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Direct sum

In mathematics, more specifically in algebra, the direct sum of a collection of abelian groups is an abelian group constructed by combining the given groups in a specific way, described below. If the input abelian groups have additional structure (for example, are vector spaces, modules, or topological abelian groups), then the direct sum also has that…

Products, Types of direct sums & Overview

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Types of direct sums

GroupDirect productCartesian productSubgroupSupport
41 related topics

Overview

MathematicsAlgebraAbelian groupsVector spacesModules
16 related topics

Homomorphisms

ProjectionHomomorphismCoproduct
3 related topics

Examples

Indexed family
1 related topics

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Overview

Examples

Types of direct sums

Homomorphisms

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Map overview Semantic statistics

Direct sum

Nodes66
Edges65
Triples48
Avg. degree1.97
Density0.030303
Components1

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Direct sum

Top relations

related to Examples · 7
Direct sum → Addition, Each Ai, Given, If, In, The, When
related to Direct sum of abelian groups · 6
Direct sum → Cartesian, For, Given, That, The, This
related to Direct sum in categories · 5
Direct sum → An, For, In, More, That
related to Direct sum of group representations · 5
Direct sum → An, Given, GL, Specifically, The
related to Direct sum of topological vector spaces · 5
Direct sum → Banach, Hausdorff, If, That, TVS
related to Direct sum of rings · 4
Direct sum → If, In, The, Thus
related to Internal and external direct sums · 4
Direct sum → For, If, In, This
is a · 3
Direct sum → coproduct, coproduct in the appropriate category, same as the direct product
related to Direct sum of modules · 3
Direct sum → Banach, Hilbert, The
related to Homomorphisms · 3
Direct sum → Given, The, Thus

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Important terminology

direct sum displaystyle groups vector product oplus many abelian modules example group spaces algebraic category given finitely defined also two

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Direct sumis asame as the direct product0.90text
Direct sumis acoproduct0.90text
Direct sumis acoproduct in the appropriate category0.90text
Direct sumrelated to Direct sum in categoriesAn0.60section
Direct sumrelated to Direct sum in categoriesIn0.60section
Direct sumrelated to Direct sum in categoriesMore0.60section
Direct sumrelated to Direct sum in categoriesFor0.60section
Direct sumrelated to Direct sum in categoriesThat0.60section
Direct sumrelated to Direct sum of abelian groupsThe0.60section
Direct sumrelated to Direct sum of abelian groupsGiven0.60section
Direct sumrelated to Direct sum of abelian groupsThat0.60section
Direct sumrelated to Direct sum of abelian groupsCartesian0.60section

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