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Jacobson radical

In mathematics, more specifically ring theory, the Jacobson radical of a ring R {\displaystyle R} is the ideal consisting of those elements in R {\displaystyle R} that annihilate all simple right R {\displaystyle R} -modules. It happens that substituting "left" in place of "right" in the definition yields the same ideal, and so the notion is left–right…

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Jacobson radical

Nodes83
Edges82
Triples79
Avg. degree1.98
Density0.024096
Components1

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Jacobson radical

Top relations

related to Properties · 16
Jacobson radical → Artinian, For, However, If, In, Jacobson, Köthe, Nakayama's, Note, R-module, Rings, T0, T1, The Jacobson, This, Tk
related to Commutative examples · 15
Jacobson radical → Artinian, Consider, For, If, In, Jacobson, Nakayama's, Since, The, The Jacobson, Then, This, X1, Xn, Z/12Z
related to Noncommutative examples · 12
Jacobson radical → Gelfand, Hilbert, If, Jacobson, Naimark, Neumann, Quiver, Rings, Spectrum, Start, The Jacobson, This
has application · 8
Jacobson radical → Although Jacobson, Another, Hilbert Nullstellensatz, If, In, Jacobson, Nakayama's, This
related to Equivalent characterizations · 8
Jacobson radical → Anderson, Ch, Fuller, Isaacs, Jacobson, Lam, The, The Jacobson
related to Commutative case · 7
Jacobson radical → Artinian, If, In, Jacobson, See, Spm, This
related to Noncommutative/general case · 5
Jacobson radical → Ann, For, Jacobson, That, This
is a · 2
Jacobson radical → intersection of all primitive ideals, zero ideal
related to Definitions · 2
Jacobson radical → Jacobson, There
related to Motivation · 2
Jacobson radical → Jacobson, Understanding

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Important terminology

radical ring jacobson ideal maximal rings right ideals intersection simple left displaystyle modules commutative case unity elements mathfrak field quasiregular

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Jacobson radicalis aintersection of all primitive ideals0.90text
Jacobson radicalis azero ideal0.90text
Andersoninstance ofThe following equivalences appear in many noncommutative algebra texts0.80text
Jacobson radicalhas applicationAlthough Jacobson0.60section
Jacobson radicalhas applicationJacobson0.60section
Jacobson radicalhas applicationNakayama's0.60section
Jacobson radicalhas applicationThis0.60section
Jacobson radicalhas applicationIf0.60section
Jacobson radicalhas applicationAnother0.60section
Jacobson radicalhas applicationIn0.60section
Jacobson radicalhas applicationHilbert Nullstellensatz0.60section
Jacobson radicalrelated to Commutative caseIn0.60section

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