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ring
(Q161172)
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From Wikidata
algebraic structure that has compatible structures of an abelian group and a monoid, in particular having multiplicative identity
ring with identity
unital ring
associative ring
associative ring with identity
associative unital ring
edit
Language
Label
Description
Also known as
default for all languages
No label defined
–
English
ring
algebraic structure that has compatible structures of an abelian group and a monoid, in particular having multiplicative identity
ring with identity
unital ring
associative ring
associative ring with identity
associative unital ring
Statements
subclass of
nonassociative ring
0 references
semiring
0 references
rng
1 reference
stated in
Algebras, rings and modules
page(s)
1
studied by
ring theory
0 references
defining formula
(
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
0 references
in defining formula
(
r
+
s
)
+
t
=
r
+
(
s
+
t
)
(
r
s
)
t
=
r
(
s
t
)
symbol represents
associativity
0 references
r
+
s
=
s
+
r
symbol represents
commutative property
0 references
0
symbol represents
additive identity
0 references
r
(
s
+
t
)
=
r
s
+
r
t
(
r
+
s
)
t
=
r
t
+
s
t
symbol represents
distributive property
0 references
−
r
symbol represents
inverse element
0 references
1
symbol represents
multiplicative identity
0 references
described by source
Great Soviet Encyclopedia (1926–1947)
statement is subject of
Q135267551
0 references
on focus list of Wikimedia project
Wikipedia:Vital articles/Level/4
point in time
31 October 2022
0 references
maintained by WikiProject
WikiProject Mathematics
0 references
underlying structure(s)
abelian group
quantity
1
1 reference
stated in
Algebras, rings and modules
page(s)
1
monoid
quantity
1
0 references
non-empty set
applies to part
abelian group
monoid
quantity
1
1 reference
stated in
Algebras, rings and modules
page(s)
1
related image
Dedekind.jpeg
262 × 326; 12 KB
0 references
has part(s)
additive identity
object of statement has role
underlying data
0 references
multiplicative identity
object of statement has role
underlying data
0 references
different from
rng
0 references
nonassociative ring
0 references
topic's main category
Category:Rings (mathematics)
1 reference
imported from Wikimedia project
German Wikipedia
Identifiers
National Library of Spain SpMaBN ID (BNE v1.0)
XX531097
0 references
Bibliothèque nationale de France ID
131630283
0 references
GND ID
4128084-2
0 references
FAST ID
1098024
0 references
National Library of Israel J9U ID
987007538867405171
1 reference
stated in
National Library of Israel
Library of Congress authority ID
sh85114140
1 reference
reference URL
https://github.com/JohnMarkOckerbloom/ftl/blob/master/data/wikimap
retrieved
3 April 2019
NL CR AUT ID
ph126754
subject named as
okruhy (algebra)
0 references
Dewey Decimal Classification
512.4
1 reference
stated in
Nuovo soggettario
BNCF Thesaurus ID
18029
retrieved
21 November 2025
BabelNet ID
03258622n
1 reference
stated in
BabelNet
BNCF Thesaurus ID
18029
0 references
De Agostini ID
anèllo+(algebra)
subject named as
anèllo
0 references
Encyclopædia Britannica Online ID
topic/ring-mathematics
subject named as
ring
0 references
topic/ring-with-unity
subject named as
ring with unity
0 references
Encyclopedia of Mathematics article ID
Ring
subject named as
Ring
0 references
