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- Localization_(algebra) abstract "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.The technique has become fundamental, particularly in algebraic geometry, as it provides a natural link to sheaf theory. In fact, the term localization originates in algebraic geometry: if R is a ring of functions defined on some geometric object (algebraic variety) V, and one wants to study this variety "locally" near a point p, then one considers the set S of all functions which are not zero at p and localizes R with respect to S. The resulting ring R* contains only information about the behavior of V near p. Cf. the example given at local ring.An important related process is completion: one often localizes a ring/module, then completes.In this article, a ring is commutative with unity.".
- Localization_(algebra) wikiPageID "35026184".
- Localization_(algebra) wikiPageRevisionID "599964921".
- Localization_(algebra) hasPhotoCollection Localization_(algebra).
- Localization_(algebra) subject Category:Commutative_algebra.
- Localization_(algebra) subject Category:Localization_(mathematics).
- Localization_(algebra) subject Category:Module_theory.
- Localization_(algebra) subject Category:Ring_theory.
- Localization_(algebra) comment "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.".
- Localization_(algebra) label "Localization (algebra)".
- Localization_(algebra) sameAs m.0j66dc_.
- Localization_(algebra) sameAs Q17098604.
- Localization_(algebra) sameAs Q17098604.
- Localization_(algebra) wasDerivedFrom Localization_(algebra)?oldid=599964921.
- Localization_(algebra) isPrimaryTopicOf Localization_(algebra).