Direct sum of modules

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Direct sum of modules with additional structure

Norm Inner product Category Algebras over a field Index set

13 related topics

Properties

Submodule Length of modules Tensor product Naturally isomorphic Commutative

10 related topics

Construction for an arbitrary family of modules

Family Set Cofinitely many Functions Disjoint union

7 related topics

Construction for vector spaces and abelian groups

Cartesian product Internal direct sum Dimension Finite Subgroup

6 related topics

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Overview

Abstract algebra
Modules Module (mathematics)
Coproduct
Direct product
Dual Dual (category theory)
Vector spaces Vector space
Field Field (mathematics)
Abelian groups Abelian group
Integers Integer
Banach spaces Banach space
Hilbert spaces Hilbert space
Decomposition of a module

Construction for vector spaces and abelian groups

Cartesian product
Internal direct sum Direct sum of modules
Dimension Dimension of a vector space
Finite Finite set
Subgroup
Rank Rank of an abelian group

Construction for an arbitrary family of modules

Family Indexed family
Set Set (mathematics)
Cofinitely many
Functions Function (mathematics)
Disjoint union
Finitely supported Compact support
Fiber bundle

Properties

Submodule
Length of modules Length of a module
Tensor product
Naturally isomorphic Natural isomorphism
Commutative
Associative
Linear homomorphisms Linear map
Homomorphism
Dual vector space Dual space
Biproduct

Universal property

Grothendieck group

Direct sum of modules with additional structure

Norm Norm (mathematics)
Inner product
Category Category (category theory)
Algebras over a field Algebra over a field
Index set
Defined over Domain of a function
Complemented Complemented subspace
C 0 {\displaystyle c_{0}} C0 space
Bilinear forms Bilinear form
Orthogonal
Inner product space
Orthogonal complement
Lindenstrauss–Tzafriri theorem Lindenstrauss–Tzafriri theorem?action=edit&redlink=1

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Nodes61

Edges60

Triples20

Avg. degree1.97

Density0.032787

Components1

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Direct sum of modules

Top relations

related to Properties · 18

Direct sum of modules → A1, Ak, An, Bourbaki, Direct, Each, Every, Hom, If, II, In, Indeed, Mi, R-linear, R-module, The, This, With

is a · 2

Direct sum of modules → biproduct, smallest module which contains the given modules as submodules with no

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Important terminology

sum direct displaystyle modules spaces product space mi hilbert vector construction every many abelian left set banach one finite functions

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
Direct sum of modules	is a	smallest module which contains the given modules as submodules with no	0.90	text
Direct sum of modules	is a	biproduct	0.90	text
Direct sum of modules	related to Properties	The	0.60	section
Direct sum of modules	related to Properties	Mi	0.60	section
Direct sum of modules	related to Properties	Bourbaki	0.60	section
Direct sum of modules	related to Properties	II	0.60	section
Direct sum of modules	related to Properties	If	0.60	section
Direct sum of modules	related to Properties	Each	0.60	section
Direct sum of modules	related to Properties	With	0.60	section
Direct sum of modules	related to Properties	Every	0.60	section
Direct sum of modules	related to Properties	This	0.60	section
Direct sum of modules	related to Properties	R-module	0.60	section

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Direct sum of modules with additional structure

Properties

Construction for an arbitrary family of modules

Construction for vector spaces and abelian groups

Key facts & relationships

Topics to explore

Overview

Construction for vector spaces and abelian groups

Construction for an arbitrary family of modules

Properties

Universal property

Grothendieck group

Direct sum of modules with additional structure

Advanced semantic analysis

Map overview Semantic statistics

Direct sum of modules

How this topic connects Entity context

Direct sum of modules

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