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Minimal ideal

In the branch of abstract algebra known as ring theory, a minimal right ideal of a ring R is a non-zero right ideal which contains no other non-zero right ideal. Likewise, a minimal left ideal is a non-zero left ideal of R containing no other non-zero left ideals of R, and a minimal ideal of R is a non-zero ideal containing no other non-zero two-sided…

Properties, Definition & Generalization

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Properties

Ring with unitySocle of a ringArtinian ringKasch ringDomains
11 related topics

Definition

SimpleModuleDual notionMaximal ideals
4 related topics

Generalization

SubmoduleBimodules
2 related topics

Overview

Abstract algebraRing theoryRingZeroIdeal
11 related topics

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Definition

Properties

Generalization

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Minimal ideal

Nodes33
Edges32
Triples24
Avg. degree1.94
Density0.060606
Components1

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Minimal ideal

Top relations

related to Properties · 16
Minimal ideal → Anderson, Any, Artinian, Brauer's, Domains, Fuller, If N1, In, Isaacs, Kasch, Lam, Many, N1N2, N2, Rings, The
related to Generalization · 8
Minimal ideal → Equivalently, If, In, Likewise, R-module RR, RR, RRR, This

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Important terminology

minimal right ideals ideal ring non-zero module rings poset isbn mr lam submodules contains left zero texts 2001 graduate mathematics

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SubjectPredicateObjectConfidenceSrc
Minimal idealrelated to GeneralizationEquivalently0.60section
Minimal idealrelated to GeneralizationThis0.60section
Minimal idealrelated to GeneralizationIf0.60section
Minimal idealrelated to GeneralizationR-module RR0.60section
Minimal idealrelated to GeneralizationLikewise0.60section
Minimal idealrelated to GeneralizationRR0.60section
Minimal idealrelated to GeneralizationIn0.60section
Minimal idealrelated to GeneralizationRRR0.60section
Minimal idealrelated to PropertiesMany0.60section
Minimal idealrelated to PropertiesAnderson0.60section
Minimal idealrelated to PropertiesFuller0.60section
Minimal idealrelated to PropertiesIsaacs0.60section

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    Min side: 3
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