Wiktionary
commutative ring
n. (context algebra ring theory English) A ring#Etymology_3 whose multiplicative operation is commutative.
Wikipedia
Commutative ring
In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative. The study of commutative rings is called commutative algebra.
Some specific kinds of commutative rings are given with the following chain of class inclusions: