Commutative Ring

A ring whose multiplication is commutative: for all a, b in R, a·b = b·a. It retains the additive abelian group structure and distributivity of a ring while adding multiplicative commutativity.

A ring (an additive abelian group equipped with a multiplication) in which the multiplication operation is commutative; many authors also assume the existence of a multiplicative identity (1 ≠ 0).

A ring in which the multiplication operation is commutative, i.e., ab=ba for all elements a and b; typically considered with the same additive abelian group and distributive properties as rings, and often studied with or without a multiplicative identity.