Simple module

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Examples

Abelian groups Subgroups Cyclic groups Prime Order

21 related topics

Simple modules and composition series

Short exact sequence Proving Fitting lemma Finite length Local ring

22 related topics

Basic properties of simple modules

Indecomposable Injective Image Endomorphism Endomorphism ring

7 related topics

The Jacobson density theorem

Jacobson density theorem Primitive ring Artinian Simple ring Matrix ring

7 related topics

Topics to explore

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Overview

Mathematics
Ring theory
Ring Ring (mathematics)
Modules Module (mathematics)
Non-zero Zero module
Submodules Submodule
If and only if
Cyclic submodule Cyclic module
Length Length of a module
Simple groups Simple group
Group theory
Unital modules Unital module

Examples

Abelian groups Abelian group
Subgroups Subgroup
Cyclic groups Cyclic group
Prime Prime number
Order Order (group theory)
Ideal Ideal (ring theory)
Minimal Minimal ideal
Conversely Converse (logic)
Quotient map Quotient module
Maximal Maximal ideal
Preimage
Kernel Kernel (algebra)
Homomorphism Module homomorphism
Surjectivity Surjective
Field Field (mathematics)
Group Group (mathematics)
Group representation
Left module
Group ring
Main article on this relationship Representation theory of finite groups
Representation theory

Basic properties of simple modules

Simple modules and composition series

The Jacobson density theorem

Advanced semantic analysis

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Map overview Semantic statistics

Nodes75

Edges74

Triples10

Avg. degree1.97

Density0.026667

Components1

How this topic connects Entity context

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Simple module

Top relations

related to The Jacobson density theorem · 6

Simple module → An, D-linear, D-space, In, Jacobson, The Jacobson

related to Basic properties of simple modules · 2

Simple module → Every, The

is a · 1

Simple module → division ring

see also · 1

Simple module → Semisimple

Important terminology Word statistics

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Important terminology

simple modules module right non-zero ideal ring submodule every theory length theorem maximal isomorphic homomorphism composition series proper cyclic group

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
Simple module	is a	division ring	0.90	text
Simple module	related to Basic properties of simple modules	The	0.60	section
Simple module	related to Basic properties of simple modules	Every	0.60	section
Simple module	related to The Jacobson density theorem	An	0.60	section
Simple module	related to The Jacobson density theorem	Jacobson	0.60	section
Simple module	related to The Jacobson density theorem	The Jacobson	0.60	section
Simple module	related to The Jacobson density theorem	In	0.60	section
Simple module	related to The Jacobson density theorem	D-linear	0.60	section
Simple module	related to The Jacobson density theorem	D-space	0.60	section
Simple module	see also	Semisimple	0.60	section

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Min side: 3

Research this topic

Explore this topic

Examples

Simple modules and composition series

Basic properties of simple modules

The Jacobson density theorem

Key facts & relationships

Topics to explore

Overview

Examples

Basic properties of simple modules

Simple modules and composition series

The Jacobson density theorem

Advanced semantic analysis

Map overview Semantic statistics

Simple module

How this topic connects Entity context

Simple module

Top relations

Important terminology Word statistics

Important terminology

Entity relationships Subject–Predicate–Object triples

Related concept clusters Concept neighborhoods

Connections between topic areas Semantic bridges