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Free module

In mathematics, a free module is a module that has a basis, that is, a generating set that is linearly independent. Every vector space is a free module, but, if the ring of the coefficients is not a division ring (not a field in the commutative case), then there exist non-free modules.

Examples, Universal property & Formal linear combinations

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Definition

Examples

Formal linear combinations

Universal property

Generalizations

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Free module

Nodes53
Edges52
Triples60
Avg. degree1.96
Density0.037736
Components1

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Free module

Top relations

related to References · 29
Free module → Academic Press, Adamson, Advanced Mathematics, An Introduction, Boyd, Cambridge Studies, Cambridge University Press, Commutative, Creative Commons Attribution/Share-Alike License, Elementary Rings, EMS Press, Encyclopedia, Free, Govorov, Group Representation Theory, Hideyuki, Iain, ISBN, Keown, Mathematics
related to Examples · 17
Free module → A-module, Also, As, Baer, For, If, Kaplansky's, Let, More, Over, R-module, Sometimes, Specker, Then, Whitehead, X2, ZFC
related to Generalizations · 8
Free module → Dedekind, Flat, For, Many, PID, Projective, See, Torsion-free
is a · 2
Free module → module that has a basis, module with a basis.An immediate consequence of the second half of the definition is that the coefficients in the first half are unique for each element of M.If R
related to Another construction · 2
Free module → Given, The
see also · 2
Free module → Free, Suslin

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Important terminology

module free displaystyle ring basis set left commutative modules r-module mathematics rank element nonzero finitely every given called elements group

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Free moduleis amodule that has a basis0.90text
Free moduleis amodule with a basis.An immediate consequence of the second half of the definition is that the coefficients in the first half are unique for each element of M.If R0.90text
Free modulerelated to Another constructionThe0.60section
Free modulerelated to Another constructionGiven0.60section
Free modulerelated to ExamplesLet0.60section
Free modulerelated to ExamplesMore0.60section
Free modulerelated to ExamplesIf0.60section
Free modulerelated to ExamplesOver0.60section
Free modulerelated to ExamplesX20.60section
Free modulerelated to ExamplesThen0.60section
Free modulerelated to ExamplesA-module0.60section
Free modulerelated to ExamplesFor0.60section

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