module (Q1642)

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generalization of vector space, with scalars in a ring instead of a field
  • module over a ring
Language Label Description Also known as
English
module
generalization of vector space, with scalars in a ring instead of a field
  • module over a ring

Statements

subclass of
abelian group
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defining formula
m+n=n+m(m,n∈M)(m+n)+p=m+(n+p)(m,n,p∈M)m+0M=m(m∈M)(−m)+m=0M(m∈M)r(sm)=(rs)m(m∈M,r,s∈R)1Rm=m(m∈M)r(m+n)=rm+rn(m,n∈M,r∈R)(r+s)m=rm+sm(m∈M,r,s∈R)
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studied in
commutative algebra
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module theory
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in defining formula
m+n=n+m(m,n∈M)
symbol represents
commutative property
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(m+n)+p=m+(n+p)(m,n,p∈M)r(sm)=(rs)m(m∈M,r,s∈R)
symbol represents
associativity
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r(m+n)=rm+rn(m,n∈M,r∈R)(r+s)m=rm+sm(m∈M,r,s∈R)
symbol represents
distributive property
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opposite of
comodule
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Identifiers

Wikidata QID
Q18848
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Freebase ID
/m/01pd2z
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stated in
Freebase Data Dumps
publication date
28 October 2013
NDL Authority ID
00564457
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Quora topic ID
Modules
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stated in
Quora
Module
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Microsoft Academic ID
35729967
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FAST ID
1024523
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Bibliothèque nationale de France ID
13163015r
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National Library of Spain ID
XX526925
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IdRef ID
027814572
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YSO ID
38369
subject named as
modulit (matematiikka)
moduler (matematik)
modules (mathematics)
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stated in
YSO-Wikidata mapping project
retrieved
27 January 2022
NL CR AUT ID
ph211266
subject named as
moduly (algebra)
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MathWorld ID
Module
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ProofWiki ID
Definition:Module
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Gran Enciclopèdia Catalana ID
modul-2
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