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

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defining formula

{\begin{aligned}m+n&=n+m&&(m,n\in M)\\(m+n)+p&=m+(n+p)&&(m,n,p\in M)\\m+0_{M}&=m&&(m\in M)\\(-m)+m&=0_{M}&&(m\in M)\\r(sm)&=(rs)m&&(m\in M,\;r,s\in R)\\1_{R}m&=m&&(m\in M)\\r(m+n)&=rm+rn&&(m,n\in M,\;r\in R)\\(r+s)m&=rm+sm&&(m\in M,\;r,s\in R)\end{aligned}}

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commutative algebra

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1 reference

imported from Wikimedia project

Polish Wikipedia

Wikimedia import URL

https://pl.wikipedia.org/w/index.php?title=Moduł_(matematyka)&oldid=64327401

on focus list of Wikimedia project

Wikipedia:Vital articles/Level/4

31 October 2022

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object has role

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in defining formula

m+n=n+m\qquad (m,n\in M)

symbol represents

commutative property

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{\begin{aligned}(m+n)+p&=m+(n+p)&&(m,n,p\in M)\\r(sm)&=(rs)m&&(m\in M,\;r,s\in R)\\\end{aligned}}

symbol represents

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0_{M}

symbol represents

additive identity

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-m

symbol represents

inverse element

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1_{R}

symbol represents

multiplicative identity

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{\begin{aligned}r(m+n)&=rm+rn&&(m,n\in M,\;r\in R)\\(r+s)m&=rm+sm&&(m\in M,\;r,s\in R)\end{aligned}}

symbol represents

distributive property

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Identifiers

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/m/01pd2z

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Freebase Data Dumps

publication date

28 October 2013

NDL Authority ID

00564457

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Modules

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Module

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module

1 reference

imported from Wikimedia project

English Wikipedia

Library of Congress authority ID

sh85086470

1 reference

https://github.com/JohnMarkOckerbloom/ftl/blob/master/data/wikimap

3 April 2019

Gran Enciclopèdia Catalana ID (former scheme)

0194835

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Microsoft Academic ID

35729967

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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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027814572

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National Library of Israel J9U ID

987007541015705171

1 reference

National Library of Israel

C35729967

1 reference

26 January 2022

https://docs.openalex.org/download-snapshot/snapshot-data-format

38369

subject named as

modulit (matematiikka)

moduler (matematik)

modules (mathematics)

1 reference

YSO-Wikidata mapping project

27 January 2022

ph211266

subject named as

moduly (algebra)

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Module

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Definition:Module

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Gran Enciclopèdia Catalana ID

modul-2

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Sitelinks

mathematics(0 entries)

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