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Artinian ring

In mathematics, specifically abstract algebra, an Artinian ring (sometimes Artin ring) is a ring that satisfies the descending chain condition on (one-sided) ideals; that is, there is no infinite descending sequence of ideals. Artinian rings are named after Emil Artin, who first discovered that the descending chain condition for ideals simultaneously…

Art, Overview & Commutative Artinian rings

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Overview

Examples and counterexamples

Modules over Artinian rings

Commutative Artinian rings

Simple Artinian ring

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Artinian ring

Nodes55
Edges54
Triples32
Avg. degree1.96
Density0.036364
Components1

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Artinian ring

Top relations

related to Simple Artinian ring · 14
Artinian ring → A-modules, AI, Artin, Artinian, Assume, If, Indeed, It, Now, One, Then, This, Thus, Wedderburn
related to Examples and counterexamples · 13
Artinian ring → A/I, An, Artinian, Dedekind, End, For, If, In, Let, Noetherian, Similarly, The, Then
related to Modules over Artinian rings · 5
Artinian ring → Artinian, Hopkins, Let, Noetherian, Then

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Important terminology

artinian ring displaystyle left right rings ideals noetherian descending chain condition simple artin ideal finite theorem commutative modules generated resp

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Artinian ringrelated to Examples and counterexamplesAn0.60section
Artinian ringrelated to Examples and counterexamplesArtinian0.60section
Artinian ringrelated to Examples and counterexamplesIn0.60section
Artinian ringrelated to Examples and counterexamplesLet0.60section
Artinian ringrelated to Examples and counterexamplesThen0.60section
Artinian ringrelated to Examples and counterexamplesSimilarly0.60section
Artinian ringrelated to Examples and counterexamplesEnd0.60section
Artinian ringrelated to Examples and counterexamplesIf0.60section
Artinian ringrelated to Examples and counterexamplesDedekind0.60section
Artinian ringrelated to Examples and counterexamplesA/I0.60section
Artinian ringrelated to Examples and counterexamplesFor0.60section
Artinian ringrelated to Examples and counterexamplesNoetherian0.60section

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