonym||ring of fractions|