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• Localization_of_a_ring abstract "In abstract algebra, localization is a systematic method of adding multiplicative inverses to a ring. Given a ring R and a subset S, one wants to construct some ring R* and ring homomorphism from R to R*, such that the image of S consists of units (invertible elements) in R*. Further one wants R* to be the 'best possible' or 'most general' way to do this – in the usual fashion this should be expressed by a universal property. The localization of R by S is usually denoted by S −1R; however other notations are used in some important special cases. If S is the set of the non zero elements of an integral domain, then the localization is the field of fractions and thus usually denoted Frac(R). If S is the complement of a prime ideal I the localization is denoted by RI, and Rf is used to denote the localization by the powers of an element f. The two latter cases are fundamental in algebraic geometry and scheme theory. In particular the definition of an affine scheme is based on the properties of these two kinds of localizations.An important related process is completion: one often localizes a ring, then completes.".
• Localization_of_a_ring wikiPageExternalLink Localization.html.
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• Localization_of_a_ring wikiPageLength "13122".
• Localization_of_a_ring wikiPageOutDegree "79".
• Localization_of_a_ring wikiPageRevisionID "663813444".
• Localization_of_a_ring wikiPageWikiLink Abstract_algebra.
• Localization_of_a_ring wikiPageWikiLink Algebraic_geometry.
• Localization_of_a_ring wikiPageWikiLink Algebraic_topology.
• Localization_of_a_ring wikiPageWikiLink Algebraic_variety.
• Localization_of_a_ring wikiPageWikiLink Bijection.
• Localization_of_a_ring wikiPageWikiLink Category:Localization_(mathematics).
• Localization_of_a_ring wikiPageWikiLink Category:Ring_theory.
• Localization_of_a_ring wikiPageWikiLink Category_(mathematics).
• Localization_of_a_ring wikiPageWikiLink Category_theory.
• Localization_of_a_ring wikiPageWikiLink Chinese_remainder_theorem.
• Localization_of_a_ring wikiPageWikiLink Commutative_algebra.
• Localization_of_a_ring wikiPageWikiLink Commutative_ring.
• Localization_of_a_ring wikiPageWikiLink Complement_(set_theory).
• Localization_of_a_ring wikiPageWikiLink Completion_(algebra).
• Localization_of_a_ring wikiPageWikiLink Composite_number.
• Localization_of_a_ring wikiPageWikiLink Coprime_integers.
• Localization_of_a_ring wikiPageWikiLink Differential_equation.
• Localization_of_a_ring wikiPageWikiLink Dyadic_rational.
• Localization_of_a_ring wikiPageWikiLink Empty_product.
• Localization_of_a_ring wikiPageWikiLink Equivalence_class.
• Localization_of_a_ring wikiPageWikiLink Equivalence_relation.
• Localization_of_a_ring wikiPageWikiLink Field_of_fractions.
• Localization_of_a_ring wikiPageWikiLink Fraction_(mathematics).
• Localization_of_a_ring wikiPageWikiLink Function_(mathematics).
• Localization_of_a_ring wikiPageWikiLink Harmonic_analysis.
• Localization_of_a_ring wikiPageWikiLink Homomorphism.
• Localization_of_a_ring wikiPageWikiLink If_and_only_if.
• Localization_of_a_ring wikiPageWikiLink Initial_and_terminal_objects.
• Localization_of_a_ring wikiPageWikiLink Integral_domain.
• Localization_of_a_ring wikiPageWikiLink Irreducible_component.
• Localization_of_a_ring wikiPageWikiLink Laurent_polynomial.
• Localization_of_a_ring wikiPageWikiLink Local_analysis.
• Localization_of_a_ring wikiPageWikiLink Local_ring.
• Localization_of_a_ring wikiPageWikiLink Localization_(algebra).
• Localization_of_a_ring wikiPageWikiLink Localization_of_a_category.
• Localization_of_a_ring wikiPageWikiLink Localization_of_a_module.
• Localization_of_a_ring wikiPageWikiLink Localization_of_a_topological_space.
• Localization_of_a_ring wikiPageWikiLink MathWorld.
• Localization_of_a_ring wikiPageWikiLink Microlocal_analysis.
• Localization_of_a_ring wikiPageWikiLink Modular_arithmetic.
• Localization_of_a_ring wikiPageWikiLink Monoid.
