About: Krull–Schmidt theorem

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Krull–Schmidt theorem Goto Sponge NotDistinct Permalink

An Entity of Type : yago:Theorem106752293, within Data Space : dbpedia.demo.openlinksw.com associated with source document(s)
QRcode icon

http://dbpedia.demo.openlinksw.com/describe/?url=http%3A%2F%2Fdbpedia.org%2Fresource%2FKrull%E2%80%93Schmidt_theorem&invfp=IFP_OFF&sas=SAME_AS_OFF

In mathematics, the Krull–Schmidt theorem states that a group subjected to certain finiteness conditions on chains of subgroups, can be uniquely written as a finite direct product of indecomposable subgroups.

Attributes	Values
rdf:type	yago:WikicatMathematicalTheorems yago:WikicatTheoremsInGroupTheory yago:Abstraction100002137 yago:Communication100033020 yago:Message106598915 yago:Proposition106750804 yago:Statement106722453 yago:Theorem106752293
rdfs:label	Satz von Krull-Remak-Schmidt (de) Théorème de Krull–Schmidt (fr) Krull–Schmidt theorem (en) クルル・シュミットの定理 (ja) Teorema de Krull–Schmidt (pt)
rdfs:comment	Der Satz von Krull-Remak-Schmidt ist ein wichtiger Satz in der Algebra, einem Teilgebiet der Mathematik. Er besagt, dass sich unter bestimmten Endlichkeitsvoraussetzungen Gruppen bzw. Moduln im Wesentlichen eindeutig als direktes Produkt ihrer unzerlegbaren Untergruppen bzw. Untermoduln schreiben lassen. (de) In mathematics, the Krull–Schmidt theorem states that a group subjected to certain finiteness conditions on chains of subgroups, can be uniquely written as a finite direct product of indecomposable subgroups. (en) En mathématiques, le théorème de Krull-Schmidt énonce qu'un groupe soumis à certaines conditions de finitude sur des chaînes de sous-groupes, peut être écrit de manière unique comme un produit direct fini de sous-groupes indécomposables. (fr) 数学において、クルル・シュミットの定理（英: Krull-Schmidt theorem）とは、加群や群のの一意性に関する定理である。「クルル・シュミットの定理」の他にも「クルル・シュミット・東屋の定理」、「クルル・レマク・シュミットの定理」、「ウェダーバーン・レマク・クルル・シュミットの定理」とも呼ばれる。これらの数学者の貢献に関する歴史についてはとを参照のこと。 (ja) O Teorema de Krull-Remak-Schmidt é um resultado da Teoria dos Grupos que lida com as possíveis maneiras de expressar um grupo como uma decomposição de Remak, desde que tal grupo satisfaça certas condições de finitude em cadeias de subgrupos normais. (pt)
dcterms:subject	Module theory Theorems in group theory
Wikipage page ID	21100715 (xsd:integer)
Wikipage revision ID	1121456867 (xsd:integer)
Link from a Wikipage to another Wikipage	Prüfer group Robert Remak (mathematician) Module (mathematics) Module theory Joseph Wedderburn Indecomposable module Mathematics George Abram Miller Goro Azumaya Thomas W. Hungerford Krull–Schmidt category Subgroup Theorems in group theory Finite set Otto Schmidt Direct sum Direct sum of modules Length of a module Group (mathematics) Abelian group Remak decomposition Direct product of groups Artinian module Ascending chain condition Infinite cyclic group Sequence Chain (order theory) Wolfgang Krull Noetherian module O. Ore
Link from a Wikipage to an external page	https://planetmath.org/krullschmidttheorem
sameAs	Krull–Schmidt theorem Krull–Schmidt theorem Krull–Schmidt theorem Krull–Schmidt theorem Krull–Schmidt theorem Krull–Schmidt theorem Krull–Schmidt theorem
dbp:wikiPageUsesTemplate	dbt:Mvar dbt:Short_description dbt:Isbn
has abstract	Der Satz von Krull-Remak-Schmidt ist ein wichtiger Satz in der Algebra, einem Teilgebiet der Mathematik. Er besagt, dass sich unter bestimmten Endlichkeitsvoraussetzungen Gruppen bzw. Moduln im Wesentlichen eindeutig als direktes Produkt ihrer unzerlegbaren Untergruppen bzw. Untermoduln schreiben lassen. (de) In mathematics, the Krull–Schmidt theorem states that a group subjected to certain finiteness conditions on chains of subgroups, can be uniquely written as a finite direct product of indecomposable subgroups. (en) En mathématiques, le théorème de Krull-Schmidt énonce qu'un groupe soumis à certaines conditions de finitude sur des chaînes de sous-groupes, peut être écrit de manière unique comme un produit direct fini de sous-groupes indécomposables. (fr) 数学において、クルル・シュミットの定理（英: Krull-Schmidt theorem）とは、加群や群のの一意性に関する定理である。「クルル・シュミットの定理」の他にも「クルル・シュミット・東屋の定理」、「クルル・レマク・シュミットの定理」、「ウェダーバーン・レマク・クルル・シュミットの定理」とも呼ばれる。これらの数学者の貢献に関する歴史についてはとを参照のこと。 (ja) O Teorema de Krull-Remak-Schmidt é um resultado da Teoria dos Grupos que lida com as possíveis maneiras de expressar um grupo como uma decomposição de Remak, desde que tal grupo satisfaça certas condições de finitude em cadeias de subgrupos normais. (pt)
prov:wasDerivedFrom	wikipedia-en:Krull–Schmidt_theorem?oldid=1121456867&ns=0
page length (characters) of wiki page	8864 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Krull–Schmidt_theorem
is Link from a Wikipage to another Wikipage of	Robert Remak (mathematician) List of abstract algebra topics Remak-Krull-Schmidt theorem Decomposition of a module Indecomposable module Noetherian ring Krull-Schmidt theorem Krull–Remak–Schmidt theorem Glossary of module theory Krull–Schmidt category Structure theorem for finitely generated modules over a principal ideal domain Otto Schmidt Length of a module Remak decomposition Direct product of groups Krull-Remak-Schmidt theorem List of theorems Krull Wolfgang Krull Schmidt's theorem Simple module Remak–Krull–Schmidt theorem Wedderburn-Remak-Krull-Schmidt theorem
is Wikipage redirect of	Remak-Krull-Schmidt theorem Krull-Schmidt theorem Krull–Remak–Schmidt theorem Remak decomposition Krull-Remak-Schmidt theorem Remak–Krull–Schmidt theorem

Faceted Search & Find service v1.17_git139 as of Feb 29 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 08.03.3330 as of Mar 19 2024, on Linux (x86_64-generic-linux-glibc212), Single-Server Edition (378 GB total memory, 67 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software