module

generalization of vector space, with scalars in a ring instead of a field

Wikidata entity: Q18848

P2534	defining formula	Math	$\begin{aligned} m + n & = n + m & (m, n \in M) \\ (m + n) + p & = m + (n + p) & (m, n, p \in M) \\ m + 0_{M} & = m & (m \in M) \\ (- m) + m & = 0_{M} & (m \in M) \\ r (s m) & = (r s) m & (m \in M, r, s \in R) \\ 1_{R} m & = m & (m \in M) \\ r (m + n) & = r m + r n & (m, n \in M, r \in R) \\ (r + s) m & = r m + s m & (m \in M, r, s \in R) \end{aligned}$	???
P1889	different from	...	Q120812 (absolute value)	absolute value
P1552	has characteristic	...	Q1761084 (length)	length
P1552	has characteristic	...	Q7280485 (radical of a module)	radical of a module
P1552	has characteristic	...	Q121217200 (base ring)	base ring
P527	has part(s)	...	Q181296 (abelian group)	abelian group
P7235	in defining formula	Math	$m + n = n + m (m, n \in M)$	???
P7235	in defining formula	Math	$- m$	???
P7235	in defining formula	Math	$\begin{aligned} (m + n) + p & = m + (n + p) & (m, n, p \in M) \\ r (s m) & = (r s) m & (m \in M, r, s \in R) \end{aligned}$	???
P7235	in defining formula	Math	$0_{M}$	???
P7235	in defining formula	Math	$1_{R}$	???
P7235	in defining formula	Math	$\begin{aligned} r (m + n) & = r m + r n & (m, n \in M, r \in R) \\ (r + s) m & = r m + s m & (m \in M, r, s \in R) \end{aligned}$	???
P6104	maintained by WikiProject	...	Q8487137 (WikiProject Mathematics)	WikiProject Mathematics
P5008	on focus list of Wikimedia project	...	Q6173448 (Wikipedia:Vital articles/Level/4)	Wikipedia:Vital articles/Level/4
P461	opposite of	...	Q5155179 (comodule)	comodule
P2579	studied by	...	Q727659 (commutative algebra)	commutative algebra
P2579	studied by	...	Q1208658 (ring theory)	ring theory
P2579	studied by	...	Q114722746 (module theory)	module theory
P279	subclass of	...	Q205464 (algebraic structure)	algebraic structure
P12322	underlying structure(s)	...	Q181296 (abelian group)	abelian group

External Ids

P13750	Arab Encyclopedia concept ID	5504
P268	Bibliothèque nationale de France ID	13163015r
P10037	Enciclopedia della Scienza e della Tecnica ID	modulo
P7554	Encyclopedia of Mathematics article ID	Module
P2163	FAST ID	1024523
P646	Freebase ID	/m/01pd2z
P12385	Gran Enciclopèdia Catalana ID	modul-2
P1296	Gran Enciclopèdia Catalana ID (former scheme)	0194835
P269	IdRef ID	027814572
P244	Library of Congress authority ID	sh85086470
P2812	MathWorld ID	Module
P6366	Microsoft Academic ID (discontinued)	35729967
P8189	National Library of Israel J9U ID	987007541015705171
P950	National Library of Spain SpMaBN ID (BNE v1.0)	XX526925
P349	NDL Authority ID	00564457
P691	NL CR AUT ID	ph211266
P4215	nLab ID	module
P3847	Open Library subject ID	modules_(algebra)
P10283	OpenAlex ID	C35729967
P6781	ProofWiki ID	Definition:Module
P3417	Quora topic ID	Module
P3417	Quora topic ID	Modules
P3365	Treccani ID	modulo
P10017	Treccani's Dizionario delle Scienze Fisiche ID	modulo
P9621	Treccani's Enciclopedia della Matematica ID	modulo-su-un-anello-a
P13591	Yale LUX ID	concept/b369f142-9a98-4b94-a3ab-ba636f35bac8
P2347	YSO ID	38369

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