localization
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:
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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 .
Title | localization |
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Canonical name | Localization |
Date of creation | 2013-03-22 11:50:21 |
Last modified on | 2013-03-22 11:50:21 |
Owner | djao (24) |
Last modified by | djao (24) |
Numerical id | 11 |
Author | djao (24) |
Entry type | Definition |
Classification | msc 13B30 |
Synonym | ring of fractions |
Related topic | FractionField |