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module (Q18848)

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

    Statements

    studied by
    commutative algebra
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    ring theory
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    module theory
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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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    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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    has characteristic
    base ring
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    length
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    radical of a module
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    has part(s)
    abelian group
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    opposite of
    comodule
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    Identifiers

    FAST ID
    1024523
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    J9U entity ID
    987007541015705171
    subject named as (monolingual text)
    Modules (Algebra) (English)
    מודולים (אלגברה) (Hebrew)
    1 reference
    stated in
    National Library of Israel
    NDL Authority ID
    00564457
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    NL CR AUT ID
    ph211266
    subject named as
    moduly (algebra)
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    IdRef ID
    027814572
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    MathWorld ID
    Module
    subject named as
    Module
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    Quora topic ID
    Modules
    1 reference
    stated in
    Quora
    Module
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    Treccani ID
    modulo
    subject named as
    Modulo
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    YSO ID
    38369
    subject named as (monolingual text)
    modulat (matematihkka) (Northern Sami)
    modulit (matematiikka) (Finnish)
    moduler (matematik) (Swedish)
    modules (mathematics) (English)
    1 reference
    stated in
    YSO-Wikidata mapping project
    retrieved
    27 January 2022
     
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                Retrieved from "https://www.wikidata.org/w/index.php?title=Q18848&oldid=2517768246"