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Commutative ring

In mathematics, a commutative ring is a ring in which the multiplication operation is commutative. The study of commutative rings is called commutative algebra. Complementarily, noncommutative algebra is the study of ring properties that are not specific to commutative rings. This distinction results from the high number of fundamental properties of…

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Overview

Definition and first examples

Divisibility

Ideals and modules

Spectrum of a commutative ring

Ring homomorphisms

Local rings

Constructing commutative rings

Homological notions

Properties

Generalizations

Applications of the commutative rings

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Map overview Semantic statistics

Commutative ring

Nodes189
Edges188
Triples58
Avg. degree1.99
Density0.010582
Components1

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Commutative ring

Top relations

see also · 28
Commutative ring → Akizuki, Almost, Artin, Banach, Cayley, Compact, Connected, Differential, Duality, Dualizing, Eben Matlis, Fermat's Last Theorem, Gorenstein, Hamilton, Ideals, Integrally, Jacobson, Krull, Mori, Morita
related to Completions · 10
Commutative ring → Analogously, Any, Complete, For, Formally, Hensel's, I-adic, If, R/In, This
related to First examples · 7
Commutative ring → An, As, German, It, The, Therefore, Zahlen
related to Flatness · 6
Commutative ring → Despite, For, If, R-algebra, R-module, The
is a · 2
Commutative ring → ring in which the multiplication operation is commutative, simplicial object in the category of commutative rings
related to Homological notions · 2
Commutative ring → Hochster, Several
related to Ideals and modules · 2
Commutative ring → For, Many
related to Simplicial commutative rings · 1
Commutative ring → They

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Important terminology

ring displaystyle rings ideal commutative local called field ideals prime example elements element noetherian regular two right properties left algebra

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Commutative ringis aring in which the multiplication operation is commutative0.90text
Commutative ringis asimplicial object in the category of commutative rings0.90text
Commutative ringrelated to CompletionsIf0.60section
Commutative ringrelated to CompletionsThis0.60section
Commutative ringrelated to CompletionsI-adic0.60section
Commutative ringrelated to CompletionsFormally0.60section
Commutative ringrelated to CompletionsR/In0.60section
Commutative ringrelated to CompletionsFor0.60section
Commutative ringrelated to CompletionsAnalogously0.60section
Commutative ringrelated to CompletionsAny0.60section
Commutative ringrelated to CompletionsComplete0.60section
Commutative ringrelated to CompletionsHensel's0.60section

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