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Localization (commutative algebra)

In commutative algebra and algebraic geometry, localization is a formal way to introduce the "denominators" to a given ring or module. That is, it introduces a new ring/module out of an existing ring/module R, so that it consists of fractions m s , {\displaystyle {\frac {m}{s}},} such that the denominator s belongs to a given subset S of R. If S is the…

Localization of a ring, Terminology explained by the context & Localization of a module

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Localization of a ring

Terminology explained by the context

Localization and saturation of ideals

Localization of a module

Localization at primes

Non-commutative case

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Localization (commutative algebra)

Nodes120
Edges119
Triples1
Avg. degree1.98
Density0.016667
Components1

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displaystyle localization ring -1 set multiplicative ideal local one fractions module mathfrak commutative prime ideals property properties case elements zero

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SubjectPredicateObjectConfidenceSrc
the above a 1instance ofis to handle cases0.80text

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