---- > [!definition] Definition. ([[commutative ring]]) > A **commutative ring** is a [[ring]] whose multiplication operation is commutative. > > [[commutative ring|Commutative rings]] are objects of [[category]] $\mathsf{CRing}$, a [[subcategory]] of $\mathsf{Ring}$ obtained by keeping only the [[commutative ring|commutative]] ones (surviving homsets are untouched). In settings where everything is commutative, one often just writes $\mathsf{Ring}$ instead of $\mathsf{CRing}$. ^definition > [!basicexample] > - $\mathbb{Z}$ is a commutative ring, as is $\mathbb{Z} / n\mathbb{Z}$. ^basic-example ---- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```