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gptkbp:instanceOf
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gptkb:mathematical_concept
|
|
gptkbp:basis_unique_up_to
|
Cardinality (if module is free and basis exists)
|
|
gptkbp:basisFor
|
Yes
|
|
gptkbp:category
|
Module theory
|
|
gptkbp:definedIn
|
gptkb:King
|
|
gptkbp:example
|
Direct sum of copies of a ring
Z^n as a free Z-module
|
|
gptkbp:field
|
gptkb:Abstract_algebra
|
|
gptkbp:generalizes
|
gptkb:Vector
|
|
gptkbp:hasProperty
|
Every element is a finite linear combination of basis elements
|
|
gptkbp:hasWikipediaPage
|
https://en.wikipedia.org/wiki/Free_module
|
|
gptkbp:heldBy
|
Module
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Free module
|
|
gptkbp:introduced
|
gptkb:Richard_Dedekind
|
|
gptkbp:is_to_module_as
|
Vector space is to field
|
|
gptkbp:not_necessarily
|
gptkb:Projective_module
gptkb:Injective_module
|
|
gptkbp:over_non-principal_ideal_domain
|
Not every submodule is free
|
|
gptkbp:over_principal_ideal_domain
|
Every submodule is free
|
|
gptkbp:rank
|
Cardinality of basis
|
|
gptkbp:relatedConcept
|
gptkb:Vector
gptkb:Projective_module
Basis (linear algebra)
Torsion-free module
|
|
gptkbp:bfsParent
|
gptkb:Projective_modules
|
|
gptkbp:bfsLayer
|
6
|