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Maximal ideal

In mathematics, more specifically in ring theory, a maximal ideal is a two-sided ideal that is maximal (with respect to set inclusion) amongst all proper ideals. In other words, I is a maximal ideal of a ring R if there are no other two-sided ideals contained between I and R.

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Maximal ideal

Nodes51
Edges50
Triples45
Avg. degree1.96
Density0.039216
Components1

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Maximal ideal

Top relations

related to Properties · 25
Maximal ideal → AB, An, Commutative, Conversely, Every, For, However, If, In, Incidentally, Jacobson, Krull, Krull's, More, R-module, R-modules, R/A, R/L, R/m, See
related to Examples · 13
Maximal ideal → Boolean, Even, Every, Generally, If, In, More, Nullstellensatz, Spm, The, Then, Therefore, This
related to Definition · 5
Maximal ideal → For, Given, R/I, The, There
is a · 2
Maximal ideal → prime ideal, two-sided ideal that is maximal

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maximal ideal ring ideals right displaystyle prime rings two-sided simple left commutative module field mathbb set proper known generated quotient

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SubjectPredicateObjectConfidenceSrc
Maximal idealis atwo-sided ideal that is maximal0.90text
Maximal idealis aprime ideal0.90text
Maximal idealrelated to DefinitionThere0.60section
Maximal idealrelated to DefinitionGiven0.60section
Maximal idealrelated to DefinitionFor0.60section
Maximal idealrelated to DefinitionThe0.60section
Maximal idealrelated to DefinitionR/I0.60section
Maximal idealrelated to ExamplesIf0.60section
Maximal idealrelated to ExamplesIn0.60section
Maximal idealrelated to ExamplesMore0.60section
Maximal idealrelated to ExamplesThe0.60section
Maximal idealrelated to ExamplesGenerally0.60section

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