Commutative binary operation

Definition with symbols
Let $$S$$ be a set and $$*$$ be a binary operation on $$S$$ (viz, $$*$$ is a map $$S$$ &times; $$S$$ &rarr; $$S$$. Then, $$*$$ is said to be commutative if, for every $$a, b, c$$ in $$S$$, the following identity holds:

$$a * b = b * a$$

If the above equation holds for particular values of $$a$$ and $$b$$, we say that $$a$$ and $$b$$ commute.

Related term
A magma where the binary operation is commutative is termed a commutative magma. For a semigroup, monoid or group, we use the word Abelian as an alternative to commutative (thus, a group where the binary operation is commutative is termed an Abelian group).

Central element
An element in a magma is termed central if it commutes with every element. The set of central elements of a magma is termed the commutative center.