Editing Commutative property (section)

==Commutative structures==
Some types of [[algebraic structure]]s involve an operation that does not require commutativity. If this operation is commutative for a specific structure, the structure is often said to be ''commutative''. So,
* a [[commutative semigroup]] is a [[semigroup]] whose operation is commutative;{{sfn|Grillet|2001|pp=1–2}}
* a [[commutative monoid]] is a [[monoid]] whose operation is commutative;{{sfn|Grillet|2001|p=3}}
* a ''commutative group'' or [[abelian group]] is a [[group (mathematics)|group]] whose operation is commutative;{{sfn|Gallian|2006|p=34}}
* a [[commutative ring]] is a [[ring (mathematics)|ring]] whose [[multiplication]] is commutative. (Addition in a ring is always commutative.){{sfn|Gallian|2006|p=236}}

However, in the case of [[algebra over a field|algebras]], the phrase "[[commutative algebra (structure)|commutative algebra]]" refers only to [[associative algebra]]s that have a commutative multiplication.{{sfn|Tuset|2025|p=[https://books.google.com/books?id=1RE1EQAAQBAJ&pg=PA99 99]}}