module
type: Item
subclass of: algebraic structure
Freebase ID: /m/01pd2z
NDL Authority ID: 00564457
Quora topic ID: Modules
Quora topic ID: Module
nLab ID: module
defining formula: m + n = n + m ( m , n ∈ M ) ( m + n ) + p = m + ( n + p ) ( m , n , p ∈ M ) m + 0 M = m ( m ∈ M ) ( − m ) + m = 0 M ( m ∈ M ) r ( s m ) = ( r s ) m ( m ∈ M , r , s ∈ R ) 1 R m = m ( m ∈ M ) r ( m + n ) = r m + r n ( m , n ∈ M , r ∈ R ) ( r + s ) m = r m + s m ( m ∈ M , r , s ∈ R )
Library of Congress Authorities ID: sh85086470
Gran Enciclopèdia Catalana ID (former scheme): 0194835
Microsoft Academic ID (discontinued): 35729967
FAST ID: 1024523
Bibliothèque nationale de France ID: 13163015r
National Library of Spain SpMaBN ID (BNE v1.0): XX526925
IdRef ID: 027814572
different from: absolute value
J9U entity ID: 987007541015705171
OpenAlex ID: C35729967
YSO ID: 38369
NL CR AUT ID: ph211266
on focus list of Wikimedia project: Wikipedia:Vital articles/Level/4
MathWorld ID: Module
has part(s): abelian group
in defining formula: m + n = n + m ( m , n ∈ M )
in defining formula: ( m + n ) + p = m + ( n + p ) ( m , n , p ∈ M ) r ( s m ) = ( r s ) m ( m ∈ M , r , s ∈ R )
in defining formula: 0 M
in defining formula: − m
in defining formula: 1 R
in defining formula: r ( m + n ) = r m + r n ( m , n ∈ M , r ∈ R ) ( r + s ) m = r m + s m ( m ∈ M , r , s ∈ R )
maintained by WikiProject: WikiProject Mathematics
ProofWiki ID: Definition:Module
Gran Enciclopèdia Catalana ID: modul-2
opposite of: comodule
Treccani's Dizionario delle Scienze Fisiche ID: modulo
Enciclopedia della Scienza e della Tecnica ID: modulo
Treccani's Enciclopedia della Matematica ID: modulo-su-un-anello-a
Treccani ID: modulo
Encyclopedia of Mathematics article ID: Module
Open Library subject ID: modules_(algebra)
underlying structure: abelian group
studied by: commutative algebra
studied by: ring theory
studied by: module theory
has characteristic: base ring
has characteristic: length
has characteristic: radical of a module
SVKKL authority ID: 0203950-moduly-algebra
label: 模 @zh
label: moduł @pl
label: module sur un anneau @fr
label: מודול @he
label: 가군 @ko
label: módulo @es
label: modulus @hu
label: modulo @it
label: Modul @de
label: 環上の加群 @ja
label: moduul @nl
label: modul @sv
label: модуль над кольцом @ru
label: mòdul sobre un anell @ca
label: moduli @fi
label: модуль над кільцем @uk
label: مدول @fa
label: модул @bg
label: πρότυπο @el
label: حلقية @ar
label: modül @tr
label: moodul @et
label: ਮੌਡਿਊਲ @pa
label: Մոդուլ օղակի վրա @hy
label: ҡулса өҫтөндә модуль @ba
label: модуль @be