module (Q1642)

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generalization of vector space, with scalars in a ring instead of a field
  • module over a ring
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    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
    1 reference
    stated in
    Freebase Data Dumps
    publication date
    28 October 2013
    NDL Authority ID
    00564457
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    Quora topic ID
    Modules
    1 reference
    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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