module (Q1642): Difference between revisions

@@ Property / subclass of @@
+abelian group
@@ Property / subclass of: abelian group / rank @@
+Normal rank
@@ Property / Freebase ID @@
+/m/01pd2z
@@ Property / Freebase ID: /m/01pd2z / rank @@
+Normal rank
@@ Property / Freebase ID: /m/01pd2z / reference @@
+stated in: Freebase Data Dumps
publication date: 28 October 2013Timestamp +2013-10-28T00:00:00Z
Timezone +00:00
Calendar Gregorian
Precision 1 day
Before 0
After 0
-Timestamp
++2013-10-28T00:00:00Z
-Timezone
++00:00
-Calendar
+Gregorian
-Precision
+day
 Before
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@@ Property / NDL Authority ID @@
+00564457
@@ Property / NDL Authority ID: 00564457 / rank @@
+Normal rank
@@ Property / Quora topic ID @@
+Modules
@@ Property / Quora topic ID: Modules / rank @@
+Normal rank
@@ Property / Quora topic ID: Modules / reference @@
+stated in: Quora
@@ Property / Quora topic ID @@
+Module
@@ Property / Quora topic ID: Module / rank @@
+Normal rank
@@ Property / nLab ID @@
+module
@@ Property / nLab ID: module / rank @@
+Normal rank
@@ Property / nLab ID: module / reference @@
+imported from Wikimedia project: English Wikipedia
@@ Property / defining formula @@
+ ${\begin{aligned}m+n&=n+m&&(m,n\in M)\\(m+n)+p&=m+(n+p)&&(m,n,p\in M)\\m+0_{M}&=m&&(m\in M)\\(-m)+m&=0_{M}&&(m\in M)\\r(sm)&=(rs)m&&(m\in M,\;r,s\in R)\\1_{R}m&=m&&(m\in M)\\r(m+n)&=rm+rn&&(m,n\in M,\;r\in R)\\(r+s)m&=rm+sm&&(m\in M,\;r,s\in R)\end{aligned}}$ 
\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_Rm &=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}
+Normal rank
@@ Property / Library of Congress authority ID @@
+sh85086470
@@ Property / Library of Congress authority ID: sh85086470 / rank @@
+Normal rank
@@ Property / Library of Congress authority ID: sh85086470 / reference @@
+reference URL: https://github.com/JohnMarkOckerbloom/ftl/blob/master/data/wikimap
retrieved: 3 April 2019Timestamp +2019-04-03T00:00:00Z
Timezone +00:00
Calendar Gregorian
Precision 1 day
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After 0
-Timestamp
++2019-04-03T00:00:00Z
-Timezone
++00:00
-Calendar
+Gregorian
-Precision
+day
 Before
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@@ Property / Gran Enciclopèdia Catalana ID (former scheme) @@
+0194835
@@ Property / Gran Enciclopèdia Catalana ID (former scheme): 0194835 / rank @@
+Normal rank
@@ Property / studied in @@
+commutative algebra
@@ Property / studied in: commutative algebra / rank @@
+Normal rank
@@ Property / studied in @@
+module theory
@@ Property / studied in: module theory / rank @@
+Normal rank
@@ Property / Microsoft Academic ID @@
+35729967
@@ Property / Microsoft Academic ID: 35729967 / rank @@
+Normal rank
@@ Property / FAST ID @@
+1024523
@@ Property / FAST ID: 1024523 / rank @@
+Normal rank
@@ Property / Bibliothèque nationale de France ID @@
+13163015r
@@ Property / Bibliothèque nationale de France ID: 13163015r / rank @@
+Normal rank
@@ Property / National Library of Spain ID @@
+XX526925
@@ Property / National Library of Spain ID: XX526925 / rank @@
+Normal rank
@@ Property / IdRef ID @@
+027814572
@@ Property / IdRef ID: 027814572 / rank @@
+Normal rank
@@ Property / different from @@
+absolute value
@@ Property / different from: absolute value / rank @@
+Normal rank
@@ Property / different from: absolute value / reference @@
+imported from Wikimedia project: Polish Wikipedia
Wikimedia import URL: https://pl.wikipedia.org/w/index.php?title=Moduł_(matematyka)&oldid=64327401
@@ Property / National Library of Israel J9U ID @@
+987007541015705171
@@ Property / National Library of Israel J9U ID: 987007541015705171 / rank @@
+Normal rank
@@ Property / National Library of Israel J9U ID: 987007541015705171 / reference @@
+stated in: National Library of Israel
@@ Property / OpenAlex ID @@
+C35729967
@@ Property / OpenAlex ID: C35729967 / rank @@
+Normal rank
