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Pure submodule

In mathematics, especially in the field of module theory, the concept of pure submodule provides a generalization of direct summand, a type of particularly well-behaved piece of a module. Pure modules are complementary to flat modules and generalize Prüfer's notion of pure subgroups. While flat modules are those modules which leave short exact sequences…

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Equivalent characterizations

MatrixFiltered colimit
2 related topics

Definition

RingSubmoduleInjective
3 related topics

Examples

SubspaceVector spaceField
3 related topics

Properties

Von Neumann regular ringFinitely presented
2 related topics

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Definition

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Properties

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Pure submodule

Nodes27
Edges26
Triples9
Avg. degree1.93
Density0.074074
Components1

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Pure submodule

Top relations

related to Properties · 6
Pure submodule → From, Neumann, Suppose, The, Then, This
related to Definition · 3
Pure submodule → Analogously, Let, Then

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Important terminology

pure displaystyle flat submodule module exact sequence modules every direct sequences -module short ring field mathematics colon right also suppose

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Pure submodulerelated to DefinitionLet0.60section
Pure submodulerelated to DefinitionThen0.60section
Pure submodulerelated to DefinitionAnalogously0.60section
Pure submodulerelated to PropertiesSuppose0.60section
Pure submodulerelated to PropertiesFrom0.60section
Pure submodulerelated to PropertiesNeumann0.60section
Pure submodulerelated to PropertiesThis0.60section
Pure submodulerelated to PropertiesThe0.60section
Pure submodulerelated to PropertiesThen0.60section

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