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Artinian module

In mathematics, specifically abstract algebra, an Artinian module is a module that satisfies the descending chain condition on its poset of submodules. They are for modules what Artinian rings are for rings, and a ring is Artinian if and only if it is an Artinian module over itself (with left or right multiplication). Both concepts are named for Emil Artin.

Art, Overview & Left and right Artinian rings, modules and bimodules

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Overview

MathematicsAbstract algebraModuleDescending chain conditionPoset
20 related topics

Left and right Artinian rings, modules and bimodules

Noncommutative ringsBimoduleAbelian groupIntegersRational numbers
9 related topics

Relation to the Noetherian condition

IsomorphicQuasicyclic groupFinite setFaithfulCommutative ring
9 related topics

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Overview

Left and right Artinian rings, modules and bimodules

Relation to the Noetherian condition

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Artinian module

Nodes42
Edges41
Triples46
Avg. degree1.95
Density0.047619
Components1

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Artinian module

Top relations

related to References · 30
Artinian module → Artin, Atiyah, Chain, Chapter, Cohn, Commutative Algebra, Composition Series, Cyclic Artinian Modules Without, First Course, Hartley, Introduction, ISBN, Lam, Lock-gray-alt-2, Lock-green, Lock-red-alt-2, London Math, Macdonald, Min-n, MR
related to Relation to the Noetherian condition · 9
Artinian module → Artinian, For, Noetherian, Note, So, The, This, Unlike, Yet
related to Left and right Artinian rings, modules and bimodules · 6
Artinian module → Artinian, For, However, R-module, The, To
is a · 1
Artinian module → module that satisfies the descending chain condition on its poset of submodules

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Important terminology

artinian module right ring left modules noetherian r-module also rings chain example condition bimodule descending finitely-generated may since submodule displaystyle

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Artinian moduleis amodule that satisfies the descending chain condition on its poset of submodules0.90text
Artinian modulerelated to Left and right Artinian rings, modules and bimodulesThe0.60section
Artinian modulerelated to Left and right Artinian rings, modules and bimodulesArtinian0.60section
Artinian modulerelated to Left and right Artinian rings, modules and bimodulesFor0.60section
Artinian modulerelated to Left and right Artinian rings, modules and bimodulesR-module0.60section
Artinian modulerelated to Left and right Artinian rings, modules and bimodulesHowever0.60section
Artinian modulerelated to Left and right Artinian rings, modules and bimodulesTo0.60section
Artinian modulerelated to ReferencesLock-green0.60section
Artinian modulerelated to ReferencesLock-gray-alt-20.60section
Artinian modulerelated to ReferencesLock-red-alt-20.60section
Artinian modulerelated to ReferencesWikisource-logo0.60section
Artinian modulerelated to ReferencesAtiyah0.60section

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