commutative ring

Algebraic structure

EntityQ858656

Subclass of: graded-commutative ring
, polynomial identity ring
, stably finite ring

Overview

From Wikipedia, the free encyclopedia · Read full article · Text CC BY-SA 4.0

In mathematics, a commutative ring is a ring in which the multiplication operation is commutative. The study of commutative rings is called commutative algebra. Complementarily, noncommutative algebra is the study of ring properties that are not specific to commutative rings. This distinction results from the high number of fundamental properties of commutative rings that do not extend to noncommutative rings.

Overview

All data

32 statements · 22% with external sources · numbers in brackets are citations

Studied by: commutative algebra
Opposite of: noncommutative ring
Members / parts: abelian group quantity: 1
commutative monoid quantity: 1
Said to be the same as: affine scheme criterion used: dual equivalence

On other databases

25 identifiers linking commutative ring across the web's reference databases

Data quality

statements

22%

externally sourced

Source last edited September 28, 2026. AIDB refreshes this page daily.

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AIDB. (2026). commutative ring (Q858656). Retrieved from https://aidb.si/e/commutative-ring-Q858656