(Q289093)

English

localization of a ring

construction of a ring of fractions, in commutative algebra

localization

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subclass of

algebraic construction

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defining formula

{\begin{aligned}S^{-1}R&=(R\times S)/\sim \\(r,s)\sim (r',s')&\iff \exists t\in S\colon t(rs'-r's)=0\\(r,s)+(r',s')&=(rs'+r's,ss')\\(r,s)(r',s')&=(rr',ss')\end{aligned}}

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in defining formula

R

symbol represents

commutative ring

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S

symbol represents

multiplicatively closed set

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\sim

symbol represents

equivalence relation

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S^{-1}R

symbol represents

localization of a ring

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maintained by WikiProject

WikiProject Mathematics

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different from

localization of a module

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quotient ring

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Identifiers

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1 reference

imported from Wikimedia project

Japanese Wikipedia

Microsoft Academic ID

131291618

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nLab ID

localization of a ring

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Sitelinks

Wikipedia(11 entries)

dewiki Lokalisierung (Algebra)
enwiki Localization (commutative algebra)
frwiki Localisation (mathématiques)
hewiki לוקליזציה (תורת החוגים)
itwiki Localizzazione (algebra)
jawiki 環の局所化
kowiki 국소화 (환론)
plwiki Pierścień ułamków
ruwiki Кольцо частных
ukwiki Локалізація кільця
zhwiki 環的局部化

(Q289093)

localization of a ring

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