nLab commutative magma

Definition

A magma $(S,\cdot)$ is called commutative if its binary operation $(-)\cdot(-) \colon S \times S$ has the property that for all $x,y \in S$ then

$$x \cdot y = y \cdot x \,.$$

Examples

Examples include commutative monoids, abelian groups, commutative rings, commutative algebras etc.

Another example of a commutative magma is a midpoint algebra.

Related concepts

• magma (noncommutative version)

• commutative invertible magma (invertible version)

• commutative unital magma? (unital version)

• commutative semigroup? (associative version)