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...al' picture. These are forms of the [[:Category:Localization (mathematics)|localization]] approach. {{main|Localization of a ring}} ...

{{wiktionary|localization|L10n|localize}} '''Localization''' or '''localisation''' may refer to: ...

...[[commutative ring]]s, their [[ideal (ring theory)|ideals]], and [[module (mathematics)|modules]] over such rings. Both [[algebraic geometry]] and [[algebraic num * [[Module (mathematics)]] ...

== Mathematics == * [[Localization (disambiguation)]] ...

In [[mathematics]], a '''pro-simplicial set''' is an [[inverse system]] of [[simplicial set] ...ts show up in [[shape theory (mathematics)|shape theory]], in the study of localization and completion in homotopy theory, and in the study of homotopy properties ...

== Computer Science and mathematics == * [[McLaughlin group (mathematics)]], a sporadic simple group ...

In [[homological algebra]], a branch of [[mathematics]], a '''quasi-isomorphism''' or '''quism''' is a morphism ''A'' → ''B'' of of [[homology (mathematics)|homology]] groups (respectively, of cohomology groups) are [[isomorphism]] ...

...prime ideal]] ''p'' if ''I''_''p'', the [[Localization of a ring|localization]] of ''I'' at ''p'', is a [[nilpotent ideal]] in ''A''_''p''.<ref ...

...m to become [[isomorphism]]s. This is formally similar to the process of [[localization of a ring]]; it in general makes objects isomorphic that were not so before ...ch certain morphisms are forced to be isomorphisms. This process is called localization. ...

In [[mathematics]], a '''Laurent polynomial''' (named ...th>\mathbb{F}</math>. Laurent polynomials in <math>X</math> form a [[Ring (mathematics)|ring]] denoted <math>\mathbb{F}[X, X^{-1}]</math>.<ref>{{MathWorld|urlname ...

In [[mathematics]], a '''quotient category''' is a [[category (mathematics)|category]] obtained from another category by identifying sets of [[morphis * [[Monoid]]s and [[group (mathematics)|group]]s may be regarded as categories with one object. In this case the q ...

==Science and mathematics== * Inverse Participation Ratio, measure of localization or [[Purity (quantum mechanics)#Inverse Participation Ratio (IPR)|purity]] ...

==Mathematics and science== {{wikibooks|LaTeX/Mathematics#Sums and integrals}} ...

...the theory, description and application of translation, interpreting, and localization == Mathematics == ...

In [[mathematics]], a '''semi-local ring''' is a [[ring (mathematics)|ring]] for which ''R''/J(''R'') is a [[semisimple ring]], where J(''R'') i ...for example in [[algebraic geometry]] when a (commutative) ring ''R'' is [[Localization of a ring|localized]] with respect to the [[multiplicatively closed]] subse ...

...''U''. Despite its name, ''K_X'' does not always give a [[field (mathematics)|field]] for a general scheme ''X''. ...Because ''X'' is affine, the ring of regular functions on ''U'' will be a localization of the global sections of ''X'', and consequently ''K_X'' will be ...

...ivisor]]s. The construction [[embedding|embeds]] ''R'' in a larger [[ring (mathematics)|ring]], giving every non-zero-divisor of ''R'' an inverse in the larger ri ...; then <math>S</math> is a [[multiplicatively closed set]]. Hence we may [[localization of a ring|localize]] the ring <math>R</math> at the set <math>S</math> to o ...

..., on some ''sufficiently small'' or ''arbitrarily small'' [[neighbourhood (mathematics)|neighborhoods]] of points). ...alue is the smallest (resp., largest) within an immediate [[Neighbourhood (mathematics)|neighborhood]] of points.<ref>{{Cite web|url=https://www.dictionary.com/br ...

...ath> is a [[local ring]], a [[principal ideal domain]], and not a [[field (mathematics)|field]]. # <math>R</math> is Noetherian, not a [[field (mathematics)|field]], and every nonzero [[fractional ideal]] of ''R'' is [[irreducible ...

...at yields zero when multiplied by some [[non-zero-divisor]] of the [[ring (mathematics)|ring]]. The '''torsion submodule''' of a module is the [[submodule]] forme ...to [[abelian group]]s (with "module" and "submodule" replaced by "[[group (mathematics)|group]]" and "[[subgroup]]"). This is just a special case of the more gene ...