Freebase ID
/m/0cyyp
subject named as
Ring (mathematics)
1 reference
stated in
Freebase Data Dumps
publication date
28 October 2013
/m/05wc5n
subject named as
Unit ring
1 reference
stated in
Freebase Data Dumps
publication date
28 October 2013
Great Russian Encyclopedia Online ID (old version)
2080425
subject named as
КОЛЕЦ ТЕОРИЯ
0 references
LMFDB knowl ID
ring
0 references
MathWorld ID
Ring
subject named as
Ring
1 reference
imported from Wikimedia project
Korean Wikipedia
UnitRing
subject named as
Unit Ring
2 references
imported from Wikimedia project
Spanish Wikipedia
imported from Wikimedia project
Korean Wikipedia
Metamath statement ID
df-ring
0 references
Microsoft Academic ID
23259944
0 references
NicoNicoPedia ID
環(数学)
0 references
nLab ID
ring
0 references
OmegaWiki Defined Meaning
384031
0 references
Online PWN Encyclopedia ID
3956882
0 references
Open Library subject ID
rings_(algebra)
subject named as
Rings (Algebra)
0 references
ProofWiki ID
Definition:Ring_with_Unity
0 references
Great Norwegian Encyclopedia ID
ring_-_matematikk
0 references
Treccani ID
anello
subject named as
anello
0 references
Treccani Vocabulary ID
anello
subject named as
anèllo
0 references
Treccani's Enciclopedia della Matematica ID
anello
subject named as
anello
publication date
2013
0 references
Yale LUX ID
concept/d68a2d2f-eaf6-4c49-9b8c-0bf16c961be5
0 references
Sitelinks
Wikipedia
(69 entries)
edit
arwiki
حلقة (رياضيات)
bawiki
Ҡулса (математика)
bewiki
Кальцо (алгебра)
bgwiki
Пръстен (алгебра)
bswiki
Prsten (matematika)
cawiki
Anell (matemàtiques)
cswiki
Okruh (algebra)
cvwiki
Ункă (математика)
cywiki
Modrwy (mathemateg)
dawiki
Ring (matematik)
dewiki
Ring (Algebra)
elwiki
Δακτύλιος (άλγεβρα)
enwiki
Ring (mathematics)
eowiki
Ringo (algebro)
eswiki
Anillo (matemática)
etwiki
Ring (algebra)
euwiki
Eraztun (matematika)
fawiki
حلقه (ریاضیات)
fiwiki
Rengas (matematiikka)
frwiki
Anneau (mathématiques)
gawiki
Fáinne (matamaitic)
glwiki
Anel (álxebra)
hewiki
חוג (מבנה אלגברי)
hrwiki
Prsten (matematika)
huwiki
Gyűrű (matematika)
hywiki
Օղակ (մաթեմատիկա)
iawiki
Anello (algebra)
idwiki
Gelanggang (matematika)
iowiki
Ringo (algebro)
itwiki
Anello (algebra)
jawiki
環 (数学)
kawiki
რგოლი (მათემატიკა)
knwiki
ರಿಂಗ್
kowiki
환 (수학)
lawiki
Anellus
lbwiki
Rank (Algeber)
lmowiki
Anell (matematega)
mkwiki
Прстен (математика)
mlwiki
വലയം (ഗണിതം)
mrwiki
रिंग
mswiki
Gelanggang (matematik)
nlwiki
Ring (wiskunde)
nnwiki
Ring i matematikk
novwiki
Ringe (matematike)
nowiki
Ring (matematikk)
plwiki
Pierścień (matematyka)
pmswiki
Anel
ptwiki
Anel (matemática)
rowiki
Inel (matematică)
ruwiki
Кольцо (математика)
scnwiki
Aneddu (matimàtica)
shwiki
Algebarski prsten
simplewiki
Ring (mathematics)
skwiki
Okruh (algebra)
slwiki
Kolobar (algebra)
srwiki
Алгебарски прстен
svwiki
Ring (matematik)
tawiki
வளையம் (கணிதம்)
thwiki
ริง (คณิตศาสตร์)
trwiki
Halka
ukwiki
Кільце (алгебра)
urwiki
حلقہ (ریاضی)
viwiki
Vành
vlswiki
Rienk (algebra)
wuuwiki
环(代数)
zh_classicalwiki
環 (代數)
zh_min_nanwiki
Khôan
zh_yuewiki
環 (代數)
zhwiki
环 (代数)
Wikibooks
(2 entries)
edit
arwikibooks
جبر/جبر تجريدي/حلقات
enwikibooks
Abstract Algebra/Rings
Wikinews
(0 entries)
edit
Wikiquote
(0 entries)
edit
Wikisource
(0 entries)
edit
Wikiversity
(1 entry)
edit
frwikiversity
Anneau (mathématiques)
Wikivoyage
(0 entries)
edit
Wiktionary
(0 entries)
edit
Multilingual sites
(0 entries)
edit
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