@@ Property / OpenAlex ID: C35729967 / reference @@
+stated in: OpenAlex
retrieved: 26 January 2022Timestamp +2022-01-26T00:00:00Z
Timezone +00:00
Calendar Gregorian
Precision 1 day
Before 0
After 0
reference URL: https://docs.openalex.org/download-snapshot/snapshot-data-format
-Timestamp
++2022-01-26T00:00:00Z
-Timezone
++00:00
-Calendar
+Gregorian
-Precision
+day
 Before
 After
@@ Property / YSO ID @@
@@ Property / YSO ID: 38369 / rank @@
+Normal rank
@@ Property / YSO ID: 38369 / qualifier @@
+subject named as: modulit (matematiikka)
@@ Property / YSO ID: 38369 / qualifier @@
+subject named as: moduler (matematik)
@@ Property / YSO ID: 38369 / qualifier @@
+subject named as: modules (mathematics)
@@ Property / YSO ID: 38369 / reference @@
+stated in: YSO-Wikidata mapping project
retrieved: 27 January 2022Timestamp +2022-01-27T00:00:00Z
Timezone +00:00
Calendar Gregorian
Precision 1 day
Before 0
After 0
-Timestamp
++2022-01-27T00:00:00Z
-Timezone
++00:00
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+Gregorian
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+day
 Before
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@@ Property / NL CR AUT ID @@
+ph211266
@@ Property / NL CR AUT ID: ph211266 / rank @@
+Normal rank
@@ Property / NL CR AUT ID: ph211266 / qualifier @@
+subject named as: moduly (algebra)
@@ Property / on focus list of Wikimedia project @@
+Wikipedia:Vital articles/Level/4
+Normal rank
+point in time: 31 October 2022Timestamp +2022-10-31T00:00:00Z
Timezone +00:00
Calendar Gregorian
Precision 1 day
Before 0
After 0
-Timestamp
++2022-10-31T00:00:00Z
-Timezone
++00:00
-Calendar
+Gregorian
-Precision
+day
 Before
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@@ Property / MathWorld ID @@
+Module
@@ Property / MathWorld ID: Module / rank @@
+Normal rank
@@ Property / has part(s) @@
+abelian group
@@ Property / has part(s): abelian group / rank @@
+Normal rank
@@ Property / has part(s) @@
+ring
@@ Property / has part(s): ring / rank @@
+Normal rank
@@ Property / has part(s): ring / qualifier @@
+object has role: base ring
@@ Property / in defining formula @@
+ $m+n=n+m\qquad (m,n\in M)$ 
m+n=n+m\qquad(m,n\in M)
@@ Property / in defining formula: $m+n=n+m\qquad (m,n\in M)$ / rank @@
+Normal rank
@@ Property / in defining formula: $m+n=n+m\qquad (m,n\in M)$ / qualifier @@
+symbol represents: commutative property
@@ Property / in defining formula @@
+ ${\begin{aligned}(m+n)+p&=m+(n+p)&&(m,n,p\in M)\\r(sm)&=(rs)m&&(m\in M,\;r,s\in R)\\\end{aligned}}$ 
\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}
+Normal rank
+symbol represents: associativity
@@ Property / in defining formula @@
+ $0_{M}$ 
0_M
@@ Property / in defining formula: $0_{M}$ / rank @@
+Normal rank
@@ Property / in defining formula: $0_{M}$ / qualifier @@
+symbol represents: additive identity
@@ Property / in defining formula @@
+ $-m$ 
-m
@@ Property / in defining formula: $-m$ / rank @@
+Normal rank
@@ Property / in defining formula: $-m$ / qualifier @@
+symbol represents: inverse element
@@ Property / in defining formula @@
+ $1_{R}$ 
1_R
@@ Property / in defining formula: $1_{R}$ / rank @@
+Normal rank
@@ Property / in defining formula: $1_{R}$ / qualifier @@
+symbol represents: multiplicative identity
@@ Property / in defining formula: $1_{R}$ / qualifier @@
+of: base ring
@@ Property / in defining formula @@
+ ${\begin{aligned}r(m+n)&=rm+rn&&(m,n\in M,\;r\in R)\\(r+s)m&=rm+sm&&(m\in M,\;r,s\in R)\end{aligned}}$ 
\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}
+Normal rank
+symbol represents: distributive property
@@ Property / ProofWiki ID @@
+Definition:Module
@@ Property / ProofWiki ID: Definition:Module / rank @@
+Normal rank
@@ Property / Gran Enciclopèdia Catalana ID @@
+modul-2
@@ Property / Gran Enciclopèdia Catalana ID: modul-2 / rank @@
+Normal rank
@@ Property / opposite of @@
+comodule
@@ Property / opposite of: comodule / rank @@
+Normal rank