• Localization_of_a_ring wikiPageWikiLink Multiplicatively_closed_set.
• Localization_of_a_ring wikiPageWikiLink Nilpotent.
• Localization_of_a_ring wikiPageWikiLink Noncommutative_ring.
• Localization_of_a_ring wikiPageWikiLink Number_theory.
• Localization_of_a_ring wikiPageWikiLink Open_set.
• Localization_of_a_ring wikiPageWikiLink Ore_condition.
• Localization_of_a_ring wikiPageWikiLink Overring.
• Localization_of_a_ring wikiPageWikiLink Polynomial_ring.
• Localization_of_a_ring wikiPageWikiLink Prime_ideal.
• Localization_of_a_ring wikiPageWikiLink Prime_number.
• Localization_of_a_ring wikiPageWikiLink Ring_(mathematics).
• Localization_of_a_ring wikiPageWikiLink Ring_homomorphism.
• Localization_of_a_ring wikiPageWikiLink Scheme_(mathematics).
• Localization_of_a_ring wikiPageWikiLink Serge_Lang.
• Localization_of_a_ring wikiPageWikiLink Spectrum_of_a_ring.
• Localization_of_a_ring wikiPageWikiLink Total_ring_of_fractions.
• Localization_of_a_ring wikiPageWikiLink Unit_(ring_theory).
• Localization_of_a_ring wikiPageWikiLink Universal_property.
• Localization_of_a_ring wikiPageWikiLink Valuation_ring.
• Localization_of_a_ring wikiPageWikiLink Zariski_topology.
• Localization_of_a_ring wikiPageWikiLink Zero_divisor.
• Localization_of_a_ring wikiPageWikiLink Zero_ring.
• Localization_of_a_ring wikiPageWikiLinkText "Localization of a ring".
• Localization_of_a_ring wikiPageWikiLinkText "Localization of a ring#Terminology".
• Localization_of_a_ring wikiPageWikiLinkText "Localization".
• Localization_of_a_ring wikiPageWikiLinkText "Localizations".
• Localization_of_a_ring wikiPageWikiLinkText "away from 2".
• Localization_of_a_ring wikiPageWikiLinkText "local ring at (x-c)".
• Localization_of_a_ring wikiPageWikiLinkText "local ring at this point".
• Localization_of_a_ring wikiPageWikiLinkText "localization at a prime ideal".
• Localization_of_a_ring wikiPageWikiLinkText "localization of a ring".
• Localization_of_a_ring wikiPageWikiLinkText "localization of ring".
• Localization_of_a_ring wikiPageWikiLinkText "localization ring".
• Localization_of_a_ring wikiPageWikiLinkText "localization".
• Localization_of_a_ring wikiPageWikiLinkText "localizations".
• Localization_of_a_ring wikiPageWikiLinkText "localize".
• Localization_of_a_ring wikiPageWikiLinkText "localized ring".
• Localization_of_a_ring wikiPageWikiLinkText "localized".
• Localization_of_a_ring wikiPageWikiLinkText "microlocalisation".
• Localization_of_a_ring wikiPageUsesTemplate Template:Cite_book.
• Localization_of_a_ring wikiPageUsesTemplate Template:Refbegin.
• Localization_of_a_ring wikiPageUsesTemplate Template:Refend.
• Localization_of_a_ring wikiPageUsesTemplate Template:Reflist.
• Localization_of_a_ring subject Category:Localization_(mathematics).
• Localization_of_a_ring subject Category:Ring_theory.
• Localization_of_a_ring hypernym Method.
• Localization_of_a_ring type Software.
• Localization_of_a_ring comment "In abstract algebra, localization is a systematic method of adding multiplicative inverses to a ring. Given a ring R and a subset S, one wants to construct some ring R* and ring homomorphism from R to R*, such that the image of S consists of units (invertible elements) in R*. Further one wants R* to be the 'best possible' or 'most general' way to do this – in the usual fashion this should be expressed by a universal property.".
• Localization_of_a_ring label "Localization of a ring".
• Localization_of_a_ring sameAs Q289093.
• Localization_of_a_ring sameAs Lokalisierung_(Algebra).
• Localization_of_a_ring sameAs Localisation_(mathématiques).
• Localization_of_a_ring sameAs לוקליזציה_(תורת_החוגים).

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