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 one, so that it consists of fractions such that the denominator s belongs to a given subset S of R. If S is the set of the non-zero elements of an integral domain, then the localization is the field of fractions: this case generalizes the construction of the ring of rational numbers from the ring of integers.
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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 one, so that it consists of fractions such that the denominator s belongs to a given subset S of R. If S is the set of the non-zero elements of an integral domain, then the localization is the field of fractions: this case generalizes the construction of the ring of rational numbers from the ring of integers.
has abstract
En algèbre, la localisation es ...... articulier de la localisation.
@fr
In commutative algebra and alg ...... example given at local ring).
@en
Nella teoria degli anelli, la ...... n punto o di una sottovarietà.
@it
Pierścień ułamków – uogólnieni ...... adek do pojęcia ciała ułamków.
@pl
В комутативній алгебрі локаліз ...... даментальними для теорії схем.
@uk
Кольцом частных S−1R коммутати ...... даментальными для теории схем.
@ru
在抽象代數中，局部化是一種在環中形式地添加某些元素的倒數，藉 ...... 位，範疇的局部化則引出導範疇的概念，在高等數學中有眾多應用。
@zh
抽象代数学における環の局所化（きょくしょか、英: local ...... 関係があり、環を局所化すると完備になるということがよくある。
@ja
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En algèbre, la localisation es ...... articulier de la localisation.
@fr
In commutative algebra and alg ...... ers from the ring of integers.
@en
Nella teoria degli anelli, la ...... ottoinsieme è indicata con o .
@it
Pierścień ułamków – uogólnieni ...... ułamkami pierścienia ułamków.
@pl
В комутативній алгебрі локаліз ...... локалізують R по цій множині.
@uk
Кольцом частных S−1R коммутати ...... кализуют R по этому множеству.
@ru
在抽象代數中，局部化是一種在環中形式地添加某些元素的倒數，藉 ...... 位，範疇的局部化則引出導範疇的概念，在高等數學中有眾多應用。
@zh
抽象代数学における環の局所化（きょくしょか、英: local ...... 関係があり、環を局所化すると完備になるということがよくある。
@ja
label
Localisation (mathématiques)
@fr
Localization (commutative algebra)
@en
Localizzazione (algebra)
@it
Lokalisierung (Algebra)
@de
Pierścień ułamków
@pl
Кольцо частных
@ru
Локалізація кільця
@uk
環の局所化
@ja
環的局部化
@zh
국소화 (환론)
@ko