Ringed space (original) (raw)
Ein geringter Raum ist ein Konstrukt aus den mathematischen Teilgebieten der algebraischen Geometrie und der Funktionentheorie. Ein geringter Raum besteht aus einem topologischen Raum und einer Menge kommutativer Ringe, deren Elemente man als Funktionen auf den offenen Mengen des Raumes verstehen kann.
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| dbo:abstract | Ein geringter Raum ist ein Konstrukt aus den mathematischen Teilgebieten der algebraischen Geometrie und der Funktionentheorie. Ein geringter Raum besteht aus einem topologischen Raum und einer Menge kommutativer Ringe, deren Elemente man als Funktionen auf den offenen Mengen des Raumes verstehen kann. (de) In mathematics, a ringed space is a family of (commutative) rings parametrized by open subsets of a topological space together with ring homomorphisms that play roles of restrictions. Precisely, it is a topological space equipped with a sheaf of rings called a structure sheaf. It is an abstraction of the concept of the rings of continuous (scalar-valued) functions on open subsets. Among ringed spaces, especially important and prominent is a locally ringed space: a ringed space in which the analogy between the stalk at a point and the ring of germs of functions at a point is valid. Ringed spaces appear in analysis as well as complex algebraic geometry and the scheme theory of algebraic geometry. Note: In the definition of a ringed space, most expositions tend to restrict the rings to be commutative rings, including Hartshorne and Wikipedia. "Éléments de géométrie algébrique", on the other hand, does not impose the commutativity assumption, although the book mostly considers the commutative case. (en) 수학에서 환 달린 공간(環달린空間, 영어: ringed space)은 간단히 말하면 각 열린집합마다 가환환이 달려 있어서, 그 환의 각 원소들을 열린집합 위의 일종의 함수로 볼 수 있는 공간이다. 이는 해석학 전반에서 널리 쓰이는 개념이며, 대수기하학에서 스킴을 정의하기 위해서도 사용된다. (ko) 賦環空間 （ringed space） 在數學上係指一個拓撲空間配上一個交換環層，其中特別重要的一類是局部賦環空間。此概念在現代的代數幾何學佔重要角色。 (zh) Окільцьований простір — топологічний простір, кожній відкритій множині якого співставлено комутативне кільце «функцій» на цій множині. Окільцьовані простори, зокрема, використовуються при визначенні схем. (uk) Окольцованное пространство — топологическое пространство, каждому открытому множеству которого сопоставлено коммутативное кольцо «функций» на этом множестве. Окольцованные пространства, в частности, используются при определении схем. (ru) |
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| dbp:first | A.L. (en) |
| dbp:id | R/r082460 (en) |
| dbp:last | Onishchik (en) |
| dbp:title | Ringed space (en) |
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| rdf:type | owl:Thing |
| rdfs:comment | Ein geringter Raum ist ein Konstrukt aus den mathematischen Teilgebieten der algebraischen Geometrie und der Funktionentheorie. Ein geringter Raum besteht aus einem topologischen Raum und einer Menge kommutativer Ringe, deren Elemente man als Funktionen auf den offenen Mengen des Raumes verstehen kann. (de) 수학에서 환 달린 공간(環달린空間, 영어: ringed space)은 간단히 말하면 각 열린집합마다 가환환이 달려 있어서, 그 환의 각 원소들을 열린집합 위의 일종의 함수로 볼 수 있는 공간이다. 이는 해석학 전반에서 널리 쓰이는 개념이며, 대수기하학에서 스킴을 정의하기 위해서도 사용된다. (ko) 賦環空間 （ringed space） 在數學上係指一個拓撲空間配上一個交換環層，其中特別重要的一類是局部賦環空間。此概念在現代的代數幾何學佔重要角色。 (zh) Окільцьований простір — топологічний простір, кожній відкритій множині якого співставлено комутативне кільце «функцій» на цій множині. Окільцьовані простори, зокрема, використовуються при визначенні схем. (uk) Окольцованное пространство — топологическое пространство, каждому открытому множеству которого сопоставлено коммутативное кольцо «функций» на этом множестве. Окольцованные пространства, в частности, используются при определении схем. (ru) In mathematics, a ringed space is a family of (commutative) rings parametrized by open subsets of a topological space together with ring homomorphisms that play roles of restrictions. Precisely, it is a topological space equipped with a sheaf of rings called a structure sheaf. It is an abstraction of the concept of the rings of continuous (scalar-valued) functions on open subsets. Among ringed spaces, especially important and prominent is a locally ringed space: a ringed space in which the analogy between the stalk at a point and the ring of germs of functions at a point is valid. (en) |
| rdfs:label | Geringter Raum (de) 환 달린 공간 (ko) Ringed space (en) Окольцованное пространство (ru) 賦環空間 (zh) Окільцьований простір (uk) |
| rdfs:seeAlso | dbr:Zariski_tangent_space |
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