ring

algebraic structure that has compatible structures of an abelian group and a monoid, in particular having multiplicative identity

Wikidata entity: Q161172

P2534	defining formula	Math	$\begin{aligned} (r + s) + t & = r + (s + t) \\ r + s & = s + r \\ r + 0 & = r \\ r + (- r) & = 0 \\ (r s) t & = r (s t) \\ 1 r = r 1 & = r \\ r (s + t) & = r s + r t \\ (r + s) t & = r t + s t \end{aligned}$	???
P1343	described by source	...	Q20078554 (Great Soviet Encyclopedia (1926–1947))	Great Soviet Encyclopedia (1926–1947)
P1889	different from	...	Q13512116 (nonassociative ring)	nonassociative ring
P1889	different from	...	Q17102802 (rng)	rng
P527	has part(s)	...	Q2767837 (additive identity)	additive identity
P527	has part(s)	...	Q68019776 (multiplicative identity)	multiplicative identity
P7235	in defining formula	Math	$0$	???
P7235	in defining formula	Math	$1$	???
P7235	in defining formula	Math	$\begin{aligned} (r + s) + t & = r + (s + t) \\ (r s) t & = r (s t) \end{aligned}$	???
P7235	in defining formula	Math	$\begin{aligned} r (s + t) & = r s + r t \\ (r + s) t & = r t + s t \end{aligned}$	???
P7235	in defining formula	Math	$- r$	???
P7235	in defining formula	Math	$r + s = s + r$	???
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
P6802	related image	CommonsMedia	http://commons.wikimedia.org/wiki/Special:FilePath/Dedekind.jpeg	???
P2579	studied by	...	Q1208658 (ring theory)	ring theory
P279	subclass of	...	Q13512116 (nonassociative ring)	nonassociative ring
P279	subclass of	...	Q17102802 (rng)	rng
P279	subclass of	...	Q1333055 (semiring)	semiring
P910	topic's main category	...	Q17329131 (Category:Rings (mathematics))	Category:Rings (mathematics)
P12322	underlying structure(s)	...	Q181296 (abelian group)	abelian group
P12322	underlying structure(s)	...	Q208237 (monoid)	monoid
P12322	underlying structure(s)	...	Q10533491 (non-empty set)	non-empty set

External Ids

P13750	Arab Encyclopedia concept ID	1015
P2581	BabelNet ID	03258622n
P2581	BabelNet ID	03258622n
P268	Bibliothèque nationale de France ID	131630283
P508	BNCF Thesaurus ID	18029
P6706	De Agostini ID	anèllo+(algebra)
P1036	Dewey Decimal Classification	512.4
P7554	Encyclopedia of Mathematics article ID	Ring
P1417	Encyclopædia Britannica Online ID	topic/ring-mathematics
P1417	Encyclopædia Britannica Online ID	topic/ring-with-unity
P2163	FAST ID	1098024
P646	Freebase ID	/m/05wc5n
P646	Freebase ID	/m/0cyyp
P227	GND ID	4128084-2
P4342	Great Norwegian Encyclopedia ID	ring_-_matematikk
P2924	Great Russian Encyclopedia Online ID (old version)	2080425
P244	Library of Congress authority ID	sh85114140
P12987	LMFDB knowl ID	ring
P2812	MathWorld ID	Ring
P12888	Metamath statement ID	df-ring
P6366	Microsoft Academic ID (discontinued)	23259944
P8189	National Library of Israel J9U ID	987007538867405171
P950	National Library of Spain SpMaBN ID (BNE v1.0)	XX531097
P6900	NicoNicoPedia ID	環(数学)
P691	NL CR AUT ID	ph126754
P4215	nLab ID	ring
P1245	OmegaWiki Defined Meaning	384031
P7305	Online PWN Encyclopedia ID	3956882
P3847	Open Library subject ID	rings_(algebra)
P6781	ProofWiki ID	Definition:Ring_with_Unity
P3365	Treccani ID	anello
P5844	Treccani Vocabulary ID	anello
P9621	Treccani's Enciclopedia della Matematica ID	anello
P13591	Yale LUX ID	concept/d68a2d2f-eaf6-4c49-9b8c-0bf16c961be5

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